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Merge remote-tracking branch 'origin/development' into MSC-Version

This commit is contained in:
Martin Diehl 2021-12-01 15:13:46 +01:00
parent f6d2bd0225 51b7a00734
commit 5abfe3c214
24 changed files with 440 additions and 239 deletions
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2
PRIVATE

@ -1 +1 @@
Subproject commit 76bb51348de75207d483d369628670e5ae51dca9 Subproject commit 02609955e53c0a5fb6cee5753419fb1ba1b9da2a

27
examples/config/phase/mechanical/plastic/phenopowerlaw_Mg.yaml
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@ -6,12 +6,12 @@ references:
output: [xi_sl, xi_tw] output: [xi_sl, xi_tw]
N_sl: [3, 3, 0, 6, 0, 6] # basal, 1. prism, -, 1. pyr<a>, -, 2. pyr<c+a> N_sl: [3, 3, 0, 6, 0, 6] # basal, prism, -, 1. pyr<a>, -, 2. pyr<c+a>
N_tw: [6, 0, 6] # tension, -, compression N_tw: [6, 0, 6] # tension, -, compression
xi_0_sl: [10.e+6, 55.e+6, 0., 60.e+6, 0., 60.e+6] xi_0_sl: [10.e+6, 55.e+6, 0., 60.e+6, 0., 60.e+6]
xi_inf_sl: [40.e+6, 135.e+6, 0., 150.e+6, 0., 150.e+6] xi_inf_sl: [40.e+6, 135.e+6, 0., 150.e+6, 0., 150.e+6]
xi_0_tw: [40.e+6, 0., 60.e+6] xi_0_tw: [40.e+6, 0., 60.e+6]
a_sl: 2.25 a_sl: 2.25
dot_gamma_0_sl: 0.001 dot_gamma_0_sl: 0.001
@ -21,9 +21,18 @@ n_tw: 20
f_sat_sl-tw: 10.0 f_sat_sl-tw: 10.0
h_0_sl-sl: 500.0e+6 h_0_sl-sl: 500.0e+6
h_0_tw-tw: 50.0e+6 h_0_tw-tw: 50.0e+6
h_0_tw-sl: 150.0e+6 h_0_tw-sl: 150.0e+6
h_sl-sl: [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] h_sl-sl: [+1.0, 1.0, 1.0, 1.0, 1.0, 1.0, -1.0, -1.0, -1.0, -1.0,
h_tw-tw: [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] -1.0, -1.0, 1.0, 1.0, -1.0, 1.0, 1.0, -1.0, 1.0, 1.0,
h_tw-sl: [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0,
h_sl-tw: [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] +1.0, 1.0, -1.0, 1.0, -1.0, 1.0, 1.0, -1.0, 1.0, -1.0,
+1.0, 1.0] # unused entries are indicated by -1.0
h_tw-tw: [+1.0, 1.0, -1.0, -1.0, -1.0, -1.0, 1.0, -1.0, 1.0, 1.0,
-1.0, 1.0] # unused entries are indicated by -1.0
h_tw-sl: [+1.0, -1.0, 1.0, -1.0, 1.0, -1.0, 1.0, -1.0, -1.0, -1.0,
-1.0, -1.0, 1.0, -1.0, 1.0, -1.0, -1.0, -1.0, -1.0, -1.0,
+1.0, -1.0, 1.0, -1.0] # unused entries are indicated by -1.0
h_sl-tw: [+1.0, -1.0, 1.0, -1.0, 1.0, -1.0, 1.0, -1.0, -1.0, -1.0,
-1.0, -1.0, 1.0, -1.0, 1.0, -1.0, -1.0, -1.0, -1.0, -1.0,
+1.0, -1.0, 1.0] # unused entries are indicated by -1.0

6
examples/config/phase/mechanical/plastic/phenopowerlaw_Ti.yaml
View File

@ -8,7 +8,7 @@ references:
https://doi.org/10.1016/j.actamat.2017.05.015 https://doi.org/10.1016/j.actamat.2017.05.015
output: [gamma_sl] output: [gamma_sl]
N_sl: [3, 3, 0, 0, 12] # basal, 1. prism, -, -, 2. pyr<c+a> N_sl: [3, 3, 0, 0, 12] # basal, 1. prism, -, -, 1. pyr<c+a>
n_sl: 20 n_sl: 20
a_sl: 2.0 a_sl: 2.0
dot_gamma_0_sl: 0.001 dot_gamma_0_sl: 0.001
@ -20,4 +20,6 @@ xi_inf_sl: [568.e+6, 150.e+7, 0.0, 0.0, 3420.e+6]
# L. Wang et al. : # L. Wang et al. :
# xi_0_sl: [127.e+6, 96.e+6, 0.0, 0.0, 240.e+6] # xi_0_sl: [127.e+6, 96.e+6, 0.0, 0.0, 240.e+6]
h_sl-sl: [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] h_sl-sl: [+1.0, 1.0, 1.0, 1.0, 1.0, 1.0, -1.0, -1.0, -1.0, -1.0,
-1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0,
+1.0, 1.0, -1.0, -1.0, 1.0, 1.0, -1.0, -1.0, 1.0, 1.0] # unused entries are indicated by -1.0

2
python/damask/VERSION
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@ -1 +1 @@
v3.0.0-alpha5-155-gbf76d9f3a v3.0.0-alpha5-210-g7e7098baf

113
python/damask/_colormap.py
View File

@ -2,6 +2,8 @@ import os
import json import json
import functools import functools
import colorsys import colorsys
from pathlib import Path
from typing import Sequence, Union, TextIO
import numpy as np import numpy as np
import matplotlib as mpl import matplotlib as mpl
@ -14,9 +16,9 @@ from PIL import Image
from . import util from . import util
from . import Table from . import Table
_eps = 216./24389. _EPS = 216./24389.
_kappa = 24389./27. _KAPPA = 24389./27.
_ref_white = np.array([.95047, 1.00000, 1.08883]) # Observer = 2, Illuminant = D65 _REF_WHITE = np.array([.95047, 1.00000, 1.08883]) # Observer = 2, Illuminant = D65
# ToDo (if needed) # ToDo (if needed)
# - support alpha channel (paraview/ASCII/input) # - support alpha channel (paraview/ASCII/input)
@ -39,20 +41,20 @@ class Colormap(mpl.colors.ListedColormap):
""" """
def __add__(self,other): def __add__(self, other: 'Colormap') -> 'Colormap':
"""Concatenate.""" """Concatenate."""
return Colormap(np.vstack((self.colors,other.colors)), return Colormap(np.vstack((self.colors,other.colors)),
f'{self.name}+{other.name}') f'{self.name}+{other.name}')
def __iadd__(self,other): def __iadd__(self, other: 'Colormap') -> 'Colormap':
"""Concatenate (in-place).""" """Concatenate (in-place)."""
return self.__add__(other) return self.__add__(other)
def __invert__(self): def __invert__(self) -> 'Colormap':
"""Reverse.""" """Reverse."""
return self.reversed() return self.reversed()
def __repr__(self): def __repr__(self) -> str:
"""Show as matplotlib figure.""" """Show as matplotlib figure."""
fig = plt.figure(self.name,figsize=(5,.5)) fig = plt.figure(self.name,figsize=(5,.5))
ax1 = fig.add_axes([0, 0, 1, 1]) ax1 = fig.add_axes([0, 0, 1, 1])
@ -64,7 +66,11 @@ class Colormap(mpl.colors.ListedColormap):
@staticmethod @staticmethod
def from_range(low,high,name='DAMASK colormap',N=256,model='rgb'): def from_range(low: Sequence[float],
high: Sequence[float],
name: str = 'DAMASK colormap',
N: int = 256,
model: str = 'rgb') -> 'Colormap':
""" """
Create a perceptually uniform colormap between given (inclusive) bounds. Create a perceptually uniform colormap between given (inclusive) bounds.
@ -145,7 +151,7 @@ class Colormap(mpl.colors.ListedColormap):
@staticmethod @staticmethod
def from_predefined(name,N=256): def from_predefined(name: str, N: int = 256) -> 'Colormap':
""" """
Select from a set of predefined colormaps. Select from a set of predefined colormaps.
@ -185,7 +191,10 @@ class Colormap(mpl.colors.ListedColormap):
return Colormap.from_range(definition['low'],definition['high'],name,N) return Colormap.from_range(definition['low'],definition['high'],name,N)
def shade(self,field,bounds=None,gap=None): def shade(self,
field: np.ndarray,
bounds: Sequence[float] = None,
gap: float = None) -> Image:
""" """
Generate PIL image of 2D field using colormap. Generate PIL image of 2D field using colormap.
@ -226,7 +235,7 @@ class Colormap(mpl.colors.ListedColormap):
mode='RGBA') mode='RGBA')
def reversed(self,name=None): def reversed(self, name: str = None) -> 'Colormap':
""" """
Reverse. Reverse.
@ -251,7 +260,7 @@ class Colormap(mpl.colors.ListedColormap):
return Colormap(np.array(rev.colors),rev.name[:-4] if rev.name.endswith('_r_r') else rev.name) return Colormap(np.array(rev.colors),rev.name[:-4] if rev.name.endswith('_r_r') else rev.name)
def _get_file_handle(self,fname,extension): def _get_file_handle(self, fname: Union[TextIO, str, Path, None], suffix: str) -> TextIO:
""" """
Provide file handle. Provide file handle.
@ -259,8 +268,7 @@ class Colormap(mpl.colors.ListedColormap):
---------- ----------
fname : file, str, pathlib.Path, or None fname : file, str, pathlib.Path, or None
Filename or filehandle, will be name of the colormap+extension if None. Filename or filehandle, will be name of the colormap+extension if None.
suffix: str
extension: str
Extension of the filename. Extension of the filename.
Returns Returns
@ -270,17 +278,14 @@ class Colormap(mpl.colors.ListedColormap):
""" """
if fname is None: if fname is None:
fhandle = open(self.name.replace(' ','_')+'.'+extension,'w',newline='\n') return open(self.name.replace(' ','_')+suffix, 'w', newline='\n')
elif isinstance(fname, (str, Path)):
return open(fname, 'w', newline='\n')
else: else:
try: return fname
fhandle = open(fname,'w',newline='\n')
except TypeError:
fhandle = fname
return fhandle
def save_paraview(self,fname=None): def save_paraview(self, fname: Union[TextIO, str, Path] = None):
""" """
Save as JSON file for use in Paraview. Save as JSON file for use in Paraview.
@ -303,12 +308,12 @@ class Colormap(mpl.colors.ListedColormap):
'RGBPoints':colors 'RGBPoints':colors
}] }]
fhandle = self._get_file_handle(fname,'json') fhandle = self._get_file_handle(fname,'.json')
json.dump(out,fhandle,indent=4) json.dump(out,fhandle,indent=4)
fhandle.write('\n') fhandle.write('\n')
def save_ASCII(self,fname=None): def save_ASCII(self, fname: Union[TextIO, str, Path] = None):
""" """
Save as ASCII file. Save as ASCII file.
@ -321,10 +326,10 @@ class Colormap(mpl.colors.ListedColormap):
""" """
labels = {'RGBA':4} if self.colors.shape[1] == 4 else {'RGB': 3} labels = {'RGBA':4} if self.colors.shape[1] == 4 else {'RGB': 3}
t = Table(self.colors,labels,f'Creator: {util.execution_stamp("Colormap")}') t = Table(self.colors,labels,f'Creator: {util.execution_stamp("Colormap")}')
t.save(self._get_file_handle(fname,'txt')) t.save(self._get_file_handle(fname,'.txt'))
def save_GOM(self,fname=None): def save_GOM(self, fname: Union[TextIO, str, Path] = None):
""" """
Save as ASCII file for use in GOM Aramis. Save as ASCII file for use in GOM Aramis.
@ -342,10 +347,10 @@ class Colormap(mpl.colors.ListedColormap):
+ ' '.join([f' 0 {c[0]} {c[1]} {c[2]} 255 1' for c in reversed((self.colors*255).astype(int))]) \ + ' '.join([f' 0 {c[0]} {c[1]} {c[2]} 255 1' for c in reversed((self.colors*255).astype(int))]) \
+ '\n' + '\n'
self._get_file_handle(fname,'legend').write(GOM_str) self._get_file_handle(fname,'.legend').write(GOM_str)
def save_gmsh(self,fname=None): def save_gmsh(self, fname: Union[TextIO, str, Path] = None):
""" """
Save as ASCII file for use in gmsh. Save as ASCII file for use in gmsh.
@ -360,11 +365,13 @@ class Colormap(mpl.colors.ListedColormap):
gmsh_str = 'View.ColorTable = {\n' \ gmsh_str = 'View.ColorTable = {\n' \
+'\n'.join([f'{c[0]},{c[1]},{c[2]},' for c in self.colors[:,:3]*255]) \ +'\n'.join([f'{c[0]},{c[1]},{c[2]},' for c in self.colors[:,:3]*255]) \
+'\n}\n' +'\n}\n'
self._get_file_handle(fname,'msh').write(gmsh_str) self._get_file_handle(fname,'.msh').write(gmsh_str)
@staticmethod @staticmethod
def _interpolate_msh(frac,low,high): def _interpolate_msh(frac,
low: np.ndarray,
high: np.ndarray) -> np.ndarray:
""" """
Interpolate in Msh color space. Interpolate in Msh color space.
@ -441,31 +448,31 @@ class Colormap(mpl.colors.ListedColormap):
@staticmethod @staticmethod
def _hsv2rgb(hsv): def _hsv2rgb(hsv: np.ndarray) -> np.ndarray:
"""H(ue) S(aturation) V(alue) to R(red) G(reen) B(lue).""" """H(ue) S(aturation) V(alue) to R(red) G(reen) B(lue)."""
return np.array(colorsys.hsv_to_rgb(hsv[0]/360.,hsv[1],hsv[2])) return np.array(colorsys.hsv_to_rgb(hsv[0]/360.,hsv[1],hsv[2]))
@staticmethod @staticmethod
def _rgb2hsv(rgb): def _rgb2hsv(rgb: np.ndarray) -> np.ndarray:
"""R(ed) G(reen) B(lue) to H(ue) S(aturation) V(alue).""" """R(ed) G(reen) B(lue) to H(ue) S(aturation) V(alue)."""
h,s,v = colorsys.rgb_to_hsv(rgb[0],rgb[1],rgb[2]) h,s,v = colorsys.rgb_to_hsv(rgb[0],rgb[1],rgb[2])
return np.array([h*360,s,v]) return np.array([h*360,s,v])
@staticmethod @staticmethod
def _hsl2rgb(hsl): def _hsl2rgb(hsl: np.ndarray) -> np.ndarray:
"""H(ue) S(aturation) L(uminance) to R(red) G(reen) B(lue).""" """H(ue) S(aturation) L(uminance) to R(red) G(reen) B(lue)."""
return np.array(colorsys.hls_to_rgb(hsl[0]/360.,hsl[2],hsl[1])) return np.array(colorsys.hls_to_rgb(hsl[0]/360.,hsl[2],hsl[1]))
@staticmethod @staticmethod
def _rgb2hsl(rgb): def _rgb2hsl(rgb: np.ndarray) -> np.ndarray:
"""R(ed) G(reen) B(lue) to H(ue) S(aturation) L(uminance).""" """R(ed) G(reen) B(lue) to H(ue) S(aturation) L(uminance)."""
h,l,s = colorsys.rgb_to_hls(rgb[0],rgb[1],rgb[2]) h,l,s = colorsys.rgb_to_hls(rgb[0],rgb[1],rgb[2])
return np.array([h*360,s,l]) return np.array([h*360,s,l])
@staticmethod @staticmethod
def _xyz2rgb(xyz): def _xyz2rgb(xyz: np.ndarray) -> np.ndarray:
""" """
CIE Xyz to R(ed) G(reen) B(lue). CIE Xyz to R(ed) G(reen) B(lue).
@ -485,7 +492,7 @@ class Colormap(mpl.colors.ListedColormap):
return np.clip(rgb,0.,1.) return np.clip(rgb,0.,1.)
@staticmethod @staticmethod
def _rgb2xyz(rgb): def _rgb2xyz(rgb: np.ndarray) -> np.ndarray:
""" """
R(ed) G(reen) B(lue) to CIE Xyz. R(ed) G(reen) B(lue) to CIE Xyz.
@ -503,7 +510,7 @@ class Colormap(mpl.colors.ListedColormap):
@staticmethod @staticmethod
def _lab2xyz(lab,ref_white=None): def _lab2xyz(lab: np.ndarray, ref_white: np.ndarray = None) -> np.ndarray:
""" """
CIE Lab to CIE Xyz. CIE Lab to CIE Xyz.
@ -516,13 +523,13 @@ class Colormap(mpl.colors.ListedColormap):
f_z = (lab[0]+16.)/116. - lab[2]/200. f_z = (lab[0]+16.)/116. - lab[2]/200.
return np.array([ return np.array([
f_x**3. if f_x**3. > _eps else (116.*f_x-16.)/_kappa, f_x**3. if f_x**3. > _EPS else (116.*f_x-16.)/_KAPPA,
((lab[0]+16.)/116.)**3 if lab[0]>_kappa*_eps else lab[0]/_kappa, ((lab[0]+16.)/116.)**3 if lab[0]>_KAPPA*_EPS else lab[0]/_KAPPA,
f_z**3. if f_z**3. > _eps else (116.*f_z-16.)/_kappa f_z**3. if f_z**3. > _EPS else (116.*f_z-16.)/_KAPPA
])*(ref_white if ref_white is not None else _ref_white) ])*(ref_white if ref_white is not None else _REF_WHITE)
@staticmethod @staticmethod
def _xyz2lab(xyz,ref_white=None): def _xyz2lab(xyz: np.ndarray, ref_white: np.ndarray = None) -> np.ndarray:
""" """
CIE Xyz to CIE Lab. CIE Xyz to CIE Lab.
@ -531,8 +538,8 @@ class Colormap(mpl.colors.ListedColormap):
http://www.brucelindbloom.com/index.html?Eqn_Lab_to_XYZ.html http://www.brucelindbloom.com/index.html?Eqn_Lab_to_XYZ.html
""" """
ref_white = ref_white if ref_white is not None else _ref_white ref_white = ref_white if ref_white is not None else _REF_WHITE
f = np.where(xyz/ref_white > _eps,(xyz/ref_white)**(1./3.),(_kappa*xyz/ref_white+16.)/116.) f = np.where(xyz/ref_white > _EPS,(xyz/ref_white)**(1./3.),(_KAPPA*xyz/ref_white+16.)/116.)
return np.array([ return np.array([
116.0 * f[1] - 16.0, 116.0 * f[1] - 16.0,
@ -542,7 +549,7 @@ class Colormap(mpl.colors.ListedColormap):
@staticmethod @staticmethod
def _lab2msh(lab): def _lab2msh(lab: np.ndarray) -> np.ndarray:
""" """
CIE Lab to Msh. CIE Lab to Msh.
@ -560,7 +567,7 @@ class Colormap(mpl.colors.ListedColormap):
]) ])
@staticmethod @staticmethod
def _msh2lab(msh): def _msh2lab(msh: np.ndarray) -> np.ndarray:
""" """
Msh to CIE Lab. Msh to CIE Lab.
@ -577,29 +584,29 @@ class Colormap(mpl.colors.ListedColormap):
]) ])
@staticmethod @staticmethod
def _lab2rgb(lab): def _lab2rgb(lab: np.ndarray) -> np.ndarray:
return Colormap._xyz2rgb(Colormap._lab2xyz(lab)) return Colormap._xyz2rgb(Colormap._lab2xyz(lab))
@staticmethod @staticmethod
def _rgb2lab(rgb): def _rgb2lab(rgb: np.ndarray) -> np.ndarray:
return Colormap._xyz2lab(Colormap._rgb2xyz(rgb)) return Colormap._xyz2lab(Colormap._rgb2xyz(rgb))
@staticmethod @staticmethod
def _msh2rgb(msh): def _msh2rgb(msh: np.ndarray) -> np.ndarray:
return Colormap._lab2rgb(Colormap._msh2lab(msh)) return Colormap._lab2rgb(Colormap._msh2lab(msh))
@staticmethod @staticmethod
def _rgb2msh(rgb): def _rgb2msh(rgb: np.ndarray) -> np.ndarray:
return Colormap._lab2msh(Colormap._rgb2lab(rgb)) return Colormap._lab2msh(Colormap._rgb2lab(rgb))
@staticmethod @staticmethod
def _hsv2msh(hsv): def _hsv2msh(hsv: np.ndarray) -> np.ndarray:
return Colormap._rgb2msh(Colormap._hsv2rgb(hsv)) return Colormap._rgb2msh(Colormap._hsv2rgb(hsv))
@staticmethod @staticmethod
def _hsl2msh(hsl): def _hsl2msh(hsl: np.ndarray) -> np.ndarray:
return Colormap._rgb2msh(Colormap._hsl2rgb(hsl)) return Colormap._rgb2msh(Colormap._hsl2rgb(hsl))
@staticmethod @staticmethod
def _xyz2msh(xyz): def _xyz2msh(xyz: np.ndarray) -> np.ndarray:
return Colormap._lab2msh(Colormap._xyz2lab(xyz)) return Colormap._lab2msh(Colormap._xyz2lab(xyz))

6
python/tests/test_Colormap.py
View File

@ -77,6 +77,12 @@ class TestColormap:
# xyz2msh # xyz2msh
assert np.allclose(Colormap._xyz2msh(xyz),msh,atol=1.e-6,rtol=0) assert np.allclose(Colormap._xyz2msh(xyz),msh,atol=1.e-6,rtol=0)
@pytest.mark.parametrize('low,high',[((0,0,0),(1,1,1)),
([0,0,0],[1,1,1])])
def test_from_range_types(self,low,high):
a = Colormap.from_range(low,high)
b = Colormap.from_range(np.array(low),np.array(high))
assert np.all(a.colors == b.colors)
@pytest.mark.parametrize('format',['ASCII','paraview','GOM','gmsh']) @pytest.mark.parametrize('format',['ASCII','paraview','GOM','gmsh'])
@pytest.mark.parametrize('model',['rgb','hsv','hsl','xyz','lab','msh']) @pytest.mark.parametrize('model',['rgb','hsv','hsl','xyz','lab','msh'])

2
python/tests/test_Result.py
View File

@ -390,7 +390,7 @@ class TestResult:
with open((ref_path/'export_VTK'/request.node.name).with_suffix('.md5'),'w') as f: with open((ref_path/'export_VTK'/request.node.name).with_suffix('.md5'),'w') as f:
f.write(cur+'\n') f.write(cur+'\n')
with open((ref_path/'export_VTK'/request.node.name).with_suffix('.md5')) as f: with open((ref_path/'export_VTK'/request.node.name).with_suffix('.md5')) as f:
assert cur == f.read()[:-1] assert cur == f.read().strip('\n')
@pytest.mark.parametrize('mode',['point','cell']) @pytest.mark.parametrize('mode',['point','cell'])
@pytest.mark.parametrize('output',[False,True]) @pytest.mark.parametrize('output',[False,True])

1
src/commercialFEM_fileList.f90
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@ -4,6 +4,7 @@
!> @details List of files needed by MSC.Marc !> @details List of files needed by MSC.Marc
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
#include "parallelization.f90" #include "parallelization.f90"
#include "constants.f90"
#include "IO.f90" #include "IO.f90"
#include "YAML_types.f90" #include "YAML_types.f90"
#include "YAML_parse.f90" #include "YAML_parse.f90"

15
src/constants.f90 Normal file
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@ -0,0 +1,15 @@
!--------------------------------------------------------------------------------------------------
!> @author Martin Diehl, KU Leuven
!> @brief physical constants
!--------------------------------------------------------------------------------------------------
module constants
use prec
implicit none
public
real(pReal), parameter :: &
T_ROOM = 300.0_pReal, & !< Room temperature in K
K_B = 1.38e-23_pReal !< Boltzmann constant in J/Kelvin
end module constants

11
src/grid/DAMASK_grid.f90
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@ -223,7 +223,11 @@ program DAMASK_grid
loadCases(l)%r = step_discretization%get_asFloat('r', defaultVal= 1.0_pReal) loadCases(l)%r = step_discretization%get_asFloat('r', defaultVal= 1.0_pReal)
loadCases(l)%f_restart = load_step%get_asInt('f_restart', defaultVal=huge(0)) loadCases(l)%f_restart = load_step%get_asInt('f_restart', defaultVal=huge(0))
loadCases(l)%f_out = load_step%get_asInt('f_out', defaultVal=1) if (load_step%get_asString('f_out',defaultVal='n/a') == 'none') then
loadCases(l)%f_out = huge(0)
else
loadCases(l)%f_out = load_step%get_asInt('f_out', defaultVal=1)
end if
loadCases(l)%estimate_rate = (load_step%get_asBool('estimate_rate',defaultVal=.true.) .and. l>1) loadCases(l)%estimate_rate = (load_step%get_asBool('estimate_rate',defaultVal=.true.) .and. l>1)
reportAndCheck: if (worldrank == 0) then reportAndCheck: if (worldrank == 0) then
@ -233,7 +237,7 @@ program DAMASK_grid
print'(2x,a)', 'F:' print'(2x,a)', 'F:'
else else
print'(2x,a)', loadCases(l)%deformation%myType//' / 1/s:' print'(2x,a)', loadCases(l)%deformation%myType//' / 1/s:'
endif end if
do i = 1, 3; do j = 1, 3 do i = 1, 3; do j = 1, 3
if (loadCases(l)%deformation%mask(i,j)) then if (loadCases(l)%deformation%mask(i,j)) then
write(IO_STDOUT,'(2x,12a)',advance='no') ' x ' write(IO_STDOUT,'(2x,12a)',advance='no') ' x '
@ -276,7 +280,8 @@ program DAMASK_grid
endif endif
print'(2x,a,1x,f0.3)', 't:', loadCases(l)%t print'(2x,a,1x,f0.3)', 't:', loadCases(l)%t
print'(2x,a,1x,i0)', 'N:', loadCases(l)%N print'(2x,a,1x,i0)', 'N:', loadCases(l)%N
print'(2x,a,1x,i0)', 'f_out:', loadCases(l)%f_out if (loadCases(l)%f_out < huge(0)) &
print'(2x,a,1x,i0)', 'f_out:', loadCases(l)%f_out
if (loadCases(l)%f_restart < huge(0)) & if (loadCases(l)%f_restart < huge(0)) &
print'(2x,a,1x,i0)', 'f_restart:', loadCases(l)%f_restart print'(2x,a,1x,i0)', 'f_restart:', loadCases(l)%f_restart

6
src/grid/grid_mech_FEM.f90
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@ -697,9 +697,9 @@ subroutine formJacobian(da_local,x_local,Jac_pre,Jac,dummy,ierr)
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
! applying boundary conditions ! applying boundary conditions
diag = (C_volAvg(1,1,1,1)/delta(1)**2.0_pReal + & diag = (C_volAvg(1,1,1,1)/delta(1)**2 + &
C_volAvg(2,2,2,2)/delta(2)**2.0_pReal + & C_volAvg(2,2,2,2)/delta(2)**2 + &
C_volAvg(3,3,3,3)/delta(3)**2.0_pReal)*detJ C_volAvg(3,3,3,3)/delta(3)**2)*detJ
call MatZeroRowsColumns(Jac,size(rows),rows,diag,PETSC_NULL_VEC,PETSC_NULL_VEC,ierr) call MatZeroRowsColumns(Jac,size(rows),rows,diag,PETSC_NULL_VEC,PETSC_NULL_VEC,ierr)
CHKERRQ(ierr) CHKERRQ(ierr)
call DMGetGlobalVector(da_local,coordinates,ierr); CHKERRQ(ierr) call DMGetGlobalVector(da_local,coordinates,ierr); CHKERRQ(ierr)

32
src/grid/spectral_utilities.f90
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@ -578,22 +578,22 @@ real(pReal) function utilities_divergenceRMS()
do k = 1, grid3; do j = 1, grid(2) do k = 1, grid3; do j = 1, grid(2)
do i = 2, grid1Red -1 ! Has somewhere a conj. complex counterpart. Therefore count it twice. do i = 2, grid1Red -1 ! Has somewhere a conj. complex counterpart. Therefore count it twice.
utilities_divergenceRMS = utilities_divergenceRMS & utilities_divergenceRMS = utilities_divergenceRMS &
+ 2.0_pReal*(sum (real(matmul(tensorField_fourier(1:3,1:3,i,j,k),& ! (sqrt(real(a)**2 + aimag(a)**2))**2 = real(a)**2 + aimag(a)**2. do not take square root and square again + 2.0_pReal*(sum (real(matmul(tensorField_fourier(1:3,1:3,i,j,k), & ! (sqrt(real(a)**2 + aimag(a)**2))**2 = real(a)**2 + aimag(a)**2, i.e. do not take square root and square again
conjg(-xi1st(1:3,i,j,k))*rescaledGeom))**2.0_pReal)& ! --> sum squared L_2 norm of vector conjg(-xi1st(1:3,i,j,k))*rescaledGeom))**2) & ! --> sum squared L_2 norm of vector
+sum(aimag(matmul(tensorField_fourier(1:3,1:3,i,j,k),& +sum(aimag(matmul(tensorField_fourier(1:3,1:3,i,j,k),&
conjg(-xi1st(1:3,i,j,k))*rescaledGeom))**2.0_pReal)) conjg(-xi1st(1:3,i,j,k))*rescaledGeom))**2))
enddo enddo
utilities_divergenceRMS = utilities_divergenceRMS & ! these two layers (DC and Nyquist) do not have a conjugate complex counterpart (if grid(1) /= 1) utilities_divergenceRMS = utilities_divergenceRMS & ! these two layers (DC and Nyquist) do not have a conjugate complex counterpart (if grid(1) /= 1)
+ sum( real(matmul(tensorField_fourier(1:3,1:3,1 ,j,k), & + sum( real(matmul(tensorField_fourier(1:3,1:3,1 ,j,k), &
conjg(-xi1st(1:3,1,j,k))*rescaledGeom))**2.0_pReal) & conjg(-xi1st(1:3,1,j,k))*rescaledGeom))**2) &
+ sum(aimag(matmul(tensorField_fourier(1:3,1:3,1 ,j,k), & + sum(aimag(matmul(tensorField_fourier(1:3,1:3,1 ,j,k), &
conjg(-xi1st(1:3,1,j,k))*rescaledGeom))**2.0_pReal) & conjg(-xi1st(1:3,1,j,k))*rescaledGeom))**2) &
+ sum( real(matmul(tensorField_fourier(1:3,1:3,grid1Red,j,k), & + sum( real(matmul(tensorField_fourier(1:3,1:3,grid1Red,j,k), &
conjg(-xi1st(1:3,grid1Red,j,k))*rescaledGeom))**2.0_pReal) & conjg(-xi1st(1:3,grid1Red,j,k))*rescaledGeom))**2) &
+ sum(aimag(matmul(tensorField_fourier(1:3,1:3,grid1Red,j,k), & + sum(aimag(matmul(tensorField_fourier(1:3,1:3,grid1Red,j,k), &
conjg(-xi1st(1:3,grid1Red,j,k))*rescaledGeom))**2.0_pReal) conjg(-xi1st(1:3,grid1Red,j,k))*rescaledGeom))**2)
enddo; enddo enddo; enddo
if (grid(1) == 1) utilities_divergenceRMS = utilities_divergenceRMS * 0.5_pReal ! counted twice in case of grid(1) == 1 if (grid(1) == 1) utilities_divergenceRMS = utilities_divergenceRMS * 0.5_pReal ! counted twice in case of grid(1) == 1
call MPI_Allreduce(MPI_IN_PLACE,utilities_divergenceRMS,1,MPI_DOUBLE,MPI_SUM,MPI_COMM_WORLD,ierr) call MPI_Allreduce(MPI_IN_PLACE,utilities_divergenceRMS,1,MPI_DOUBLE,MPI_SUM,MPI_COMM_WORLD,ierr)
if (ierr /=0) error stop 'MPI error' if (ierr /=0) error stop 'MPI error'
utilities_divergenceRMS = sqrt(utilities_divergenceRMS) * wgt ! RMS in real space calculated with Parsevals theorem from Fourier space utilities_divergenceRMS = sqrt(utilities_divergenceRMS) * wgt ! RMS in real space calculated with Parsevals theorem from Fourier space
@ -630,7 +630,7 @@ real(pReal) function utilities_curlRMS()
-tensorField_fourier(l,1,i,j,k)*xi1st(2,i,j,k)*rescaledGeom(2)) -tensorField_fourier(l,1,i,j,k)*xi1st(2,i,j,k)*rescaledGeom(2))
enddo enddo
utilities_curlRMS = utilities_curlRMS & utilities_curlRMS = utilities_curlRMS &
+2.0_pReal*sum(curl_fourier%re**2.0_pReal+curl_fourier%im**2.0_pReal) ! Has somewhere a conj. complex counterpart. Therefore count it twice. +2.0_pReal*sum(curl_fourier%re**2+curl_fourier%im**2) ! Has somewhere a conj. complex counterpart. Therefore count it twice.
enddo enddo
do l = 1, 3 do l = 1, 3
curl_fourier = (+tensorField_fourier(l,3,1,j,k)*xi1st(2,1,j,k)*rescaledGeom(2) & curl_fourier = (+tensorField_fourier(l,3,1,j,k)*xi1st(2,1,j,k)*rescaledGeom(2) &
@ -641,7 +641,7 @@ real(pReal) function utilities_curlRMS()
-tensorField_fourier(l,1,1,j,k)*xi1st(2,1,j,k)*rescaledGeom(2)) -tensorField_fourier(l,1,1,j,k)*xi1st(2,1,j,k)*rescaledGeom(2))
enddo enddo
utilities_curlRMS = utilities_curlRMS & utilities_curlRMS = utilities_curlRMS &
+ sum(curl_fourier%re**2.0_pReal + curl_fourier%im**2.0_pReal) ! this layer (DC) does not have a conjugate complex counterpart (if grid(1) /= 1) + sum(curl_fourier%re**2 + curl_fourier%im**2) ! this layer (DC) does not have a conjugate complex counterpart (if grid(1) /= 1)
do l = 1, 3 do l = 1, 3
curl_fourier = (+tensorField_fourier(l,3,grid1Red,j,k)*xi1st(2,grid1Red,j,k)*rescaledGeom(2) & curl_fourier = (+tensorField_fourier(l,3,grid1Red,j,k)*xi1st(2,grid1Red,j,k)*rescaledGeom(2) &
-tensorField_fourier(l,2,grid1Red,j,k)*xi1st(3,grid1Red,j,k)*rescaledGeom(3)) -tensorField_fourier(l,2,grid1Red,j,k)*xi1st(3,grid1Red,j,k)*rescaledGeom(3))
@ -651,13 +651,13 @@ real(pReal) function utilities_curlRMS()
-tensorField_fourier(l,1,grid1Red,j,k)*xi1st(2,grid1Red,j,k)*rescaledGeom(2)) -tensorField_fourier(l,1,grid1Red,j,k)*xi1st(2,grid1Red,j,k)*rescaledGeom(2))
enddo enddo
utilities_curlRMS = utilities_curlRMS & utilities_curlRMS = utilities_curlRMS &
+ sum(curl_fourier%re**2.0_pReal + curl_fourier%im**2.0_pReal) ! this layer (Nyquist) does not have a conjugate complex counterpart (if grid(1) /= 1) + sum(curl_fourier%re**2 + curl_fourier%im**2) ! this layer (Nyquist) does not have a conjugate complex counterpart (if grid(1) /= 1)
enddo; enddo enddo; enddo
call MPI_Allreduce(MPI_IN_PLACE,utilities_curlRMS,1,MPI_DOUBLE,MPI_SUM,MPI_COMM_WORLD,ierr) call MPI_Allreduce(MPI_IN_PLACE,utilities_curlRMS,1,MPI_DOUBLE,MPI_SUM,MPI_COMM_WORLD,ierr)
if (ierr /=0) error stop 'MPI error' if (ierr /=0) error stop 'MPI error'
utilities_curlRMS = sqrt(utilities_curlRMS) * wgt utilities_curlRMS = sqrt(utilities_curlRMS) * wgt
if (grid(1) == 1) utilities_curlRMS = utilities_curlRMS * 0.5_pReal ! counted twice in case of grid(1) == 1 if (grid(1) == 1) utilities_curlRMS = utilities_curlRMS * 0.5_pReal ! counted twice in case of grid(1) == 1
end function utilities_curlRMS end function utilities_curlRMS
@ -836,13 +836,13 @@ subroutine utilities_constitutiveResponse(P,P_av,C_volAvg,C_minmaxAvg,&
dPdF_min = huge(1.0_pReal) dPdF_min = huge(1.0_pReal)
dPdF_norm_min = huge(1.0_pReal) dPdF_norm_min = huge(1.0_pReal)
do i = 1, product(grid(1:2))*grid3 do i = 1, product(grid(1:2))*grid3
if (dPdF_norm_max < sum(homogenization_dPdF(1:3,1:3,1:3,1:3,i)**2.0_pReal)) then if (dPdF_norm_max < sum(homogenization_dPdF(1:3,1:3,1:3,1:3,i)**2)) then
dPdF_max = homogenization_dPdF(1:3,1:3,1:3,1:3,i) dPdF_max = homogenization_dPdF(1:3,1:3,1:3,1:3,i)
dPdF_norm_max = sum(homogenization_dPdF(1:3,1:3,1:3,1:3,i)**2.0_pReal) dPdF_norm_max = sum(homogenization_dPdF(1:3,1:3,1:3,1:3,i)**2)
endif endif
if (dPdF_norm_min > sum(homogenization_dPdF(1:3,1:3,1:3,1:3,i)**2.0_pReal)) then if (dPdF_norm_min > sum(homogenization_dPdF(1:3,1:3,1:3,1:3,i)**2)) then
dPdF_min = homogenization_dPdF(1:3,1:3,1:3,1:3,i) dPdF_min = homogenization_dPdF(1:3,1:3,1:3,1:3,i)
dPdF_norm_min = sum(homogenization_dPdF(1:3,1:3,1:3,1:3,i)**2.0_pReal) dPdF_norm_min = sum(homogenization_dPdF(1:3,1:3,1:3,1:3,i)**2)
endif endif
enddo enddo

2
src/homogenization_mechanical_RGC.f90
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@ -546,7 +546,7 @@ module function RGC_updateState(P,F,avgF,dt,dPdF,ce) result(doneAndHappy)
do k = 1,3; do l = 1,3 do k = 1,3; do l = 1,3
nDef(i,j) = nDef(i,j) - nVect(k)*gDef(i,l)*math_LeviCivita(j,k,l) ! compute the interface mismatch tensor from the jump of deformation gradient nDef(i,j) = nDef(i,j) - nVect(k)*gDef(i,l)*math_LeviCivita(j,k,l) ! compute the interface mismatch tensor from the jump of deformation gradient
end do; end do end do; end do
nDefNorm = nDefNorm + nDef(i,j)**2.0_pReal ! compute the norm of the mismatch tensor nDefNorm = nDefNorm + nDef(i,j)**2 ! compute the norm of the mismatch tensor
end do; end do end do; end do
nDefNorm = max(nDefToler,sqrt(nDefNorm)) ! approximation to zero mismatch if mismatch is zero (singularity) nDefNorm = max(nDefToler,sqrt(nDefNorm)) ! approximation to zero mismatch if mismatch is zero (singularity)
nMis(abs(intFace(1)),iGrain) = nMis(abs(intFace(1)),iGrain) + nDefNorm ! total amount of mismatch experienced by the grain (at all six interfaces) nMis(abs(intFace(1)),iGrain) = nMis(abs(intFace(1)),iGrain) + nDefNorm ! total amount of mismatch experienced by the grain (at all six interfaces)

122
src/lattice.f90
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@ -219,18 +219,18 @@ module lattice
2, -1, -1, 0, 0, 1, -1, 0, & 2, -1, -1, 0, 0, 1, -1, 0, &
-1, 2, -1, 0, -1, 0, 1, 0, & -1, 2, -1, 0, -1, 0, 1, 0, &
-1, -1, 2, 0, 1, -1, 0, 0, & -1, -1, 2, 0, 1, -1, 0, 0, &
! <-11.0>{11.0}/2nd order prismatic compound systems (plane normal independent of c/a-ratio) ! <-11.0>{11.0}/2. order prismatic compound systems (plane normal independent of c/a-ratio)
-1, 1, 0, 0, 1, 1, -2, 0, & -1, 1, 0, 0, 1, 1, -2, 0, &
0, -1, 1, 0, -2, 1, 1, 0, & 0, -1, 1, 0, -2, 1, 1, 0, &
1, 0, -1, 0, 1, -2, 1, 0, & 1, 0, -1, 0, 1, -2, 1, 0, &
! <-1-1.0>{-11.1}/1st order pyramidal <a> systems (direction independent of c/a-ratio) ! <-1-1.0>{-11.1}/1. order pyramidal <a> systems (direction independent of c/a-ratio)
-1, 2, -1, 0, 1, 0, -1, 1, & -1, 2, -1, 0, 1, 0, -1, 1, &
-2, 1, 1, 0, 0, 1, -1, 1, & -2, 1, 1, 0, 0, 1, -1, 1, &
-1, -1, 2, 0, -1, 1, 0, 1, & -1, -1, 2, 0, -1, 1, 0, 1, &
1, -2, 1, 0, -1, 0, 1, 1, & 1, -2, 1, 0, -1, 0, 1, 1, &
2, -1, -1, 0, 0, -1, 1, 1, & 2, -1, -1, 0, 0, -1, 1, 1, &
1, 1, -2, 0, 1, -1, 0, 1, & 1, 1, -2, 0, 1, -1, 0, 1, &
! <11.3>{-10.1}/1st order pyramidal <c+a> systems (direction independent of c/a-ratio) ! <11.3>{-10.1}/1. order pyramidal <c+a> systems (direction independent of c/a-ratio)
-2, 1, 1, 3, 1, 0, -1, 1, & -2, 1, 1, 3, 1, 0, -1, 1, &
-1, -1, 2, 3, 1, 0, -1, 1, & -1, -1, 2, 3, 1, 0, -1, 1, &
-1, -1, 2, 3, 0, 1, -1, 1, & -1, -1, 2, 3, 0, 1, -1, 1, &
@ -243,7 +243,7 @@ module lattice
-1, 2, -1, 3, 0, -1, 1, 1, & -1, 2, -1, 3, 0, -1, 1, 1, &
-1, 2, -1, 3, 1, -1, 0, 1, & -1, 2, -1, 3, 1, -1, 0, 1, &
-2, 1, 1, 3, 1, -1, 0, 1, & -2, 1, 1, 3, 1, -1, 0, 1, &
! <11.3>{-1-1.2}/2nd order pyramidal <c+a> systems ! <11.3>{-1-1.2}/2. order pyramidal <c+a> systems
-1, -1, 2, 3, 1, 1, -2, 2, & -1, -1, 2, 3, 1, 1, -2, 2, &
1, -2, 1, 3, -1, 2, -1, 2, & 1, -2, 1, 3, -1, 2, -1, 2, &
2, -1, -1, 3, -2, 1, 1, 2, & 2, -1, -1, 3, -2, 1, 1, 2, &
@ -405,7 +405,7 @@ module lattice
contains contains
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief module initialization !> @brief Module initialization
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
subroutine lattice_init subroutine lattice_init
@ -417,7 +417,7 @@ end subroutine lattice_init
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief characteristic shear for twinning !> @brief Characteristic shear for twinning
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
function lattice_characteristicShear_Twin(Ntwin,lattice,CoverA) result(characteristicShear) function lattice_characteristicShear_Twin(Ntwin,lattice,CoverA) result(characteristicShear)
@ -473,13 +473,13 @@ function lattice_characteristicShear_Twin(Ntwin,lattice,CoverA) result(character
p = sum(HEX_NTWINSYSTEM(1:f-1))+s p = sum(HEX_NTWINSYSTEM(1:f-1))+s
select case(HEX_SHEARTWIN(p)) ! from Christian & Mahajan 1995 p.29 select case(HEX_SHEARTWIN(p)) ! from Christian & Mahajan 1995 p.29
case (1) ! <-10.1>{10.2} case (1) ! <-10.1>{10.2}
characteristicShear(a) = (3.0_pReal-cOverA**2.0_pReal)/sqrt(3.0_pReal)/CoverA characteristicShear(a) = (3.0_pReal-cOverA**2)/sqrt(3.0_pReal)/CoverA
case (2) ! <11.6>{-1-1.1} case (2) ! <11.6>{-1-1.1}
characteristicShear(a) = 1.0_pReal/cOverA characteristicShear(a) = 1.0_pReal/cOverA
case (3) ! <10.-2>{10.1} case (3) ! <10.-2>{10.1}
characteristicShear(a) = (4.0_pReal*cOverA**2.0_pReal-9.0_pReal)/sqrt(48.0_pReal)/cOverA characteristicShear(a) = (4.0_pReal*cOverA**2-9.0_pReal)/sqrt(48.0_pReal)/cOverA
case (4) ! <11.-3>{11.2} case (4) ! <11.-3>{11.2}
characteristicShear(a) = 2.0_pReal*(cOverA**2.0_pReal-2.0_pReal)/3.0_pReal/cOverA characteristicShear(a) = 2.0_pReal*(cOverA**2-2.0_pReal)/3.0_pReal/cOverA
end select end select
case default case default
call IO_error(137,ext_msg='lattice_characteristicShear_Twin: '//trim(lattice)) call IO_error(137,ext_msg='lattice_characteristicShear_Twin: '//trim(lattice))
@ -491,7 +491,7 @@ end function lattice_characteristicShear_Twin
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief rotated elasticity matrices for twinning in 6x6-matrix notation !> @brief Rotated elasticity matrices for twinning in 6x6-matrix notation
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
function lattice_C66_twin(Ntwin,C66,lattice,CoverA) function lattice_C66_twin(Ntwin,C66,lattice,CoverA)
@ -522,14 +522,14 @@ function lattice_C66_twin(Ntwin,C66,lattice,CoverA)
do i = 1, sum(Ntwin) do i = 1, sum(Ntwin)
call R%fromAxisAngle([coordinateSystem(1:3,2,i),PI],P=1) ! ToDo: Why always 180 deg? call R%fromAxisAngle([coordinateSystem(1:3,2,i),PI],P=1) ! ToDo: Why always 180 deg?
lattice_C66_twin(1:6,1:6,i) = math_3333toVoigt66(R%rotTensor4(math_Voigt66to3333(C66))) lattice_C66_twin(1:6,1:6,i) = R%rotStiffness(C66)
enddo enddo
end function lattice_C66_twin end function lattice_C66_twin
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief rotated elasticity matrices for transformation in 6x6-matrix notation !> @brief Rotated elasticity matrices for transformation in 6x6-matrix notation
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
function lattice_C66_trans(Ntrans,C_parent66,lattice_target, & function lattice_C66_trans(Ntrans,C_parent66,lattice_target, &
cOverA_trans,a_bcc,a_fcc) cOverA_trans,a_bcc,a_fcc)
@ -548,6 +548,8 @@ function lattice_C66_trans(Ntrans,C_parent66,lattice_target, &
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
! elasticity matrix of the target phase in cube orientation ! elasticity matrix of the target phase in cube orientation
if (lattice_target == 'hP') then if (lattice_target == 'hP') then
! https://doi.org/10.1063/1.1663858 eq. (16), eq. (18), eq. (19)
! https://doi.org/10.1016/j.actamat.2016.07.032 eq. (47), eq. (48)
if (cOverA_trans < 1.0_pReal .or. cOverA_trans > 2.0_pReal) & if (cOverA_trans < 1.0_pReal .or. cOverA_trans > 2.0_pReal) &
call IO_error(131,ext_msg='lattice_C66_trans: '//trim(lattice_target)) call IO_error(131,ext_msg='lattice_C66_trans: '//trim(lattice_target))
C_bar66(1,1) = (C_parent66(1,1) + C_parent66(1,2) + 2.0_pReal*C_parent66(4,4))/2.0_pReal C_bar66(1,1) = (C_parent66(1,1) + C_parent66(1,2) + 2.0_pReal*C_parent66(4,4))/2.0_pReal
@ -558,11 +560,11 @@ function lattice_C66_trans(Ntrans,C_parent66,lattice_target, &
C_bar66(1,4) = (C_parent66(1,1) - C_parent66(1,2) - 2.0_pReal*C_parent66(4,4)) /(3.0_pReal*sqrt(2.0_pReal)) C_bar66(1,4) = (C_parent66(1,1) - C_parent66(1,2) - 2.0_pReal*C_parent66(4,4)) /(3.0_pReal*sqrt(2.0_pReal))
C_target_unrotated66 = 0.0_pReal C_target_unrotated66 = 0.0_pReal
C_target_unrotated66(1,1) = C_bar66(1,1) - C_bar66(1,4)**2.0_pReal/C_bar66(4,4) C_target_unrotated66(1,1) = C_bar66(1,1) - C_bar66(1,4)**2/C_bar66(4,4)
C_target_unrotated66(1,2) = C_bar66(1,2) + C_bar66(1,4)**2.0_pReal/C_bar66(4,4) C_target_unrotated66(1,2) = C_bar66(1,2) + C_bar66(1,4)**2/C_bar66(4,4)
C_target_unrotated66(1,3) = C_bar66(1,3) C_target_unrotated66(1,3) = C_bar66(1,3)
C_target_unrotated66(3,3) = C_bar66(3,3) C_target_unrotated66(3,3) = C_bar66(3,3)
C_target_unrotated66(4,4) = C_bar66(4,4) - C_bar66(1,4)**2.0_pReal/(0.5_pReal*(C_bar66(1,1) - C_bar66(1,2))) C_target_unrotated66(4,4) = C_bar66(4,4) - C_bar66(1,4)**2/(0.5_pReal*(C_bar66(1,1) - C_bar66(1,2)))
C_target_unrotated66 = lattice_symmetrize_C66(C_target_unrotated66,'hP') C_target_unrotated66 = lattice_symmetrize_C66(C_target_unrotated66,'hP')
elseif (lattice_target == 'cI') then elseif (lattice_target == 'cI') then
if (a_bcc <= 0.0_pReal .or. a_fcc <= 0.0_pReal) & if (a_bcc <= 0.0_pReal .or. a_fcc <= 0.0_pReal) &
@ -581,14 +583,14 @@ function lattice_C66_trans(Ntrans,C_parent66,lattice_target, &
do i = 1,sum(Ntrans) do i = 1,sum(Ntrans)
call R%fromMatrix(Q(1:3,1:3,i)) call R%fromMatrix(Q(1:3,1:3,i))
lattice_C66_trans(1:6,1:6,i) = math_3333toVoigt66(R%rotTensor4(math_Voigt66to3333(C_target_unrotated66))) lattice_C66_trans(1:6,1:6,i) = R%rotStiffness(C_target_unrotated66)
enddo enddo
end function lattice_C66_trans end function lattice_C66_trans
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief non-Schmid projections for bcc with up to 6 coefficients !> @brief Non-schmid projections for bcc with up to 6 coefficients
! Koester et al. 2012, Acta Materialia 60 (2012) 3894–3901, eq. (17) ! Koester et al. 2012, Acta Materialia 60 (2012) 3894–3901, eq. (17)
! Gröger et al. 2008, Acta Materialia 56 (2008) 5412–5425, table 1 ! Gröger et al. 2008, Acta Materialia 56 (2008) 5412–5425, table 1
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
@ -635,7 +637,7 @@ end function lattice_nonSchmidMatrix
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief slip-slip interaction matrix !> @brief Slip-slip interaction matrix
!> details only active slip systems are considered !> details only active slip systems are considered
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
function lattice_interaction_SlipBySlip(Nslip,interactionValues,lattice) result(interactionMatrix) function lattice_interaction_SlipBySlip(Nslip,interactionValues,lattice) result(interactionMatrix)
@ -751,22 +753,23 @@ function lattice_interaction_SlipBySlip(Nslip,interactionValues,lattice) result(
integer, dimension(HEX_NSLIP,HEX_NSLIP), parameter :: & integer, dimension(HEX_NSLIP,HEX_NSLIP), parameter :: &
HEX_INTERACTIONSLIPSLIP = reshape( [& HEX_INTERACTIONSLIPSLIP = reshape( [&
! basal prism 2. prism 1. pyr<a> 1. pyr<c+a> 2. pyr<c+a>
1, 2, 2, 3, 3, 3, 7, 7, 7, 13,13,13,13,13,13, 21,21,21,21,21,21,21,21,21,21,21,21, 31,31,31,31,31,31, & ! -----> acting (forest) 1, 2, 2, 3, 3, 3, 7, 7, 7, 13,13,13,13,13,13, 21,21,21,21,21,21,21,21,21,21,21,21, 31,31,31,31,31,31, & ! -----> acting (forest)
2, 1, 2, 3, 3, 3, 7, 7, 7, 13,13,13,13,13,13, 21,21,21,21,21,21,21,21,21,21,21,21, 31,31,31,31,31,31, & ! | 2, 1, 2, 3, 3, 3, 7, 7, 7, 13,13,13,13,13,13, 21,21,21,21,21,21,21,21,21,21,21,21, 31,31,31,31,31,31, & ! | basal
2, 2, 1, 3, 3, 3, 7, 7, 7, 13,13,13,13,13,13, 21,21,21,21,21,21,21,21,21,21,21,21, 31,31,31,31,31,31, & ! | 2, 2, 1, 3, 3, 3, 7, 7, 7, 13,13,13,13,13,13, 21,21,21,21,21,21,21,21,21,21,21,21, 31,31,31,31,31,31, & ! |
! v ! v
6, 6, 6, 4, 5, 5, 8, 8, 8, 14,14,14,14,14,14, 22,22,22,22,22,22,22,22,22,22,22,22, 32,32,32,32,32,32, & ! reacting (primary) 6, 6, 6, 4, 5, 5, 8, 8, 8, 14,14,14,14,14,14, 22,22,22,22,22,22,22,22,22,22,22,22, 32,32,32,32,32,32, & ! reacting (primary)
6, 6, 6, 5, 4, 5, 8, 8, 8, 14,14,14,14,14,14, 22,22,22,22,22,22,22,22,22,22,22,22, 32,32,32,32,32,32, & 6, 6, 6, 5, 4, 5, 8, 8, 8, 14,14,14,14,14,14, 22,22,22,22,22,22,22,22,22,22,22,22, 32,32,32,32,32,32, & ! prism
6, 6, 6, 5, 5, 4, 8, 8, 8, 14,14,14,14,14,14, 22,22,22,22,22,22,22,22,22,22,22,22, 32,32,32,32,32,32, & 6, 6, 6, 5, 5, 4, 8, 8, 8, 14,14,14,14,14,14, 22,22,22,22,22,22,22,22,22,22,22,22, 32,32,32,32,32,32, &
12,12,12, 11,11,11, 9,10,10, 15,15,15,15,15,15, 23,23,23,23,23,23,23,23,23,23,23,23, 33,33,33,33,33,33, & 12,12,12, 11,11,11, 9,10,10, 15,15,15,15,15,15, 23,23,23,23,23,23,23,23,23,23,23,23, 33,33,33,33,33,33, &
12,12,12, 11,11,11, 10, 9,10, 15,15,15,15,15,15, 23,23,23,23,23,23,23,23,23,23,23,23, 33,33,33,33,33,33, & 12,12,12, 11,11,11, 10, 9,10, 15,15,15,15,15,15, 23,23,23,23,23,23,23,23,23,23,23,23, 33,33,33,33,33,33, & ! 2. prism
12,12,12, 11,11,11, 10,10, 9, 15,15,15,15,15,15, 23,23,23,23,23,23,23,23,23,23,23,23, 33,33,33,33,33,33, & 12,12,12, 11,11,11, 10,10, 9, 15,15,15,15,15,15, 23,23,23,23,23,23,23,23,23,23,23,23, 33,33,33,33,33,33, &
20,20,20, 19,19,19, 18,18,18, 16,17,17,17,17,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, & 20,20,20, 19,19,19, 18,18,18, 16,17,17,17,17,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, &
20,20,20, 19,19,19, 18,18,18, 17,16,17,17,17,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, & 20,20,20, 19,19,19, 18,18,18, 17,16,17,17,17,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, &
20,20,20, 19,19,19, 18,18,18, 17,17,16,17,17,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, & 20,20,20, 19,19,19, 18,18,18, 17,17,16,17,17,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, &
20,20,20, 19,19,19, 18,18,18, 17,17,17,16,17,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, & 20,20,20, 19,19,19, 18,18,18, 17,17,17,16,17,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, & ! 1. pyr<a>
20,20,20, 19,19,19, 18,18,18, 17,17,17,17,16,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, & 20,20,20, 19,19,19, 18,18,18, 17,17,17,17,16,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, &
20,20,20, 19,19,19, 18,18,18, 17,17,17,17,17,16, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, & 20,20,20, 19,19,19, 18,18,18, 17,17,17,17,17,16, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, &
@ -776,7 +779,7 @@ function lattice_interaction_SlipBySlip(Nslip,interactionValues,lattice) result(
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,25,26,26,26,26,26,26,26,26, 35,35,35,35,35,35, & 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,25,26,26,26,26,26,26,26,26, 35,35,35,35,35,35, &
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,25,26,26,26,26,26,26,26, 35,35,35,35,35,35, & 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,25,26,26,26,26,26,26,26, 35,35,35,35,35,35, &
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,25,26,26,26,26,26,26, 35,35,35,35,35,35, & 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,25,26,26,26,26,26,26, 35,35,35,35,35,35, &
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,25,26,26,26,26,26, 35,35,35,35,35,35, & 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,25,26,26,26,26,26, 35,35,35,35,35,35, & ! 1. pyr<c+a>
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,26,25,26,26,26,26, 35,35,35,35,35,35, & 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,26,25,26,26,26,26, 35,35,35,35,35,35, &
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,26,26,25,26,26,26, 35,35,35,35,35,35, & 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,26,26,25,26,26,26, 35,35,35,35,35,35, &
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,26,26,26,25,26,26, 35,35,35,35,35,35, & 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,26,26,26,25,26,26, 35,35,35,35,35,35, &
@ -786,7 +789,7 @@ function lattice_interaction_SlipBySlip(Nslip,interactionValues,lattice) result(
42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 36,37,37,37,37,37, & 42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 36,37,37,37,37,37, &
42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,36,37,37,37,37, & 42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,36,37,37,37,37, &
42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,37,36,37,37,37, & 42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,37,36,37,37,37, &
42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,37,37,36,37,37, & 42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,37,37,36,37,37, & ! 2. pyr<c+a>
42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,37,37,37,36,37, & 42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,37,37,37,36,37, &
42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,37,37,37,37,36 & 42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,37,37,37,37,36 &
],shape(HEX_INTERACTIONSLIPSLIP)) !< Slip-slip interaction types for hex (onion peel naming scheme) ],shape(HEX_INTERACTIONSLIPSLIP)) !< Slip-slip interaction types for hex (onion peel naming scheme)
@ -883,7 +886,7 @@ end function lattice_interaction_SlipBySlip
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief twin-twin interaction matrix !> @brief Twin-twin interaction matrix
!> details only active twin systems are considered !> details only active twin systems are considered
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
function lattice_interaction_TwinByTwin(Ntwin,interactionValues,lattice) result(interactionMatrix) function lattice_interaction_TwinByTwin(Ntwin,interactionValues,lattice) result(interactionMatrix)
@ -932,31 +935,32 @@ function lattice_interaction_TwinByTwin(Ntwin,interactionValues,lattice) result(
!< 3: other interaction !< 3: other interaction
integer, dimension(HEX_NTWIN,HEX_NTWIN), parameter :: & integer, dimension(HEX_NTWIN,HEX_NTWIN), parameter :: &
HEX_INTERACTIONTWINTWIN = reshape( [& HEX_INTERACTIONTWINTWIN = reshape( [&
! <-10.1>{10.2} <11.6>{-1-1.1} <10.-2>{10.1} <11.-3>{11.2}
1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! -----> acting 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! -----> acting
2, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! | 2, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! |
2, 2, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! | 2, 2, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! |
2, 2, 2, 1, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! v 2, 2, 2, 1, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! v <-10.1>{10.2}
2, 2, 2, 2, 1, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! reacting 2, 2, 2, 2, 1, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! reacting
2, 2, 2, 2, 2, 1, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & 2, 2, 2, 2, 2, 1, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, &
6, 6, 6, 6, 6, 6, 4, 5, 5, 5, 5, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, & 6, 6, 6, 6, 6, 6, 4, 5, 5, 5, 5, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, &
6, 6, 6, 6, 6, 6, 5, 4, 5, 5, 5, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, & 6, 6, 6, 6, 6, 6, 5, 4, 5, 5, 5, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, &
6, 6, 6, 6, 6, 6, 5, 5, 4, 5, 5, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, & 6, 6, 6, 6, 6, 6, 5, 5, 4, 5, 5, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, &
6, 6, 6, 6, 6, 6, 5, 5, 5, 4, 5, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, & 6, 6, 6, 6, 6, 6, 5, 5, 5, 4, 5, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, & ! <11.6>{-1-1.1}
6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 4, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, & 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 4, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, &
6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 4, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, & 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 4, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, &
12,12,12,12,12,12, 11,11,11,11,11,11, 9,10,10,10,10,10, 15,15,15,15,15,15, & 12,12,12,12,12,12, 11,11,11,11,11,11, 9,10,10,10,10,10, 15,15,15,15,15,15, &
12,12,12,12,12,12, 11,11,11,11,11,11, 10, 9,10,10,10,10, 15,15,15,15,15,15, & 12,12,12,12,12,12, 11,11,11,11,11,11, 10, 9,10,10,10,10, 15,15,15,15,15,15, &
12,12,12,12,12,12, 11,11,11,11,11,11, 10,10, 9,10,10,10, 15,15,15,15,15,15, & 12,12,12,12,12,12, 11,11,11,11,11,11, 10,10, 9,10,10,10, 15,15,15,15,15,15, &
12,12,12,12,12,12, 11,11,11,11,11,11, 10,10,10, 9,10,10, 15,15,15,15,15,15, & 12,12,12,12,12,12, 11,11,11,11,11,11, 10,10,10, 9,10,10, 15,15,15,15,15,15, & ! <10.-2>{10.1}
12,12,12,12,12,12, 11,11,11,11,11,11, 10,10,10,10, 9,10, 15,15,15,15,15,15, & 12,12,12,12,12,12, 11,11,11,11,11,11, 10,10,10,10, 9,10, 15,15,15,15,15,15, &
12,12,12,12,12,12, 11,11,11,11,11,11, 10,10,10,10,10, 9, 15,15,15,15,15,15, & 12,12,12,12,12,12, 11,11,11,11,11,11, 10,10,10,10,10, 9, 15,15,15,15,15,15, &
20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 16,17,17,17,17,17, & 20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 16,17,17,17,17,17, &
20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,16,17,17,17,17, & 20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,16,17,17,17,17, &
20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,17,16,17,17,17, & 20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,17,16,17,17,17, &
20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,17,17,16,17,17, & 20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,17,17,16,17,17, & ! <11.-3>{11.2}
20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,17,17,17,16,17, & 20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,17,17,17,16,17, &
20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,17,17,17,17,16 & 20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,17,17,17,17,16 &
],shape(HEX_INTERACTIONTWINTWIN)) !< Twin-twin interaction types for hex ],shape(HEX_INTERACTIONTWINTWIN)) !< Twin-twin interaction types for hex
@ -981,7 +985,7 @@ end function lattice_interaction_TwinByTwin
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief trans-trans interaction matrix !> @brief Trans-trans interaction matrix
!> details only active trans systems are considered !> details only active trans systems are considered
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
function lattice_interaction_TransByTrans(Ntrans,interactionValues,lattice) result(interactionMatrix) function lattice_interaction_TransByTrans(Ntrans,interactionValues,lattice) result(interactionMatrix)
@ -1023,7 +1027,7 @@ end function lattice_interaction_TransByTrans
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief slip-twin interaction matrix !> @brief Slip-twin interaction matrix
!> details only active slip and twin systems are considered !> details only active slip and twin systems are considered
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
function lattice_interaction_SlipByTwin(Nslip,Ntwin,interactionValues,lattice) result(interactionMatrix) function lattice_interaction_SlipByTwin(Nslip,Ntwin,interactionValues,lattice) result(interactionMatrix)
@ -1123,22 +1127,23 @@ function lattice_interaction_SlipByTwin(Nslip,Ntwin,interactionValues,lattice) r
integer, dimension(HEX_NTWIN,HEX_NSLIP), parameter :: & integer, dimension(HEX_NTWIN,HEX_NSLIP), parameter :: &
HEX_INTERACTIONSLIPTWIN = reshape( [& HEX_INTERACTIONSLIPTWIN = reshape( [&
! <-10.1>{10.2} <11.6>{-1-1.1} <10.-2>{10.1} <11.-3>{11.2}
1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, & ! ----> twin (acting) 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, & ! ----> twin (acting)
1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, & ! | 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, & ! | basal
1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, & ! | 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, & ! |
! v ! v
5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, & ! slip (reacting) 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, & ! slip (reacting)
5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, & 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, & ! prism
5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, & 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, &
9, 9, 9, 9, 9, 9, 10,10,10,10,10,10, 11,11,11,11,11,11, 12,12,12,12,12,12, & 9, 9, 9, 9, 9, 9, 10,10,10,10,10,10, 11,11,11,11,11,11, 12,12,12,12,12,12, &
9, 9, 9, 9, 9, 9, 10,10,10,10,10,10, 11,11,11,11,11,11, 12,12,12,12,12,12, & 9, 9, 9, 9, 9, 9, 10,10,10,10,10,10, 11,11,11,11,11,11, 12,12,12,12,12,12, & ! 2.prism
9, 9, 9, 9, 9, 9, 10,10,10,10,10,10, 11,11,11,11,11,11, 12,12,12,12,12,12, & 9, 9, 9, 9, 9, 9, 10,10,10,10,10,10, 11,11,11,11,11,11, 12,12,12,12,12,12, &
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, & 13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, & 13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, & 13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, & 13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, & ! 1. pyr<a>
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, & 13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, & 13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
@ -1148,7 +1153,7 @@ function lattice_interaction_SlipByTwin(Nslip,Ntwin,interactionValues,lattice) r
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & ! 1. pyr<c+a>
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
@ -1158,7 +1163,7 @@ function lattice_interaction_SlipByTwin(Nslip,Ntwin,interactionValues,lattice) r
21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, & 21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, &
21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, & 21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, &
21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, & 21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, &
21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, & 21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, & ! 2. pyr<c+a>
21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, & 21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, &
21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24 & 21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24 &
],shape(HEX_INTERACTIONSLIPTWIN)) !< Slip-twin interaction types for hex ],shape(HEX_INTERACTIONSLIPTWIN)) !< Slip-twin interaction types for hex
@ -1186,7 +1191,7 @@ end function lattice_interaction_SlipByTwin
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief slip-trans interaction matrix !> @brief Slip-trans interaction matrix
!> details only active slip and trans systems are considered !> details only active slip and trans systems are considered
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
function lattice_interaction_SlipByTrans(Nslip,Ntrans,interactionValues,lattice) result(interactionMatrix) function lattice_interaction_SlipByTrans(Nslip,Ntrans,interactionValues,lattice) result(interactionMatrix)
@ -1239,7 +1244,7 @@ function lattice_interaction_SlipByTrans(Nslip,Ntrans,interactionValues,lattice)
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief twin-slip interaction matrix !> @brief Twin-slip interaction matrix
!> details only active twin and slip systems are considered !> details only active twin and slip systems are considered
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
function lattice_interaction_TwinBySlip(Ntwin,Nslip,interactionValues,lattice) result(interactionMatrix) function lattice_interaction_TwinBySlip(Ntwin,Nslip,interactionValues,lattice) result(interactionMatrix)
@ -1262,31 +1267,32 @@ function lattice_interaction_TwinBySlip(Ntwin,Nslip,interactionValues,lattice) r
integer, dimension(HEX_NSLIP,HEX_NTWIN), parameter :: & integer, dimension(HEX_NSLIP,HEX_NTWIN), parameter :: &
HEX_INTERACTIONTWINSLIP = reshape( [& HEX_INTERACTIONTWINSLIP = reshape( [&
! basal prism 2. prism 1. pyr<a> 1. pyr<c+a> 2. pyr<c+a>
1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! ----> slip (acting) 1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! ----> slip (acting)
1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! | 1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! |
1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! | 1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! |
1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! v 1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! v <-10.1>{10.2}
1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! twin (reacting) 1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! twin (reacting)
1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & 1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, &
2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, & 2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, &
2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, & 2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, &
2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, & 2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, &
2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, & 2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, & ! <11.6>{-1-1.1}
2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, & 2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, &
2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, & 2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, &
3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, & 3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, &
3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, & 3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, &
3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, & 3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, &
3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, & 3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, & ! <10.-2>{10.1}
3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, & 3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, &
3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, & 3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, &
4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, & 4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, &
4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, & 4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, &
4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, & 4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, &
4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, & 4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, & ! <11.-3>{11.2}
4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, & 4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, &
4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24 & 4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24 &
],shape(HEX_INTERACTIONTWINSLIP)) !< Twin-slip interaction types for hex ],shape(HEX_INTERACTIONTWINSLIP)) !< Twin-slip interaction types for hex
@ -1483,7 +1489,7 @@ end function lattice_SchmidMatrix_cleavage
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief slip direction of slip systems (|| b) !> @brief Slip direction of slip systems (|| b)
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
function lattice_slip_direction(Nslip,lattice,cOverA) result(d) function lattice_slip_direction(Nslip,lattice,cOverA) result(d)
@ -1501,7 +1507,7 @@ end function lattice_slip_direction
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief normal direction of slip systems (|| n) !> @brief Normal direction of slip systems (|| n)
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
function lattice_slip_normal(Nslip,lattice,cOverA) result(n) function lattice_slip_normal(Nslip,lattice,cOverA) result(n)
@ -1519,7 +1525,7 @@ end function lattice_slip_normal
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief transverse direction of slip systems (|| t = b x n) !> @brief Transverse direction of slip systems (|| t = b x n)
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
function lattice_slip_transverse(Nslip,lattice,cOverA) result(t) function lattice_slip_transverse(Nslip,lattice,cOverA) result(t)
@ -1537,7 +1543,7 @@ end function lattice_slip_transverse
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief labels of slip systems !> @brief Labels of slip systems
!> details only active slip systems are considered !> details only active slip systems are considered
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
function lattice_labels_slip(Nslip,lattice) result(labels) function lattice_labels_slip(Nslip,lattice) result(labels)
@ -1578,7 +1584,7 @@ end function lattice_labels_slip
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief return 3x3 tensor with symmetry according to given Bravais lattice !> @brief Return 3x3 tensor with symmetry according to given Bravais lattice
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
pure function lattice_symmetrize_33(T,lattice) result(T_sym) pure function lattice_symmetrize_33(T,lattice) result(T_sym)
@ -1605,7 +1611,7 @@ end function lattice_symmetrize_33
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief return stiffness matrix in 6x6 notation with symmetry according to given Bravais lattice !> @brief Return stiffness matrix in 6x6 notation with symmetry according to given Bravais lattice
!> @details J. A. Rayne and B. S. Chandrasekhar Phys. Rev. 120, 1658 Erratum Phys. Rev. 122, 1962 !> @details J. A. Rayne and B. S. Chandrasekhar Phys. Rev. 120, 1658 Erratum Phys. Rev. 122, 1962
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
pure function lattice_symmetrize_C66(C66,lattice) result(C66_sym) pure function lattice_symmetrize_C66(C66,lattice) result(C66_sym)
@ -1651,7 +1657,7 @@ end function lattice_symmetrize_C66
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief labels of twin systems !> @brief Labels for twin systems
!> details only active twin systems are considered !> details only active twin systems are considered
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
function lattice_labels_twin(Ntwin,lattice) result(labels) function lattice_labels_twin(Ntwin,lattice) result(labels)
@ -1689,7 +1695,7 @@ end function lattice_labels_twin
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief projection of the transverse direction onto the slip plane !> @brief Projection of the transverse direction onto the slip plane
!> @details: This projection is used to calculate forest hardening for edge dislocations !> @details: This projection is used to calculate forest hardening for edge dislocations
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
function slipProjection_transverse(Nslip,lattice,cOverA) result(projection) function slipProjection_transverse(Nslip,lattice,cOverA) result(projection)
@ -1713,7 +1719,7 @@ end function slipProjection_transverse
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief projection of the slip direction onto the slip plane !> @brief Projection of the slip direction onto the slip plane
!> @details: This projection is used to calculate forest hardening for screw dislocations !> @details: This projection is used to calculate forest hardening for screw dislocations
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
function slipProjection_direction(Nslip,lattice,cOverA) result(projection) function slipProjection_direction(Nslip,lattice,cOverA) result(projection)
@ -1779,7 +1785,7 @@ end function coordinateSystem_slip
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief populate reduced interaction matrix !> @brief Populate reduced interaction matrix
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
function buildInteraction(reacting_used,acting_used,reacting_max,acting_max,values,matrix) function buildInteraction(reacting_used,acting_used,reacting_max,acting_max,values,matrix)
@ -1822,7 +1828,7 @@ end function buildInteraction
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief build a local coordinate system on slip, twin, trans, cleavage systems !> @brief Build a local coordinate system on slip, twin, trans, cleavage systems
!> @details Order: Direction, plane (normal), and common perpendicular !> @details Order: Direction, plane (normal), and common perpendicular
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
function buildCoordinateSystem(active,potential,system,lattice,cOverA) function buildCoordinateSystem(active,potential,system,lattice,cOverA)
@ -1889,7 +1895,7 @@ end function buildCoordinateSystem
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief helper function to define transformation systems !> @brief Helper function to define transformation systems
! Needed to calculate Schmid matrix and rotated stiffness matrices. ! Needed to calculate Schmid matrix and rotated stiffness matrices.
! @details: set c/a = 0.0 for fcc -> bcc transformation ! @details: set c/a = 0.0 for fcc -> bcc transformation
! set a_Xcc = 0.0 for fcc -> hex transformation ! set a_Xcc = 0.0 for fcc -> hex transformation
@ -2073,7 +2079,7 @@ end function getlabels
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief equivalent Poisson's ratio (ν) !> @brief Equivalent Poisson's ratio (ν)
!> @details https://doi.org/10.1143/JPSJ.20.635 !> @details https://doi.org/10.1143/JPSJ.20.635
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
function lattice_equivalent_nu(C,assumption) result(nu) function lattice_equivalent_nu(C,assumption) result(nu)
@ -2106,7 +2112,7 @@ end function lattice_equivalent_nu
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief equivalent shear modulus (μ) !> @brief Equivalent shear modulus (μ)
!> @details https://doi.org/10.1143/JPSJ.20.635 !> @details https://doi.org/10.1143/JPSJ.20.635
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
function lattice_equivalent_mu(C,assumption) result(mu) function lattice_equivalent_mu(C,assumption) result(mu)
@ -2135,7 +2141,7 @@ end function lattice_equivalent_mu
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief check correctness of some lattice functions !> @brief Check correctness of some lattice functions.
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
subroutine selfTest subroutine selfTest

85
src/math.f90
View File

@ -806,7 +806,7 @@ pure function math_sym3333to66(m3333,weighted)
w = merge(NRMMANDEL,1.0_pReal,weighted) w = merge(NRMMANDEL,1.0_pReal,weighted)
else else
w = NRMMANDEL w = NRMMANDEL
endif end if
#ifndef __INTEL_COMPILER #ifndef __INTEL_COMPILER
do concurrent(i=1:6, j=1:6) do concurrent(i=1:6, j=1:6)
@ -841,20 +841,83 @@ pure function math_66toSym3333(m66,weighted)
w = merge(INVNRMMANDEL,1.0_pReal,weighted) w = merge(INVNRMMANDEL,1.0_pReal,weighted)
else else
w = INVNRMMANDEL w = INVNRMMANDEL
endif end if
do i=1,6; do j=1,6 do i=1,6; do j=1,6
math_66toSym3333(MAPNYE(1,i),MAPNYE(2,i),MAPNYE(1,j),MAPNYE(2,j)) = w(i)*w(j)*m66(i,j) math_66toSym3333(MAPNYE(1,i),MAPNYE(2,i),MAPNYE(1,j),MAPNYE(2,j)) = w(i)*w(j)*m66(i,j)
math_66toSym3333(MAPNYE(2,i),MAPNYE(1,i),MAPNYE(1,j),MAPNYE(2,j)) = w(i)*w(j)*m66(i,j) math_66toSym3333(MAPNYE(2,i),MAPNYE(1,i),MAPNYE(1,j),MAPNYE(2,j)) = w(i)*w(j)*m66(i,j)
math_66toSym3333(MAPNYE(1,i),MAPNYE(2,i),MAPNYE(2,j),MAPNYE(1,j)) = w(i)*w(j)*m66(i,j) math_66toSym3333(MAPNYE(1,i),MAPNYE(2,i),MAPNYE(2,j),MAPNYE(1,j)) = w(i)*w(j)*m66(i,j)
math_66toSym3333(MAPNYE(2,i),MAPNYE(1,i),MAPNYE(2,j),MAPNYE(1,j)) = w(i)*w(j)*m66(i,j) math_66toSym3333(MAPNYE(2,i),MAPNYE(1,i),MAPNYE(2,j),MAPNYE(1,j)) = w(i)*w(j)*m66(i,j)
enddo; enddo end do; end do
end function math_66toSym3333 end function math_66toSym3333
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief convert 6x6 Voigt matrix into symmetric 3x3x3x3 matrix !> @brief Convert 6 Voigt stress vector into symmetric 3x3 tensor.
!--------------------------------------------------------------------------------------------------
pure function math_Voigt6to33_stress(sigma_tilde) result(sigma)
real(pReal), dimension(3,3) :: sigma
real(pReal), dimension(6), intent(in) :: sigma_tilde
sigma = reshape([sigma_tilde(1), sigma_tilde(6), sigma_tilde(5), &
sigma_tilde(6), sigma_tilde(2), sigma_tilde(4), &
sigma_tilde(5), sigma_tilde(4), sigma_tilde(3)],[3,3])
end function math_Voigt6to33_stress
!--------------------------------------------------------------------------------------------------
!> @brief Convert 6 Voigt strain vector into symmetric 3x3 tensor.
!--------------------------------------------------------------------------------------------------
pure function math_Voigt6to33_strain(epsilon_tilde) result(epsilon)
real(pReal), dimension(3,3) :: epsilon
real(pReal), dimension(6), intent(in) :: epsilon_tilde
epsilon = reshape([ epsilon_tilde(1), 0.5_pReal*epsilon_tilde(6), 0.5_pReal*epsilon_tilde(5), &
0.5_pReal*epsilon_tilde(6), epsilon_tilde(2), 0.5_pReal*epsilon_tilde(4), &
0.5_pReal*epsilon_tilde(5), 0.5_pReal*epsilon_tilde(4), epsilon_tilde(3)],[3,3])
end function math_Voigt6to33_strain
!--------------------------------------------------------------------------------------------------
!> @brief Convert 3x3 tensor into 6 Voigt stress vector.
!--------------------------------------------------------------------------------------------------
pure function math_33toVoigt6_stress(sigma) result(sigma_tilde)
real(pReal), dimension(6) :: sigma_tilde
real(pReal), dimension(3,3), intent(in) :: sigma
sigma_tilde = [sigma(1,1), sigma(2,2), sigma(3,3), &
sigma(3,2), sigma(3,1), sigma(1,2)]
end function math_33toVoigt6_stress
!--------------------------------------------------------------------------------------------------
!> @brief Convert 3x3 tensor into 6 Voigt strain vector.
!--------------------------------------------------------------------------------------------------
pure function math_33toVoigt6_strain(epsilon) result(epsilon_tilde)
real(pReal), dimension(6) :: epsilon_tilde
real(pReal), dimension(3,3), intent(in) :: epsilon
epsilon_tilde = [ epsilon(1,1), epsilon(2,2), epsilon(3,3), &
2.0_pReal*epsilon(3,2), 2.0_pReal*epsilon(3,1), 2.0_pReal*epsilon(1,2)]
end function math_33toVoigt6_strain
!--------------------------------------------------------------------------------------------------
!> @brief Convert 6x6 Voigt matrix into symmetric 3x3x3x3 matrix.
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
pure function math_Voigt66to3333(m66) pure function math_Voigt66to3333(m66)
@ -864,18 +927,18 @@ pure function math_Voigt66to3333(m66)
integer :: i,j integer :: i,j
do i=1,6; do j=1, 6 do i=1,6; do j=1,6
math_Voigt66to3333(MAPVOIGT(1,i),MAPVOIGT(2,i),MAPVOIGT(1,j),MAPVOIGT(2,j)) = m66(i,j) math_Voigt66to3333(MAPVOIGT(1,i),MAPVOIGT(2,i),MAPVOIGT(1,j),MAPVOIGT(2,j)) = m66(i,j)
math_Voigt66to3333(MAPVOIGT(2,i),MAPVOIGT(1,i),MAPVOIGT(1,j),MAPVOIGT(2,j)) = m66(i,j) math_Voigt66to3333(MAPVOIGT(2,i),MAPVOIGT(1,i),MAPVOIGT(1,j),MAPVOIGT(2,j)) = m66(i,j)
math_Voigt66to3333(MAPVOIGT(1,i),MAPVOIGT(2,i),MAPVOIGT(2,j),MAPVOIGT(1,j)) = m66(i,j) math_Voigt66to3333(MAPVOIGT(1,i),MAPVOIGT(2,i),MAPVOIGT(2,j),MAPVOIGT(1,j)) = m66(i,j)
math_Voigt66to3333(MAPVOIGT(2,i),MAPVOIGT(1,i),MAPVOIGT(2,j),MAPVOIGT(1,j)) = m66(i,j) math_Voigt66to3333(MAPVOIGT(2,i),MAPVOIGT(1,i),MAPVOIGT(2,j),MAPVOIGT(1,j)) = m66(i,j)
enddo; enddo end do; end do
end function math_Voigt66to3333 end function math_Voigt66to3333
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief convert symmetric 3x3x3x3 matrix into 6x6 Voigt matrix !> @brief Convert symmetric 3x3x3x3 matrix into 6x6 Voigt matrix.
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
pure function math_3333toVoigt66(m3333) pure function math_3333toVoigt66(m3333)
@ -924,7 +987,7 @@ real(pReal) function math_sampleGaussVar(mu, sigma, width)
do do
call random_number(rnd) call random_number(rnd)
scatter = width_ * (2.0_pReal * rnd(1) - 1.0_pReal) scatter = width_ * (2.0_pReal * rnd(1) - 1.0_pReal)
if (rnd(2) <= exp(-0.5_pReal * scatter ** 2.0_pReal)) exit ! test if scattered value is drawn if (rnd(2) <= exp(-0.5_pReal * scatter**2)) exit ! test if scattered value is drawn
enddo enddo
math_sampleGaussVar = scatter * sigma math_sampleGaussVar = scatter * sigma
@ -1086,15 +1149,15 @@ function math_eigvalsh33(m)
I = math_invariantsSym33(m) ! invariants are coefficients in characteristic polynomial apart for the sign of c0 and c2 in http://arxiv.org/abs/physics/0610206 I = math_invariantsSym33(m) ! invariants are coefficients in characteristic polynomial apart for the sign of c0 and c2 in http://arxiv.org/abs/physics/0610206
P = I(2)-I(1)**2.0_pReal/3.0_pReal ! different from http://arxiv.org/abs/physics/0610206 (this formulation was in DAMASK) P = I(2)-I(1)**2/3.0_pReal ! different from http://arxiv.org/abs/physics/0610206 (this formulation was in DAMASK)
Q = product(I(1:2))/3.0_pReal & Q = product(I(1:2))/3.0_pReal &
- 2.0_pReal/27.0_pReal*I(1)**3.0_pReal & - 2.0_pReal/27.0_pReal*I(1)**3 &
- I(3) ! different from http://arxiv.org/abs/physics/0610206 (this formulation was in DAMASK) - I(3) ! different from http://arxiv.org/abs/physics/0610206 (this formulation was in DAMASK)
if (all(abs([P,Q]) < TOL)) then if (all(abs([P,Q]) < TOL)) then
math_eigvalsh33 = math_eigvalsh(m) math_eigvalsh33 = math_eigvalsh(m)
else else
rho=sqrt(-3.0_pReal*P**3.0_pReal)/9.0_pReal rho=sqrt(-3.0_pReal*P**3)/9.0_pReal
phi=acos(math_clip(-Q/rho*0.5_pReal,-1.0_pReal,1.0_pReal)) phi=acos(math_clip(-Q/rho*0.5_pReal,-1.0_pReal,1.0_pReal))
math_eigvalsh33 = 2.0_pReal*rho**(1.0_pReal/3.0_pReal)* & math_eigvalsh33 = 2.0_pReal*rho**(1.0_pReal/3.0_pReal)* &
[cos( phi /3.0_pReal), & [cos( phi /3.0_pReal), &

1
src/phase.f90
View File

@ -5,6 +5,7 @@
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
module phase module phase
use prec use prec
use constants
use math use math
use rotations use rotations
use IO use IO

3
src/phase_damage.f90
View File

@ -388,8 +388,7 @@ module function phase_K_phi(co,ce) result(K)
real(pReal), dimension(3,3) :: K real(pReal), dimension(3,3) :: K
real(pReal), parameter :: l = 1.0_pReal real(pReal), parameter :: l = 1.0_pReal
K = crystallite_push33ToRef(co,ce,param(material_phaseID(co,ce))%D) & K = crystallite_push33ToRef(co,ce,param(material_phaseID(co,ce))%D) * l**2
* l**2.0_pReal
end function phase_K_phi end function phase_K_phi

4
src/phase_damage_anisobrittle.f90
View File

@ -129,7 +129,7 @@ module subroutine anisobrittle_dotState(S, ph,en)
traction_t = math_tensordot(S,prm%cleavage_systems(1:3,1:3,2,i)) traction_t = math_tensordot(S,prm%cleavage_systems(1:3,1:3,2,i))
traction_n = math_tensordot(S,prm%cleavage_systems(1:3,1:3,3,i)) traction_n = math_tensordot(S,prm%cleavage_systems(1:3,1:3,3,i))
traction_crit = prm%g_crit(i)*damage_phi(ph,en)**2.0_pReal traction_crit = prm%g_crit(i)*damage_phi(ph,en)**2
damageState(ph)%dotState(1,en) = damageState(ph)%dotState(1,en) & damageState(ph)%dotState(1,en) = damageState(ph)%dotState(1,en) &
+ prm%dot_o / prm%s_crit(i) & + prm%dot_o / prm%s_crit(i) &
@ -190,7 +190,7 @@ module subroutine damage_anisobrittle_LiAndItsTangent(Ld, dLd_dTstar, S, ph,en)
dLd_dTstar = 0.0_pReal dLd_dTstar = 0.0_pReal
associate(prm => param(ph)) associate(prm => param(ph))
do i = 1,prm%sum_N_cl do i = 1,prm%sum_N_cl
traction_crit = prm%g_crit(i)*damage_phi(ph,en)**2.0_pReal traction_crit = prm%g_crit(i)*damage_phi(ph,en)**2
traction_d = math_tensordot(S,prm%cleavage_systems(1:3,1:3,1,i)) traction_d = math_tensordot(S,prm%cleavage_systems(1:3,1:3,1,i))
if (abs(traction_d) > traction_crit + tol_math_check) then if (abs(traction_d) > traction_crit + tol_math_check) then

14
src/phase_mechanical_eigen_thermalexpansion.f90
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@ -58,14 +58,14 @@ module function thermalexpansion_init(kinematics_length) result(myKinematics)
associate(prm => param(kinematics_thermal_expansion_instance(p))) associate(prm => param(kinematics_thermal_expansion_instance(p)))
kinematic_type => kinematics%get(k) kinematic_type => kinematics%get(k)
prm%T_ref = kinematic_type%get_asFloat('T_ref', defaultVal=0.0_pReal) prm%T_ref = kinematic_type%get_asFloat('T_ref', defaultVal=T_ROOM)
prm%A(1,1,1) = kinematic_type%get_asFloat('A_11') prm%A(1,1,1) = kinematic_type%get_asFloat('A_11')
prm%A(1,1,2) = kinematic_type%get_asFloat('A_11,T',defaultVal=0.0_pReal) prm%A(1,1,2) = kinematic_type%get_asFloat('A_11,T', defaultVal=0.0_pReal)
prm%A(1,1,3) = kinematic_type%get_asFloat('A_11,T^2',defaultVal=0.0_pReal) prm%A(1,1,3) = kinematic_type%get_asFloat('A_11,T^2',defaultVal=0.0_pReal)
if (any(phase_lattice(p) == ['hP','tI'])) then if (any(phase_lattice(p) == ['hP','tI'])) then
prm%A(3,3,1) = kinematic_type%get_asFloat('A_33') prm%A(3,3,1) = kinematic_type%get_asFloat('A_33')
prm%A(3,3,2) = kinematic_type%get_asFloat('A_33,T',defaultVal=0.0_pReal) prm%A(3,3,2) = kinematic_type%get_asFloat('A_33,T', defaultVal=0.0_pReal)
prm%A(3,3,3) = kinematic_type%get_asFloat('A_33,T^2',defaultVal=0.0_pReal) prm%A(3,3,3) = kinematic_type%get_asFloat('A_33,T^2',defaultVal=0.0_pReal)
end if end if
do i=1, size(prm%A,3) do i=1, size(prm%A,3)
@ -98,14 +98,14 @@ module subroutine thermalexpansion_LiAndItsTangent(Li, dLi_dTstar, ph,me)
associate(prm => param(kinematics_thermal_expansion_instance(ph))) associate(prm => param(kinematics_thermal_expansion_instance(ph)))
Li = dot_T * ( & Li = dot_T * ( &
prm%A(1:3,1:3,1)*(T - prm%T_ref)**0 & ! constant coefficient prm%A(1:3,1:3,1) & ! constant coefficient
+ prm%A(1:3,1:3,2)*(T - prm%T_ref)**1 & ! linear coefficient + prm%A(1:3,1:3,2)*(T - prm%T_ref)**1 & ! linear coefficient
+ prm%A(1:3,1:3,3)*(T - prm%T_ref)**2 & ! quadratic coefficient + prm%A(1:3,1:3,3)*(T - prm%T_ref)**2 & ! quadratic coefficient
) / & ) / &
(1.0_pReal & (1.0_pReal &
+ prm%A(1:3,1:3,1)*(T - prm%T_ref)**1 / 1. & + prm%A(1:3,1:3,1)*(T - prm%T_ref)**1 / 1.0_pReal &
+ prm%A(1:3,1:3,2)*(T - prm%T_ref)**2 / 2. & + prm%A(1:3,1:3,2)*(T - prm%T_ref)**2 / 2.0_pReal &
+ prm%A(1:3,1:3,3)*(T - prm%T_ref)**3 / 3. & + prm%A(1:3,1:3,3)*(T - prm%T_ref)**3 / 3.0_pReal &
) )
end associate end associate
dLi_dTstar = 0.0_pReal dLi_dTstar = 0.0_pReal

79
src/phase_mechanical_elastic.f90
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@ -1,13 +1,15 @@
submodule(phase:mechanical) elastic submodule(phase:mechanical) elastic
type :: tParameters type :: tParameters
real(pReal) :: & real(pReal),dimension(3) :: &
C_11 = 0.0_pReal, & C_11 = 0.0_pReal, &
C_12 = 0.0_pReal, & C_12 = 0.0_pReal, &
C_13 = 0.0_pReal, & C_13 = 0.0_pReal, &
C_33 = 0.0_pReal, & C_33 = 0.0_pReal, &
C_44 = 0.0_pReal, & C_44 = 0.0_pReal, &
C_66 = 0.0_pReal C_66 = 0.0_pReal
real(pReal) :: &
T_ref
end type tParameters end type tParameters
type(tParameters), allocatable, dimension(:) :: param type(tParameters), allocatable, dimension(:) :: param
@ -28,7 +30,7 @@ module subroutine elastic_init(phases)
phase, & phase, &
mech, & mech, &
elastic elastic
logical :: thermal_active
print'(/,1x,a)', '<<<+- phase:mechanical:elastic init -+>>>' print'(/,1x,a)', '<<<+- phase:mechanical:elastic init -+>>>'
print'(/,1x,a)', '<<<+- phase:mechanical:elastic:Hooke init -+>>>' print'(/,1x,a)', '<<<+- phase:mechanical:elastic:Hooke init -+>>>'
@ -45,15 +47,35 @@ module subroutine elastic_init(phases)
associate(prm => param(ph)) associate(prm => param(ph))
prm%C_11 = elastic%get_asFloat('C_11') prm%T_ref = elastic%get_asFloat('T_ref', defaultVal=T_ROOM)
prm%C_12 = elastic%get_asFloat('C_12')
prm%C_44 = elastic%get_asFloat('C_44') prm%C_11(1) = elastic%get_asFloat('C_11')
prm%C_11(2) = elastic%get_asFloat('C_11,T', defaultVal=0.0_pReal)
prm%C_11(3) = elastic%get_asFloat('C_11,T^2',defaultVal=0.0_pReal)
prm%C_12(1) = elastic%get_asFloat('C_12')
prm%C_12(2) = elastic%get_asFloat('C_12,T', defaultVal=0.0_pReal)
prm%C_12(3) = elastic%get_asFloat('C_12,T^2',defaultVal=0.0_pReal)
prm%C_44(1) = elastic%get_asFloat('C_44')
prm%C_44(2) = elastic%get_asFloat('C_44,T', defaultVal=0.0_pReal)
prm%C_44(3) = elastic%get_asFloat('C_44,T^2',defaultVal=0.0_pReal)
if (any(phase_lattice(ph) == ['hP','tI'])) then if (any(phase_lattice(ph) == ['hP','tI'])) then
prm%C_13 = elastic%get_asFloat('C_13') prm%C_13(1) = elastic%get_asFloat('C_13')
prm%C_33 = elastic%get_asFloat('C_33') prm%C_13(2) = elastic%get_asFloat('C_13,T', defaultVal=0.0_pReal)
prm%C_13(3) = elastic%get_asFloat('C_13,T^2',defaultVal=0.0_pReal)
prm%C_33(1) = elastic%get_asFloat('C_33')
prm%C_33(2) = elastic%get_asFloat('C_33,T', defaultVal=0.0_pReal)
prm%C_33(3) = elastic%get_asFloat('C_33,T^2',defaultVal=0.0_pReal)
end if
if (phase_lattice(ph) == 'tI') then
prm%C_66(1) = elastic%get_asFloat('C_66')
prm%C_66(2) = elastic%get_asFloat('C_66,T', defaultVal=0.0_pReal)
prm%C_66(3) = elastic%get_asFloat('C_66,T^2',defaultVal=0.0_pReal)
end if end if
if (phase_lattice(ph) == 'tI') prm%C_66 = elastic%get_asFloat('C_66')
end associate end associate
end do end do
@ -69,21 +91,44 @@ module function elastic_C66(ph,en) result(C66)
integer, intent(in) :: & integer, intent(in) :: &
ph, & ph, &
en en
real(pReal), dimension(6,6) :: C66 real(pReal), dimension(6,6) :: C66
real(pReal) :: T
associate(prm => param(ph)) associate(prm => param(ph))
C66 = 0.0_pReal C66 = 0.0_pReal
C66(1,1) = prm%C_11 T = thermal_T(ph,en)
C66(1,2) = prm%C_12
C66(4,4) = prm%C_44 C66(1,1) = prm%C_11(1) &
+ prm%C_11(2)*(T - prm%T_ref)**1 &
+ prm%C_11(3)*(T - prm%T_ref)**2
C66(1,2) = prm%C_12(1) &
+ prm%C_12(2)*(T - prm%T_ref)**1 &
+ prm%C_12(3)*(T - prm%T_ref)**2
C66(4,4) = prm%C_44(1) &
+ prm%C_44(2)*(T - prm%T_ref)**1 &
+ prm%C_44(3)*(T - prm%T_ref)**2
if (any(phase_lattice(ph) == ['hP','tI'])) then if (any(phase_lattice(ph) == ['hP','tI'])) then
C66(1,3) = prm%C_13 C66(1,3) = prm%C_13(1) &
C66(3,3) = prm%C_33 + prm%C_13(2)*(T - prm%T_ref)**1 &
+ prm%C_13(3)*(T - prm%T_ref)**2
C66(3,3) = prm%C_33(1) &
+ prm%C_33(2)*(T - prm%T_ref)**1 &
+ prm%C_33(3)*(T - prm%T_ref)**2
end if end if
if (phase_lattice(ph) == 'tI') C66(6,6) = prm%C_66 if (phase_lattice(ph) == 'tI') then
C66(6,6) = prm%C_66(1) &
+ prm%C_66(2)*(T - prm%T_ref)**1 &
+ prm%C_66(3)*(T - prm%T_ref)**2
end if
C66 = lattice_symmetrize_C66(C66,phase_lattice(ph)) C66 = lattice_symmetrize_C66(C66,phase_lattice(ph))
@ -148,15 +193,17 @@ module subroutine phase_hooke_SandItsTangents(S, dS_dFe, dS_dFi, &
dS_dFi !< derivative of 2nd P-K stress with respect to intermediate deformation gradient dS_dFi !< derivative of 2nd P-K stress with respect to intermediate deformation gradient
real(pReal), dimension(3,3) :: E real(pReal), dimension(3,3) :: E
real(pReal), dimension(6,6) :: C66
real(pReal), dimension(3,3,3,3) :: C real(pReal), dimension(3,3,3,3) :: C
integer :: & integer :: &
i, j i, j
C = math_Voigt66to3333(phase_damage_C66(phase_homogenizedC66(ph,en),ph,en)) C66 = phase_damage_C66(phase_homogenizedC66(ph,en),ph,en)
C = math_Voigt66to3333(C66)
E = 0.5_pReal*(matmul(transpose(Fe),Fe)-math_I3) !< Green-Lagrange strain in unloaded configuration E = 0.5_pReal*(matmul(transpose(Fe),Fe)-math_I3) !< Green-Lagrange strain in unloaded configuration
S = math_mul3333xx33(C,matmul(matmul(transpose(Fi),E),Fi)) !< 2PK stress in lattice configuration in work conjugate with GL strain pulled back to lattice configuration S = math_Voigt6to33_stress(matmul(C66,math_33toVoigt6_strain(matmul(matmul(transpose(Fi),E),Fi))))!< 2PK stress in lattice configuration in work conjugate with GL strain pulled back to lattice configuration
do i =1,3; do j=1,3 do i =1,3; do j=1,3
dS_dFe(i,j,1:3,1:3) = matmul(Fe,matmul(matmul(Fi,C(i,j,1:3,1:3)),transpose(Fi))) !< dS_ij/dFe_kl = C_ijmn * Fi_lm * Fi_on * Fe_ko dS_dFe(i,j,1:3,1:3) = matmul(Fe,matmul(matmul(Fi,C(i,j,1:3,1:3)),transpose(Fi))) !< dS_ij/dFe_kl = C_ijmn * Fi_lm * Fi_on * Fe_ko

13
src/phase_mechanical_plastic_dislotungsten.f90
View File

@ -7,9 +7,6 @@
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
submodule(phase:plastic) dislotungsten submodule(phase:plastic) dislotungsten
real(pReal), parameter :: &
kB = 1.38e-23_pReal !< Boltzmann constant in J/Kelvin
type :: tParameters type :: tParameters
real(pReal) :: & real(pReal) :: &
D = 1.0_pReal, & !< grain size D = 1.0_pReal, & !< grain size
@ -169,7 +166,7 @@ module function plastic_dislotungsten_init() result(myPlasticity)
prm%D = pl%get_asFloat('D') prm%D = pl%get_asFloat('D')
prm%D_0 = pl%get_asFloat('D_0') prm%D_0 = pl%get_asFloat('D_0')
prm%Q_cl = pl%get_asFloat('Q_cl') prm%Q_cl = pl%get_asFloat('Q_cl')
prm%f_at = pl%get_asFloat('f_at') * prm%b_sl**3.0_pReal prm%f_at = pl%get_asFloat('f_at') * prm%b_sl**3
prm%dipoleformation = .not. pl%get_asBool('no_dipole_formation', defaultVal = .false.) prm%dipoleformation = .not. pl%get_asBool('no_dipole_formation', defaultVal = .false.)
@ -344,7 +341,7 @@ module subroutine dislotungsten_dotState(Mp,T,ph,en)
dot_rho_dip_formation = merge(2.0_pReal*(d_hat-prm%d_caron)*stt%rho_mob(:,en)*dot%gamma_sl(:,en)/prm%b_sl, & dot_rho_dip_formation = merge(2.0_pReal*(d_hat-prm%d_caron)*stt%rho_mob(:,en)*dot%gamma_sl(:,en)/prm%b_sl, &
0.0_pReal, & 0.0_pReal, &
prm%dipoleformation) prm%dipoleformation)
v_cl = (3.0_pReal*mu*prm%D_0*exp(-prm%Q_cl/(kB*T))*prm%f_at/(2.0_pReal*PI*kB*T)) & v_cl = (3.0_pReal*mu*prm%D_0*exp(-prm%Q_cl/(K_B*T))*prm%f_at/(2.0_pReal*PI*K_B*T)) &
* (1.0_pReal/(d_hat+prm%d_caron)) * (1.0_pReal/(d_hat+prm%d_caron))
dot_rho_dip_climb = (4.0_pReal*v_cl*stt%rho_dip(:,en))/(d_hat-prm%d_caron) ! ToDo: Discuss with Franz: Stress dependency? dot_rho_dip_climb = (4.0_pReal*v_cl*stt%rho_dip(:,en))/(d_hat-prm%d_caron) ! ToDo: Discuss with Franz: Stress dependency?
end where end where
@ -475,7 +472,7 @@ pure subroutine kinetics(Mp,T,ph,en, &
if (present(tau_pos_out)) tau_pos_out = tau_pos if (present(tau_pos_out)) tau_pos_out = tau_pos
if (present(tau_neg_out)) tau_neg_out = tau_neg if (present(tau_neg_out)) tau_neg_out = tau_neg
associate(BoltzmannRatio => prm%Q_s/(kB*T), & associate(BoltzmannRatio => prm%Q_s/(K_B*T), &
b_rho_half => stt%rho_mob(:,en) * prm%b_sl * 0.5_pReal, & b_rho_half => stt%rho_mob(:,en) * prm%b_sl * 0.5_pReal, &
effectiveLength => dst%Lambda_sl(:,en) - prm%w) effectiveLength => dst%Lambda_sl(:,en) - prm%w)
@ -501,7 +498,7 @@ pure subroutine kinetics(Mp,T,ph,en, &
* StressRatio_pminus1 / prm%tau_Peierls * StressRatio_pminus1 / prm%tau_Peierls
dtk = -1.0_pReal * t_k / tau_pos dtk = -1.0_pReal * t_k / tau_pos
dvel = -1.0_pReal * prm%h * (dtk + dtn) / (t_n + t_k)**2.0_pReal dvel = -1.0_pReal * prm%h * (dtk + dtn) / (t_n + t_k)**2
ddot_gamma_dtau_pos = b_rho_half * dvel ddot_gamma_dtau_pos = b_rho_half * dvel
else where significantPositiveTau2 else where significantPositiveTau2
@ -531,7 +528,7 @@ pure subroutine kinetics(Mp,T,ph,en, &
* StressRatio_pminus1 / prm%tau_Peierls * StressRatio_pminus1 / prm%tau_Peierls
dtk = -1.0_pReal * t_k / tau_neg dtk = -1.0_pReal * t_k / tau_neg
dvel = -1.0_pReal * prm%h * (dtk + dtn) / (t_n + t_k)**2.0_pReal dvel = -1.0_pReal * prm%h * (dtk + dtn) / (t_n + t_k)**2
ddot_gamma_dtau_neg = b_rho_half * dvel ddot_gamma_dtau_neg = b_rho_half * dvel
else where significantNegativeTau2 else where significantNegativeTau2

27
src/phase_mechanical_plastic_dislotwin.f90
View File

@ -9,9 +9,6 @@
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
submodule(phase:plastic) dislotwin submodule(phase:plastic) dislotwin
real(pReal), parameter :: &
kB = 1.38e-23_pReal !< Boltzmann constant in J/Kelvin
type :: tParameters type :: tParameters
real(pReal) :: & real(pReal) :: &
Q_cl = 1.0_pReal, & !< activation energy for dislocation climb Q_cl = 1.0_pReal, & !< activation energy for dislocation climb
@ -31,7 +28,7 @@ submodule(phase:plastic) dislotwin
delta_G = 1.0_pReal, & !< Free energy difference between austensite and martensite delta_G = 1.0_pReal, & !< Free energy difference between austensite and martensite
i_tr = 1.0_pReal, & !< adjustment parameter to calculate MFP for transformation i_tr = 1.0_pReal, & !< adjustment parameter to calculate MFP for transformation
h = 1.0_pReal, & !< Stack height of hex nucleus h = 1.0_pReal, & !< Stack height of hex nucleus
T_ref = 0.0_pReal, & T_ref = T_ROOM, &
a_cI = 1.0_pReal, & a_cI = 1.0_pReal, &
a_cF = 1.0_pReal a_cF = 1.0_pReal
real(pReal), dimension(2) :: & real(pReal), dimension(2) :: &
@ -597,7 +594,7 @@ module subroutine dislotwin_LpAndItsTangent(Lp,dLp_dMp,Mp,T,ph,en)
shearBandingContribution: if (dNeq0(prm%v_sb)) then shearBandingContribution: if (dNeq0(prm%v_sb)) then
E_kB_T = prm%E_sb/(kB*T) E_kB_T = prm%E_sb/(K_B*T)
call math_eigh33(eigValues,eigVectors,Mp) ! is Mp symmetric by design? call math_eigh33(eigValues,eigVectors,Mp) ! is Mp symmetric by design?
do i = 1,6 do i = 1,6
@ -694,8 +691,8 @@ module subroutine dislotwin_dotState(Mp,T,ph,en)
* (prm%Gamma_sf(1) + prm%Gamma_sf(2) * T) / (mu*prm%b_sl(i)), & * (prm%Gamma_sf(1) + prm%Gamma_sf(2) * T) / (mu*prm%b_sl(i)), &
1.0_pReal, & 1.0_pReal, &
prm%ExtendedDislocations) prm%ExtendedDislocations)
v_cl = 2.0_pReal*prm%omega*b_d**2.0_pReal*exp(-prm%Q_cl/(kB*T)) & v_cl = 2.0_pReal*prm%omega*b_d**2*exp(-prm%Q_cl/(K_B*T)) &
* (exp(abs(sigma_cl)*prm%b_sl(i)**3.0_pReal/(kB*T)) - 1.0_pReal) * (exp(abs(sigma_cl)*prm%b_sl(i)**3/(K_B*T)) - 1.0_pReal)
dot_rho_dip_climb(i) = 4.0_pReal*v_cl*stt%rho_dip(i,en) & dot_rho_dip_climb(i) = 4.0_pReal*v_cl*stt%rho_dip(i,en) &
/ (d_hat-prm%d_caron(i)) / (d_hat-prm%d_caron(i))
@ -787,14 +784,14 @@ module subroutine dislotwin_dependentState(T,ph,en)
+ 3.0_pReal*prm%b_tr*mu/(prm%L_tr*prm%b_tr) & + 3.0_pReal*prm%b_tr*mu/(prm%L_tr*prm%b_tr) &
+ prm%h*prm%delta_G/(3.0_pReal*prm%b_tr) + prm%h*prm%delta_G/(3.0_pReal*prm%b_tr)
dst%V_tw(:,en) = (PI/4.0_pReal)*prm%t_tw*dst%Lambda_tw(:,en)**2.0_pReal dst%V_tw(:,en) = (PI/4.0_pReal)*prm%t_tw*dst%Lambda_tw(:,en)**2
dst%V_tr(:,en) = (PI/4.0_pReal)*prm%t_tr*dst%Lambda_tr(:,en)**2.0_pReal dst%V_tr(:,en) = (PI/4.0_pReal)*prm%t_tr*dst%Lambda_tr(:,en)**2
x0 = mu*prm%b_tw**2.0_pReal/(Gamma*8.0_pReal*PI)*(2.0_pReal+nu)/(1.0_pReal-nu) ! ToDo: In the paper, this is the Burgers vector for slip x0 = mu*prm%b_tw**2/(Gamma*8.0_pReal*PI)*(2.0_pReal+nu)/(1.0_pReal-nu) ! ToDo: In the paper, this is the Burgers vector for slip
dst%tau_r_tw(:,en) = mu*prm%b_tw/(2.0_pReal*PI)*(1.0_pReal/(x0+prm%x_c_tw)+cos(pi/3.0_pReal)/x0) dst%tau_r_tw(:,en) = mu*prm%b_tw/(2.0_pReal*PI)*(1.0_pReal/(x0+prm%x_c_tw)+cos(pi/3.0_pReal)/x0)
x0 = mu*prm%b_tr**2.0_pReal/(Gamma*8.0_pReal*PI)*(2.0_pReal+nu)/(1.0_pReal-nu) ! ToDo: In the paper, this is the Burgers vector for slip x0 = mu*prm%b_tr**2/(Gamma*8.0_pReal*PI)*(2.0_pReal+nu)/(1.0_pReal-nu) ! ToDo: In the paper, this is the Burgers vector for slip
dst%tau_r_tr(:,en) = mu*prm%b_tr/(2.0_pReal*PI)*(1.0_pReal/(x0+prm%x_c_tr)+cos(pi/3.0_pReal)/x0) dst%tau_r_tr(:,en) = mu*prm%b_tr/(2.0_pReal*PI)*(1.0_pReal/(x0+prm%x_c_tr)+cos(pi/3.0_pReal)/x0)
end associate end associate
@ -907,7 +904,7 @@ pure subroutine kinetics_sl(Mp,T,ph,en, &
significantStress: where(tau_eff > tol_math_check) significantStress: where(tau_eff > tol_math_check)
stressRatio = tau_eff/prm%tau_0 stressRatio = tau_eff/prm%tau_0
StressRatio_p = stressRatio** prm%p StressRatio_p = stressRatio** prm%p
Q_kB_T = prm%Q_sl/(kB*T) Q_kB_T = prm%Q_sl/(K_B*T)
v_wait_inverse = exp(Q_kB_T*(1.0_pReal-StressRatio_p)** prm%q) & v_wait_inverse = exp(Q_kB_T*(1.0_pReal-StressRatio_p)** prm%q) &
/ prm%v_0 / prm%v_0
v_run_inverse = prm%B/(tau_eff*prm%b_sl) v_run_inverse = prm%B/(tau_eff*prm%b_sl)
@ -920,7 +917,7 @@ pure subroutine kinetics_sl(Mp,T,ph,en, &
/ prm%tau_0 / prm%tau_0
dV_run_inverse_dTau = -1.0_pReal * v_run_inverse/tau_eff dV_run_inverse_dTau = -1.0_pReal * v_run_inverse/tau_eff
dV_dTau = -1.0_pReal * (dV_wait_inverse_dTau+dV_run_inverse_dTau) & dV_dTau = -1.0_pReal * (dV_wait_inverse_dTau+dV_run_inverse_dTau) &
/ (v_wait_inverse+v_run_inverse)**2.0_pReal / (v_wait_inverse+v_run_inverse)**2
ddot_gamma_dtau = dV_dTau*stt%rho_mob(:,en)*prm%b_sl ddot_gamma_dtau = dV_dTau*stt%rho_mob(:,en)*prm%b_sl
else where significantStress else where significantStress
dot_gamma_sl = 0.0_pReal dot_gamma_sl = 0.0_pReal
@ -980,7 +977,7 @@ pure subroutine kinetics_tw(Mp,T,dot_gamma_sl,ph,en,&
Ndot0=(abs(dot_gamma_sl(s1))*(stt%rho_mob(s2,en)+stt%rho_dip(s2,en))+& Ndot0=(abs(dot_gamma_sl(s1))*(stt%rho_mob(s2,en)+stt%rho_dip(s2,en))+&
abs(dot_gamma_sl(s2))*(stt%rho_mob(s1,en)+stt%rho_dip(s1,en)))/& abs(dot_gamma_sl(s2))*(stt%rho_mob(s1,en)+stt%rho_dip(s1,en)))/&
(prm%L_tw*prm%b_sl(i))*& (prm%L_tw*prm%b_sl(i))*&
(1.0_pReal-exp(-prm%V_cs/(kB*T)*(dst%tau_r_tw(i,en)-tau(i)))) (1.0_pReal-exp(-prm%V_cs/(K_B*T)*(dst%tau_r_tw(i,en)-tau(i))))
else else
Ndot0=0.0_pReal Ndot0=0.0_pReal
end if end if
@ -1049,7 +1046,7 @@ pure subroutine kinetics_tr(Mp,T,dot_gamma_sl,ph,en,&
Ndot0=(abs(dot_gamma_sl(s1))*(stt%rho_mob(s2,en)+stt%rho_dip(s2,en))+& Ndot0=(abs(dot_gamma_sl(s1))*(stt%rho_mob(s2,en)+stt%rho_dip(s2,en))+&
abs(dot_gamma_sl(s2))*(stt%rho_mob(s1,en)+stt%rho_dip(s1,en)))/& abs(dot_gamma_sl(s2))*(stt%rho_mob(s1,en)+stt%rho_dip(s1,en)))/&
(prm%L_tr*prm%b_sl(i))*& (prm%L_tr*prm%b_sl(i))*&
(1.0_pReal-exp(-prm%V_cs/(kB*T)*(dst%tau_r_tr(i,en)-tau(i)))) (1.0_pReal-exp(-prm%V_cs/(K_B*T)*(dst%tau_r_tr(i,en)-tau(i))))
else else
Ndot0=0.0_pReal Ndot0=0.0_pReal
end if end if

33
src/phase_mechanical_plastic_nonlocal.f90
View File

@ -19,9 +19,6 @@ submodule(phase:plastic) nonlocal
type(tGeometry), dimension(:), allocatable :: geom type(tGeometry), dimension(:), allocatable :: geom
real(pReal), parameter :: &
kB = 1.38e-23_pReal !< Boltzmann constant in J/Kelvin
! storage order of dislocation types ! storage order of dislocation types
integer, dimension(*), parameter :: & integer, dimension(*), parameter :: &
sgl = [1,2,3,4,5,6,7,8] !< signed (single) sgl = [1,2,3,4,5,6,7,8] !< signed (single)
@ -623,7 +620,7 @@ module subroutine nonlocal_dependentState(ph, en, ip, el)
* spread(( 1.0_pReal - prm%f_F & * spread(( 1.0_pReal - prm%f_F &
+ prm%f_F & + prm%f_F &
* log(0.35_pReal * prm%b_sl * sqrt(max(stt%rho_forest(:,en),prm%rho_significant))) & * log(0.35_pReal * prm%b_sl * sqrt(max(stt%rho_forest(:,en),prm%rho_significant))) &
/ log(0.35_pReal * prm%b_sl * 1e6_pReal))** 2.0_pReal,2,prm%sum_N_sl) / log(0.35_pReal * prm%b_sl * 1e6_pReal))**2,2,prm%sum_N_sl)
else else
myInteractionMatrix = prm%h_sl_sl myInteractionMatrix = prm%h_sl_sl
end if end if
@ -649,7 +646,7 @@ module subroutine nonlocal_dependentState(ph, en, ip, el)
rhoExcess(1,:) = rho_edg_delta rhoExcess(1,:) = rho_edg_delta
rhoExcess(2,:) = rho_scr_delta rhoExcess(2,:) = rho_scr_delta
FVsize = geom(ph)%V_0(en) ** (1.0_pReal/3.0_pReal) FVsize = geom(ph)%V_0(en)**(1.0_pReal/3.0_pReal)
!* loop through my neighborhood and get the connection vectors (in lattice frame) and the excess densities !* loop through my neighborhood and get the connection vectors (in lattice frame) and the excess densities
@ -1094,9 +1091,9 @@ module subroutine nonlocal_dotState(Mp, Temperature,timestep, &
! thermally activated annihilation of edge dipoles by climb ! thermally activated annihilation of edge dipoles by climb
rhoDotThermalAnnihilation = 0.0_pReal rhoDotThermalAnnihilation = 0.0_pReal
D_SD = prm%D_0 * exp(-prm%Q_cl / (kB * Temperature)) ! eq. 3.53 D_SD = prm%D_0 * exp(-prm%Q_cl / (K_B * Temperature)) ! eq. 3.53
v_climb = D_SD * mu * prm%V_at & v_climb = D_SD * mu * prm%V_at &
/ (PI * (1.0_pReal-nu) * (dUpper(:,1) + dLower(:,1)) * kB * Temperature) ! eq. 3.54 / (PI * (1.0_pReal-nu) * (dUpper(:,1) + dLower(:,1)) * K_B * Temperature) ! eq. 3.54
forall (s = 1:prm%sum_N_sl, dUpper(s,1) > dLower(s,1)) & forall (s = 1:prm%sum_N_sl, dUpper(s,1) > dLower(s,1)) &
rhoDotThermalAnnihilation(s,9) = max(- 4.0_pReal * rhoDip(s,1) * v_climb(s) / (dUpper(s,1) - dLower(s,1)), & rhoDotThermalAnnihilation(s,9) = max(- 4.0_pReal * rhoDip(s,1) * v_climb(s) / (dUpper(s,1) - dLower(s,1)), &
- rhoDip(s,1) / timestep - rhoDotAthermalAnnihilation(s,9) & - rhoDip(s,1) / timestep - rhoDotAthermalAnnihilation(s,9) &
@ -1307,10 +1304,10 @@ function rhoDotFlux(timestep,ph,en,ip,el)
* math_inner(m(1:3,s,t), normal_neighbor2me) * area ! positive line length that wants to enter through this interface * math_inner(m(1:3,s,t), normal_neighbor2me) * area ! positive line length that wants to enter through this interface
where (compatibility(c,:,s,n,ip,el) > 0.0_pReal) & where (compatibility(c,:,s,n,ip,el) > 0.0_pReal) &
rhoDotFlux(:,t) = rhoDotFlux(1:ns,t) & rhoDotFlux(:,t) = rhoDotFlux(1:ns,t) &
+ lineLength/IPvolume(ip,el)*compatibility(c,:,s,n,ip,el)**2.0_pReal ! transferring to equally signed mobile dislocation type + lineLength/IPvolume(ip,el)*compatibility(c,:,s,n,ip,el)**2 ! transferring to equally signed mobile dislocation type
where (compatibility(c,:,s,n,ip,el) < 0.0_pReal) & where (compatibility(c,:,s,n,ip,el) < 0.0_pReal) &
rhoDotFlux(:,topp) = rhoDotFlux(:,topp) & rhoDotFlux(:,topp) = rhoDotFlux(:,topp) &
+ lineLength/IPvolume(ip,el)*compatibility(c,:,s,n,ip,el)**2.0_pReal ! transferring to opposite signed mobile dislocation type + lineLength/IPvolume(ip,el)*compatibility(c,:,s,n,ip,el)**2 ! transferring to opposite signed mobile dislocation type
end if end if
end do end do
@ -1339,7 +1336,7 @@ function rhoDotFlux(timestep,ph,en,ip,el)
c = (t + 1) / 2 c = (t + 1) / 2
if (v0(s,t) * math_inner(m(1:3,s,t), normal_me2neighbor) > 0.0_pReal ) then ! flux from en to my neighbor == leaving flux for en (might also be a pure flux from my mobile density to dead density if interface not at all transmissive) if (v0(s,t) * math_inner(m(1:3,s,t), normal_me2neighbor) > 0.0_pReal ) then ! flux from en to my neighbor == leaving flux for en (might also be a pure flux from my mobile density to dead density if interface not at all transmissive)
if (v0(s,t) * neighbor_v0(s,t) >= 0.0_pReal) then ! no sign change in flux density if (v0(s,t) * neighbor_v0(s,t) >= 0.0_pReal) then ! no sign change in flux density
transmissivity = sum(compatibility(c,:,s,n,ip,el)**2.0_pReal) ! overall transmissivity from this slip system to my neighbor transmissivity = sum(compatibility(c,:,s,n,ip,el)**2) ! overall transmissivity from this slip system to my neighbor
else ! sign change in flux density means sign change in stress which does not allow for dislocations to arive at the neighbor else ! sign change in flux density means sign change in stress which does not allow for dislocations to arive at the neighbor
transmissivity = 0.0_pReal transmissivity = 0.0_pReal
end if end if
@ -1666,14 +1663,14 @@ pure subroutine kinetics(v, dv_dtau, dv_dtauNS, tau, tauNS, tauThreshold, c, T,
!* Peierls contribution !* Peierls contribution
tauEff = max(0.0_pReal, abs(tauNS(s)) - tauThreshold(s)) tauEff = max(0.0_pReal, abs(tauNS(s)) - tauThreshold(s))
lambda_P = prm%b_sl(s) lambda_P = prm%b_sl(s)
activationVolume_P = prm%w *prm%b_sl(s)**3.0_pReal activationVolume_P = prm%w *prm%b_sl(s)**3
criticalStress_P = prm%peierlsStress(s,c) criticalStress_P = prm%peierlsStress(s,c)
activationEnergy_P = criticalStress_P * activationVolume_P activationEnergy_P = criticalStress_P * activationVolume_P
tauRel_P = min(1.0_pReal, tauEff / criticalStress_P) tauRel_P = min(1.0_pReal, tauEff / criticalStress_P)
tPeierls = 1.0_pReal / prm%nu_a & tPeierls = 1.0_pReal / prm%nu_a &
* exp(activationEnergy_P / (kB * T) & * exp(activationEnergy_P / (K_B * T) &
* (1.0_pReal - tauRel_P**prm%p)**prm%q) * (1.0_pReal - tauRel_P**prm%p)**prm%q)
dtPeierls_dtau = merge(tPeierls * prm%p * prm%q * activationVolume_P / (kB * T) & dtPeierls_dtau = merge(tPeierls * prm%p * prm%q * activationVolume_P / (K_B * T) &
* (1.0_pReal - tauRel_P**prm%p)**(prm%q-1.0_pReal) * tauRel_P**(prm%p-1.0_pReal), & * (1.0_pReal - tauRel_P**prm%p)**(prm%q-1.0_pReal) * tauRel_P**(prm%p-1.0_pReal), &
0.0_pReal, & 0.0_pReal, &
tauEff < criticalStress_P) tauEff < criticalStress_P)
@ -1681,12 +1678,12 @@ pure subroutine kinetics(v, dv_dtau, dv_dtauNS, tau, tauNS, tauThreshold, c, T,
! Contribution from solid solution strengthening ! Contribution from solid solution strengthening
tauEff = abs(tau(s)) - tauThreshold(s) tauEff = abs(tau(s)) - tauThreshold(s)
lambda_S = prm%b_sl(s) / sqrt(prm%c_sol) lambda_S = prm%b_sl(s) / sqrt(prm%c_sol)
activationVolume_S = prm%f_sol * prm%b_sl(s)**3.0_pReal / sqrt(prm%c_sol) activationVolume_S = prm%f_sol * prm%b_sl(s)**3 / sqrt(prm%c_sol)
criticalStress_S = prm%Q_sol / activationVolume_S criticalStress_S = prm%Q_sol / activationVolume_S
tauRel_S = min(1.0_pReal, tauEff / criticalStress_S) tauRel_S = min(1.0_pReal, tauEff / criticalStress_S)
tSolidSolution = 1.0_pReal / prm%nu_a & tSolidSolution = 1.0_pReal / prm%nu_a &
* exp(prm%Q_sol / (kB * T)* (1.0_pReal - tauRel_S**prm%p)**prm%q) * exp(prm%Q_sol / (K_B * T)* (1.0_pReal - tauRel_S**prm%p)**prm%q)
dtSolidSolution_dtau = merge(tSolidSolution * prm%p * prm%q * activationVolume_S / (kB * T) & dtSolidSolution_dtau = merge(tSolidSolution * prm%p * prm%q * activationVolume_S / (K_B * T) &
* (1.0_pReal - tauRel_S**prm%p)**(prm%q-1.0_pReal)* tauRel_S**(prm%p-1.0_pReal), & * (1.0_pReal - tauRel_S**prm%p)**(prm%q-1.0_pReal)* tauRel_S**(prm%p-1.0_pReal), &
0.0_pReal, & 0.0_pReal, &
tauEff < criticalStress_S) tauEff < criticalStress_S)
@ -1697,8 +1694,8 @@ pure subroutine kinetics(v, dv_dtau, dv_dtauNS, tau, tauNS, tauThreshold, c, T,
v(s) = sign(1.0_pReal,tau(s)) & v(s) = sign(1.0_pReal,tau(s)) &
/ (tPeierls / lambda_P + tSolidSolution / lambda_S + prm%B /(prm%b_sl(s) * tauEff)) / (tPeierls / lambda_P + tSolidSolution / lambda_S + prm%B /(prm%b_sl(s) * tauEff))
dv_dtau(s) = v(s)**2.0_pReal * (dtSolidSolution_dtau / lambda_S + prm%B / (prm%b_sl(s) * tauEff**2.0_pReal)) dv_dtau(s) = v(s)**2 * (dtSolidSolution_dtau / lambda_S + prm%B / (prm%b_sl(s) * tauEff**2))
dv_dtauNS(s) = v(s)**2.0_pReal * dtPeierls_dtau / lambda_P dv_dtauNS(s) = v(s)**2 * dtPeierls_dtau / lambda_P
end if end if
end do end do

73
src/rotations.f90
View File

@ -75,6 +75,7 @@ module rotations
procedure, public :: rotVector procedure, public :: rotVector
procedure, public :: rotTensor2 procedure, public :: rotTensor2
procedure, public :: rotTensor4 procedure, public :: rotTensor4
procedure, public :: rotStiffness
procedure, public :: misorientation procedure, public :: misorientation
procedure, public :: standardize procedure, public :: standardize
end type rotation end type rotation
@ -339,8 +340,7 @@ end function rotTensor2
!--------------------------------------------------------------------------------------------------- !---------------------------------------------------------------------------------------------------
!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH !> @brief Rotate a rank-4 tensor passively (default) or actively.
!> @brief rotate a rank-4 tensor passively (default) or actively
!> @details: rotation is based on rotation matrix !> @details: rotation is based on rotation matrix
!! ToDo: Need to check active/passive !!! !! ToDo: Need to check active/passive !!!
!--------------------------------------------------------------------------------------------------- !---------------------------------------------------------------------------------------------------
@ -354,6 +354,7 @@ pure function rotTensor4(self,T,active) result(tRot)
real(pReal), dimension(3,3) :: R real(pReal), dimension(3,3) :: R
integer :: i,j,k,l,m,n,o,p integer :: i,j,k,l,m,n,o,p
if (present(active)) then if (present(active)) then
R = merge(transpose(self%asMatrix()),self%asMatrix(),active) R = merge(transpose(self%asMatrix()),self%asMatrix(),active)
else else
@ -371,7 +372,47 @@ end function rotTensor4
!--------------------------------------------------------------------------------------------------- !---------------------------------------------------------------------------------------------------
!> @brief misorientation !> @brief Rotate a rank-4 tensor in Voigt 6x6 notation passively (default) or actively.
!> @details: https://scicomp.stackexchange.com/questions/35600
!! ToDo: Need to check active/passive !!!
!---------------------------------------------------------------------------------------------------
pure function rotStiffness(self,C,active) result(cRot)
real(pReal), dimension(6,6) :: cRot
class(rotation), intent(in) :: self
real(pReal), intent(in), dimension(6,6) :: C
logical, intent(in), optional :: active
real(pReal), dimension(3,3) :: R
real(pReal), dimension(6,6) :: M
if (present(active)) then
R = merge(transpose(self%asMatrix()),self%asMatrix(),active)
else
R = self%asMatrix()
endif
M = reshape([R(1,1)**2.0_pReal, R(2,1)**2.0_pReal, R(3,1)**2.0_pReal, &
R(2,1)*R(3,1), R(1,1)*R(3,1), R(1,1)*R(2,1), &
R(1,2)**2.0_pReal, R(2,2)**2.0_pReal, R(3,2)**2.0_pReal, &
R(2,2)*R(3,2), R(1,2)*R(3,2), R(1,2)*R(2,2), &
R(1,3)**2.0_pReal, R(2,3)**2.0_pReal, R(3,3)**2.0_pReal, &
R(2,3)*R(3,3), R(1,3)*R(3,3), R(1,3)*R(2,3), &
2.0_pReal*R(1,2)*R(1,3), 2.0_pReal*R(2,2)*R(2,3), 2.0_pReal*R(3,2)*R(3,3), &
R(2,2)*R(3,3)+R(2,3)*R(3,2), R(1,2)*R(3,3)+R(1,3)*R(3,2), R(1,2)*R(2,3)+R(1,3)*R(2,2), &
2.0_pReal*R(1,3)*R(1,1), 2.0_pReal*R(2,3)*R(2,1), 2.0_pReal*R(3,3)*R(3,1), &
R(2,3)*R(3,1)+R(2,1)*R(3,3), R(1,3)*R(3,1)+R(1,1)*R(3,3), R(1,3)*R(2,1)+R(1,1)*R(2,3), &
2.0_pReal*R(1,1)*R(1,2), 2.0_pReal*R(2,1)*R(2,2), 2.0_pReal*R(3,1)*R(3,2), &
R(2,1)*R(3,2)+R(2,2)*R(3,1), R(1,1)*R(3,2)+R(1,2)*R(3,1), R(1,1)*R(2,2)+R(1,2)*R(2,1)],[6,6])
cRot = matmul(M,matmul(C,transpose(M)))
end function rotStiffness
!---------------------------------------------------------------------------------------------------
!> @brief Misorientation.
!--------------------------------------------------------------------------------------------------- !---------------------------------------------------------------------------------------------------
pure elemental function misorientation(self,other) pure elemental function misorientation(self,other)
@ -386,7 +427,7 @@ end function misorientation
!--------------------------------------------------------------------------------------------------- !---------------------------------------------------------------------------------------------------
!> @author Marc De Graef, Carnegie Mellon University !> @author Marc De Graef, Carnegie Mellon University
!> @brief convert unit quaternion to rotation matrix !> @brief Convert unit quaternion to rotation matrix.
!--------------------------------------------------------------------------------------------------- !---------------------------------------------------------------------------------------------------
pure function qu2om(qu) result(om) pure function qu2om(qu) result(om)
@ -395,8 +436,8 @@ pure function qu2om(qu) result(om)
real(pReal) :: qq real(pReal) :: qq
qq = qu(1)**2-sum(qu(2:4)**2)
qq = qu(1)**2-sum(qu(2:4)**2)
om(1,1) = qq+2.0_pReal*qu(2)**2 om(1,1) = qq+2.0_pReal*qu(2)**2
om(2,2) = qq+2.0_pReal*qu(3)**2 om(2,2) = qq+2.0_pReal*qu(3)**2
@ -416,7 +457,7 @@ end function qu2om
!--------------------------------------------------------------------------------------------------- !---------------------------------------------------------------------------------------------------
!> @author Marc De Graef, Carnegie Mellon University !> @author Marc De Graef, Carnegie Mellon University
!> @brief convert unit quaternion to Euler angles !> @brief Convert unit quaternion to Euler angles.
!--------------------------------------------------------------------------------------------------- !---------------------------------------------------------------------------------------------------
pure function qu2eu(qu) result(eu) pure function qu2eu(qu) result(eu)
@ -425,6 +466,7 @@ pure function qu2eu(qu) result(eu)
real(pReal) :: q12, q03, chi real(pReal) :: q12, q03, chi
q03 = qu(1)**2+qu(4)**2 q03 = qu(1)**2+qu(4)**2
q12 = qu(2)**2+qu(3)**2 q12 = qu(2)**2+qu(3)**2
chi = sqrt(q03*q12) chi = sqrt(q03*q12)
@ -578,7 +620,7 @@ pure function om2eu(om) result(eu)
real(pReal) :: zeta real(pReal) :: zeta
if (dNeq(abs(om(3,3)),1.0_pReal,1.e-8_pReal)) then if (dNeq(abs(om(3,3)),1.0_pReal,1.e-8_pReal)) then
zeta = 1.0_pReal/sqrt(math_clip(1.0_pReal-om(3,3)**2.0_pReal,1e-64_pReal,1.0_pReal)) zeta = 1.0_pReal/sqrt(math_clip(1.0_pReal-om(3,3)**2,1e-64_pReal,1.0_pReal))
eu = [atan2(om(3,1)*zeta,-om(3,2)*zeta), & eu = [atan2(om(3,1)*zeta,-om(3,2)*zeta), &
acos(math_clip(om(3,3),-1.0_pReal,1.0_pReal)), & acos(math_clip(om(3,3),-1.0_pReal,1.0_pReal)), &
atan2(om(1,3)*zeta, om(2,3)*zeta)] atan2(om(1,3)*zeta, om(2,3)*zeta)]
@ -1099,7 +1141,7 @@ pure function ho2ax(ho) result(ax)
+0.000003953714684212874_pReal, -0.00000036555001439719544_pReal ] +0.000003953714684212874_pReal, -0.00000036555001439719544_pReal ]
! normalize h and store the magnitude ! normalize h and store the magnitude
hmag_squared = sum(ho**2.0_pReal) hmag_squared = sum(ho**2)
if (dEq0(hmag_squared)) then if (dEq0(hmag_squared)) then
ax = [ 0.0_pReal, 0.0_pReal, 1.0_pReal, 0.0_pReal ] ax = [ 0.0_pReal, 0.0_pReal, 1.0_pReal, 0.0_pReal ]
else else
@ -1379,6 +1421,7 @@ subroutine selfTest()
real(pReal), dimension(3) :: x, eu, ho, v3 real(pReal), dimension(3) :: x, eu, ho, v3
real(pReal), dimension(3,3) :: om, t33 real(pReal), dimension(3,3) :: om, t33
real(pReal), dimension(3,3,3,3) :: t3333 real(pReal), dimension(3,3,3,3) :: t3333
real(pReal), dimension(6,6) :: C
real :: A,B real :: A,B
integer :: i integer :: i
@ -1412,6 +1455,7 @@ subroutine selfTest()
if(qu(1)<0.0_pReal) qu = qu * (-1.0_pReal) if(qu(1)<0.0_pReal) qu = qu * (-1.0_pReal)
endif endif
if(.not. quaternion_equal(om2qu(qu2om(qu)),qu)) error stop 'om2qu/qu2om' if(.not. quaternion_equal(om2qu(qu2om(qu)),qu)) error stop 'om2qu/qu2om'
if(.not. quaternion_equal(eu2qu(qu2eu(qu)),qu)) error stop 'eu2qu/qu2eu' if(.not. quaternion_equal(eu2qu(qu2eu(qu)),qu)) error stop 'eu2qu/qu2eu'
if(.not. quaternion_equal(ax2qu(qu2ax(qu)),qu)) error stop 'ax2qu/qu2ax' if(.not. quaternion_equal(ax2qu(qu2ax(qu)),qu)) error stop 'ax2qu/qu2ax'
@ -1447,20 +1491,25 @@ subroutine selfTest()
call R%fromMatrix(om) call R%fromMatrix(om)
call random_number(v3) call random_number(v3)
if(all(dNeq(R%rotVector(R%rotVector(v3),active=.true.),v3,1.0e-12_pReal))) & if (any(dNeq(R%rotVector(R%rotVector(v3),active=.true.),v3,1.0e-12_pReal))) &
error stop 'rotVector' error stop 'rotVector'
call random_number(t33) call random_number(t33)
if(all(dNeq(R%rotTensor2(R%rotTensor2(t33),active=.true.),t33,1.0e-12_pReal))) & if (any(dNeq(R%rotTensor2(R%rotTensor2(t33),active=.true.),t33,1.0e-12_pReal))) &
error stop 'rotTensor2' error stop 'rotTensor2'
call random_number(t3333) call random_number(t3333)
if(all(dNeq(R%rotTensor4(R%rotTensor4(t3333),active=.true.),t3333,1.0e-12_pReal))) & if (any(dNeq(R%rotTensor4(R%rotTensor4(t3333),active=.true.),t3333,1.0e-12_pReal))) &
error stop 'rotTensor4' error stop 'rotTensor4'
call random_number(C)
C = C+transpose(C)
if (any(dNeq(R%rotStiffness(C),math_3333toVoigt66(R%rotate(math_Voigt66to3333(C))),1.0e-12_pReal))) &
error stop 'rotStiffness'
call R%fromQuaternion(qu * (1.0_pReal + merge(+5.e-9_pReal,-5.e-9_pReal, mod(i,2) == 0))) ! allow reasonable tolerance for ASCII/YAML call R%fromQuaternion(qu * (1.0_pReal + merge(+5.e-9_pReal,-5.e-9_pReal, mod(i,2) == 0))) ! allow reasonable tolerance for ASCII/YAML
enddo end do
contains contains