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Merge remote-tracking branch 'origin/development' into clean-and-polish-damage

This commit is contained in:
Martin Diehl 2020-03-10 13:49:11 +01:00
parent aa75591ea9 0dea7a3c7e
commit 705ee908a2
34 changed files with 3751 additions and 4959 deletions
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7
.gitattributes vendored
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@ -8,3 +8,10 @@
*.jpg binary
*.hdf5 binary
*.pdf binary
# ignore files from MSC.Marc in language statistics
installation/mods_MarcMentat/* linguist-vendored
src/MarcInclude/* linguist-vendored
# ignore reference files for tests in language statistics
python/tests/reference/* linguist-vendored

7
.gitlab-ci.yml
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@ -142,13 +142,6 @@ Pre_General:
- master
- release
grid_geometryPacking:
stage: preprocessing
script: grid_geometryPacking/test.py
except:
- master
- release
###################################################################################################
Post_AverageDown:
stage: postprocessing

2
VERSION
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@ -1 +1 @@
v2.0.3-1747-ga2e8e5b1
v2.0.3-1862-g0b340a6d

8
processing/post/DADF5_postResults.py
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@ -52,15 +52,15 @@ for filename in options.filenames:
table = damask.Table(np.ones(np.product(results.grid),dtype=int)*int(inc[3:]),{'inc':(1,)})
table.add('pos',coords.reshape((-1,3)))
results.set_visible('materialpoints',False)
results.set_visible('constituents', True)
results.pick('materialpoints',False)
results.pick('constituents', True)
for label in options.con:
x = results.get_dataset_location(label)
if len(x) != 0:
table.add(label,results.read_dataset(x,0,plain=True).reshape((results.grid.prod(),-1)))
results.set_visible('constituents', False)
results.set_visible('materialpoints',True)
results.pick('constituents', False)
results.pick('materialpoints',True)
for label in options.mat:
x = results.get_dataset_location(label)
if len(x) != 0:

1139
processing/post/postResults.py
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21
processing/pre/seeds_fromDistribution.py
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@ -221,13 +221,9 @@ baseFile=os.path.splitext(os.path.basename(options.seedFile))[0]
points = np.array(options.grid).prod().astype('float')
# ----------- calculate target distribution and bin edges
targetGeomFile = os.path.splitext(os.path.basename(options.target))[0]+'.geom'
targetGeomTable = damask.ASCIItable(targetGeomFile,None,labeled=False,readonly=True)
targetGeomTable.head_read()
info,devNull = targetGeomTable.head_getGeom()
nMicrostructures = info['microstructures']
targetVolFrac = np.bincount(targetGeomTable.microstructure_read(info['grid']))[1:nMicrostructures+1]/\
float(info['grid'].prod())
targetGeom = damask.Geom.from_file(os.path.splitext(os.path.basename(options.target))[0]+'.geom')
nMicrostructures = len(np.unique(targetGeom.microstructure))
targetVolFrac = np.bincount(targetGeom.microstructure.flatten())/targetGeom.grid.prod().astype(np.float)
target=[]
for i in range(1,nMicrostructures+1):
targetHist,targetBins = np.histogram(targetVolFrac,bins=i) #bin boundaries
@ -251,13 +247,12 @@ initialGeomVFile = StringIO()
initialGeomVFile.write(damask.util.execute('geom_fromVoronoiTessellation '+
' -g '+' '.join(list(map(str, options.grid))),bestSeedsVFile)[0])
initialGeomVFile.seek(0)
initialGeomTable = damask.ASCIItable(initialGeomVFile,None,labeled=False,readonly=True)
initialGeomTable.head_read()
info,devNull = initialGeomTable.head_getGeom()
initialGeom = damask.Geom.from_file(initialGeomVFile)
if info['microstructures'] != nMicrostructures: damask.util.croak('error. Microstructure count mismatch')
if len(np.unique(targetGeom.microstructure)) != nMicrostructures:
damask.util.croak('error. Microstructure count mismatch')
initialData = np.bincount(initialGeomTable.microstructure_read(info['grid']))/points
initialData = np.bincount(initialGeom.microstructure.flatten())/points
for i in range(nMicrostructures):
initialHist = np.histogram(initialData,bins=target[i]['bins'])[0]
target[i]['error']=np.sqrt(np.square(np.array(target[i]['histogram']-initialHist)).sum())
@ -273,7 +268,7 @@ for i in range(nMicrostructures):
if options.maxseeds < 1:
maxSeeds = info['microstructures']
maxSeeds = len(np.unique(initialGeom.microstructure))
else:
maxSeeds = options.maxseeds

13
python/README
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@ -1,13 +0,0 @@
DAMASK - The Düsseldorf Advanced Material Simulation Kit
Visit damask.mpie.de for installation and usage instructions
CONTACT INFORMATION
Max-Planck-Institut für Eisenforschung GmbH
Max-Planck-Str. 1
40237 Düsseldorf
Germany
Email: DAMASK@mpie.de
https://damask.mpie.de
https://magit1.mpie.de

1
python/README Symbolic link
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@ -0,0 +1 @@
../README

2
python/damask/Lambert.py
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@ -131,12 +131,12 @@ def BallToCube(ball):
# inverse M_1
cube = np.array([ Tinv[0], Tinv[1], (-1.0 if xyz3[2] < 0.0 else 1.0) * rs / np.sqrt(6.0/np.pi) ]) /sc
# reverse the coordinates back to the regular order according to the original pyramid number
cube = cube[p]
return cube
def get_order(xyz):
"""
Get order of the coordinates.

8
python/damask/__init__.py
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@ -13,9 +13,11 @@ from .asciitable import ASCIItable # noqa
from .config import Material # noqa
from .colormaps import Colormap, Color # noqa
from .orientation import Symmetry, Lattice, Rotation, Orientation # noqa
from .dadf5 import DADF5 # noqa
from .dadf5 import DADF5 as Result # noqa
from .rotation import Rotation # noqa
from .lattice import Symmetry, Lattice# noqa
from .orientation import Orientation # noqa
from .result import Result # noqa
from .result import Result as DADF5 # noqa
from .geom import Geom # noqa
from .solver import Solver # noqa

47
python/damask/asciitable.py
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@ -16,7 +16,7 @@ class ASCIItable():
def __init__(self,
name = None,
outname = None,
buffered = False, # flush writes
buffered = False, # is ignored, only exists for compatibility reasons
labeled = True, # assume table has labels
readonly = False, # no reading from file
):
@ -63,7 +63,6 @@ class ASCIItable():
except AttributeError:
return str(string)
# ------------------------------------------------------------------
def _quote(self,
what):
@ -71,6 +70,7 @@ class ASCIItable():
return '{quote}{content}{quote}'.format(
quote = ('"' if str(what)=='' or re.search(r"\s",str(what)) else ''),
content = what)
# ------------------------------------------------------------------
def close(self,
dismiss = False):
@ -178,15 +178,11 @@ class ASCIItable():
'grid': lambda x: int(x),
'size': lambda x: float(x),
'origin': lambda x: float(x),
'homogenization': lambda x: int(x),
'microstructures': lambda x: int(x),
}
info = {
'grid': np.zeros(3,'i'),
'size': np.zeros(3,'d'),
'origin': np.zeros(3,'d'),
'homogenization': 0,
'microstructures': 0,
}
extra_header = []
@ -375,15 +371,6 @@ class ASCIItable():
self.tags = list(self.__IO__['tags']) # restore label info found in header (as COPY, not link)
self.__IO__['labeled'] = len(self.tags) > 0
# ------------------------------------------------------------------
def data_skipLines(self,
count):
"""Wind forward by count number of lines."""
for i in range(count):
alive = self.data_read()
return alive
# ------------------------------------------------------------------
def data_read(self,
advance = True,
@ -473,33 +460,3 @@ class ASCIItable():
for item in what: self.data_append(item)
except TypeError:
self.data += [str(what)]
# ------------------------------------------------------------------
def microstructure_read(self,
grid,
type = 'i',
strict = False):
"""Read microstructure data (from .geom format)."""
def datatype(item):
return int(item) if type.lower() == 'i' else float(item)
N = grid.prod() # expected number of microstructure indices in data
microstructure = np.zeros(N,type) # initialize as flat array
i = 0
while i < N and self.data_read():
items = self.data
if len(items) > 2:
if items[1].lower() == 'of':
items = np.ones(datatype(items[0]))*datatype(items[2])
elif items[1].lower() == 'to':
items = np.linspace(datatype(items[0]),datatype(items[2]),
abs(datatype(items[2])-datatype(items[0]))+1,dtype=int)
else: items = list(map(datatype,items))
else: items = list(map(datatype,items))
s = min(len(items), N-i) # prevent overflow of microstructure array
microstructure[i:i+s] = items[:s]
i += len(items)
return (microstructure, i == N and not self.data_read()) if strict else microstructure # check for proper point count and end of file

20
python/damask/colormaps.py
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@ -10,7 +10,6 @@ class Color():
]
# ------------------------------------------------------------------
def __init__(self,
model = 'RGB',
color = np.zeros(3,'d')):
@ -49,20 +48,17 @@ class Color():
self.color = np.array(color,'d')
# ------------------------------------------------------------------
def __repr__(self):
"""Color model and values."""
return 'Model: %s Color: %s'%(self.model,str(self.color))
# ------------------------------------------------------------------
def __str__(self):
"""Color model and values."""
return self.__repr__()
# ------------------------------------------------------------------
def convertTo(self,toModel = 'RGB'):
def convert_to(self,toModel = 'RGB'):
"""
Change the color model permanently.
@ -88,8 +84,7 @@ class Color():
return self
# ------------------------------------------------------------------
def expressAs(self,asModel = 'RGB'):
def express_as(self,asModel = 'RGB'):
"""
Return the color in a different model.
@ -99,7 +94,7 @@ class Color():
color model
"""
return self.__class__(self.model,self.color).convertTo(asModel)
return self.__class__(self.model,self.color).convert_to(asModel)
@ -293,6 +288,7 @@ class Color():
self.model = converted.model
self.color = converted.color
def _XYZ2CIELAB(self):
"""
Convert CIE XYZ to CIE Lab.
@ -498,13 +494,13 @@ class Colormap():
def interpolate_linear(lo, hi, frac):
"""Linear interpolation between lo and hi color at given fraction; output in model of lo color."""
interpolation = (1.0 - frac) * np.array(lo.color[:]) \
+ frac * np.array(hi.expressAs(lo.model).color[:])
+ frac * np.array(hi.express_as(lo.model).color[:])
return Color(lo.model,interpolation)
if self.interpolate == 'perceptualuniform':
return interpolate_Msh(self.left.expressAs('MSH').color,
self.right.expressAs('MSH').color,fraction)
return interpolate_Msh(self.left.express_as('MSH').color,
self.right.express_as('MSH').color,fraction)
elif self.interpolate == 'linear':
return interpolate_linear(self.left,
self.right,fraction)
@ -528,7 +524,7 @@ class Colormap():
"""
format = format.lower() # consistent comparison basis
frac = 0.5*(np.array(crop) + 1.0) # rescale crop range to fractions
colors = [self.color(float(i)/(steps-1)*(frac[1]-frac[0])+frac[0]).expressAs(model).color for i in range(steps)]
colors = [self.color(float(i)/(steps-1)*(frac[1]-frac[0])+frac[0]).express_as(model).color for i in range(steps)]
if format == 'paraview':
colormap = ['[\n {{\n "ColorSpace": "RGB", "Name": "{}", "DefaultMap": true,\n "RGBPoints" : ['.format(name)] \
+ [' {:4d},{:8.6f},{:8.6f},{:8.6f},'.format(i,color[0],color[1],color[2],) \

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python/damask/dadf5.py
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2
python/damask/geom.py
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@ -269,7 +269,7 @@ class Geom():
comments = []
for i,line in enumerate(content[:header_length]):
items = line.lower().strip().split()
key = items[0] if len(items) > 0 else ''
key = items[0] if items else ''
if key == 'grid':
grid = np.array([ int(dict(zip(items[1::2],items[2::2]))[i]) for i in ['a','b','c']])
elif key == 'size':

24
python/damask/grid_filters.py
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@ -1,7 +1,7 @@
from scipy import spatial
import numpy as np
def __ks(size,grid,first_order=False):
def _ks(size,grid,first_order=False):
"""
Get wave numbers operator.
@ -34,7 +34,7 @@ def curl(size,field):
"""
n = np.prod(field.shape[3:])
k_s = __ks(size,field.shape[:3],True)
k_s = _ks(size,field.shape[:3],True)
e = np.zeros((3, 3, 3))
e[0, 1, 2] = e[1, 2, 0] = e[2, 0, 1] = +1.0 # Levi-Civita symbol
@ -58,7 +58,7 @@ def divergence(size,field):
"""
n = np.prod(field.shape[3:])
k_s = __ks(size,field.shape[:3],True)
k_s = _ks(size,field.shape[:3],True)
field_fourier = np.fft.rfftn(field,axes=(0,1,2))
divergence = (np.einsum('ijkl,ijkl ->ijk', k_s,field_fourier)*2.0j*np.pi if n == 3 else # vector, 3 -> 1
@ -78,7 +78,7 @@ def gradient(size,field):
"""
n = np.prod(field.shape[3:])
k_s = __ks(size,field.shape[:3],True)
k_s = _ks(size,field.shape[:3],True)
field_fourier = np.fft.rfftn(field,axes=(0,1,2))
gradient = (np.einsum('ijkl,ijkm->ijkm', field_fourier,k_s)*2.0j*np.pi if n == 1 else # scalar, 1 -> 3
@ -110,6 +110,7 @@ def cell_coord0(grid,size,origin=np.zeros(3)):
return np.concatenate((z[:,:,:,None],y[:,:,:,None],x[:,:,:,None]),axis = 3)
def cell_displacement_fluct(size,F):
"""
Cell center displacement field from fluctuation part of the deformation gradient field.
@ -124,7 +125,7 @@ def cell_displacement_fluct(size,F):
"""
integrator = 0.5j*size/np.pi
k_s = __ks(size,F.shape[:3],False)
k_s = _ks(size,F.shape[:3],False)
k_s_squared = np.einsum('...l,...l',k_s,k_s)
k_s_squared[0,0,0] = 1.0
@ -136,6 +137,7 @@ def cell_displacement_fluct(size,F):
return np.fft.irfftn(displacement,axes=(0,1,2),s=F.shape[:3])
def cell_displacement_avg(size,F):
"""
Cell center displacement field from average part of the deformation gradient field.
@ -151,6 +153,7 @@ def cell_displacement_avg(size,F):
F_avg = np.average(F,axis=(0,1,2))
return np.einsum('ml,ijkl->ijkm',F_avg-np.eye(3),cell_coord0(F.shape[:3][::-1],size))
def cell_displacement(size,F):
"""
Cell center displacement field from deformation gradient field.
@ -165,6 +168,7 @@ def cell_displacement(size,F):
"""
return cell_displacement_avg(size,F) + cell_displacement_fluct(size,F)
def cell_coord(size,F,origin=np.zeros(3)):
"""
Cell center positions.
@ -181,6 +185,7 @@ def cell_coord(size,F,origin=np.zeros(3)):
"""
return cell_coord0(F.shape[:3][::-1],size,origin) + cell_displacement(size,F)
def cell_coord0_gridSizeOrigin(coord0,ordered=True):
"""
Return grid 'DNA', i.e. grid, size, and origin from array of cell positions.
@ -221,6 +226,7 @@ def cell_coord0_gridSizeOrigin(coord0,ordered=True):
return (grid,size,origin)
def coord0_check(coord0):
"""
Check whether coordinates lie on a regular grid.
@ -234,7 +240,6 @@ def coord0_check(coord0):
cell_coord0_gridSizeOrigin(coord0,ordered=True)
def node_coord0(grid,size,origin=np.zeros(3)):
"""
Nodal positions (undeformed).
@ -256,6 +261,7 @@ def node_coord0(grid,size,origin=np.zeros(3)):
return np.concatenate((z[:,:,:,None],y[:,:,:,None],x[:,:,:,None]),axis = 3)
def node_displacement_fluct(size,F):
"""
Nodal displacement field from fluctuation part of the deformation gradient field.
@ -270,6 +276,7 @@ def node_displacement_fluct(size,F):
"""
return cell_2_node(cell_displacement_fluct(size,F))
def node_displacement_avg(size,F):
"""
Nodal displacement field from average part of the deformation gradient field.
@ -285,6 +292,7 @@ def node_displacement_avg(size,F):
F_avg = np.average(F,axis=(0,1,2))
return np.einsum('ml,ijkl->ijkm',F_avg-np.eye(3),node_coord0(F.shape[:3][::-1],size))
def node_displacement(size,F):
"""
Nodal displacement field from deformation gradient field.
@ -299,6 +307,7 @@ def node_displacement(size,F):
"""
return node_displacement_avg(size,F) + node_displacement_fluct(size,F)
def node_coord(size,F,origin=np.zeros(3)):
"""
Nodal positions.
@ -315,6 +324,7 @@ def node_coord(size,F,origin=np.zeros(3)):
"""
return node_coord0(F.shape[:3][::-1],size,origin) + node_displacement(size,F)
def cell_2_node(cell_data):
"""Interpolate periodic cell data to nodal data."""
n = ( cell_data + np.roll(cell_data,1,(0,1,2))
@ -323,6 +333,7 @@ def cell_2_node(cell_data):
return np.pad(n,((0,1),(0,1),(0,1))+((0,0),)*len(cell_data.shape[3:]),mode='wrap')
def node_2_cell(node_data):
"""Interpolate periodic nodal data to cell data."""
c = ( node_data + np.roll(node_data,1,(0,1,2))
@ -331,6 +342,7 @@ def node_2_cell(node_data):
return c[:-1,:-1,:-1]
def node_coord0_gridSizeOrigin(coord0,ordered=False):
"""
Return grid 'DNA', i.e. grid, size, and origin from array of nodal positions.

641
python/damask/lattice.py Normal file
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@ -0,0 +1,641 @@
import numpy as np
from .rotation import Rotation
P = -1
# ******************************************************************************************
class Symmetry:
"""
Symmetry operations for lattice systems.
References
----------
https://en.wikipedia.org/wiki/Crystal_system
"""
lattices = [None,'orthorhombic','tetragonal','hexagonal','cubic',]
def __init__(self, symmetry = None):
"""
Symmetry Definition.
Parameters
----------
symmetry : str, optional
label of the crystal system
"""
if symmetry is not None and symmetry.lower() not in Symmetry.lattices:
raise KeyError('Symmetry/crystal system "{}" is unknown'.format(symmetry))
self.lattice = symmetry.lower() if isinstance(symmetry,str) else symmetry
def __copy__(self):
"""Copy."""
return self.__class__(self.lattice)
copy = __copy__
def __repr__(self):
"""Readable string."""
return '{}'.format(self.lattice)
def __eq__(self, other):
"""
Equal to other.
Parameters
----------
other : Symmetry
Symmetry to check for equality.
"""
return self.lattice == other.lattice
def __neq__(self, other):
"""
Not Equal to other.
Parameters
----------
other : Symmetry
Symmetry to check for inequality.
"""
return not self.__eq__(other)
def __cmp__(self,other):
"""
Linear ordering.
Parameters
----------
other : Symmetry
Symmetry to check for for order.
"""
myOrder = Symmetry.lattices.index(self.lattice)
otherOrder = Symmetry.lattices.index(other.lattice)
return (myOrder > otherOrder) - (myOrder < otherOrder)
def symmetryOperations(self,members=[]):
"""List (or single element) of symmetry operations as rotations."""
if self.lattice == 'cubic':
symQuats = [
[ 1.0, 0.0, 0.0, 0.0 ],
[ 0.0, 1.0, 0.0, 0.0 ],
[ 0.0, 0.0, 1.0, 0.0 ],
[ 0.0, 0.0, 0.0, 1.0 ],
[ 0.0, 0.0, 0.5*np.sqrt(2), 0.5*np.sqrt(2) ],
[ 0.0, 0.0, 0.5*np.sqrt(2),-0.5*np.sqrt(2) ],
[ 0.0, 0.5*np.sqrt(2), 0.0, 0.5*np.sqrt(2) ],
[ 0.0, 0.5*np.sqrt(2), 0.0, -0.5*np.sqrt(2) ],
[ 0.0, 0.5*np.sqrt(2),-0.5*np.sqrt(2), 0.0 ],
[ 0.0, -0.5*np.sqrt(2),-0.5*np.sqrt(2), 0.0 ],
[ 0.5, 0.5, 0.5, 0.5 ],
[-0.5, 0.5, 0.5, 0.5 ],
[-0.5, 0.5, 0.5, -0.5 ],
[-0.5, 0.5, -0.5, 0.5 ],
[-0.5, -0.5, 0.5, 0.5 ],
[-0.5, -0.5, 0.5, -0.5 ],
[-0.5, -0.5, -0.5, 0.5 ],
[-0.5, 0.5, -0.5, -0.5 ],
[-0.5*np.sqrt(2), 0.0, 0.0, 0.5*np.sqrt(2) ],
[ 0.5*np.sqrt(2), 0.0, 0.0, 0.5*np.sqrt(2) ],
[-0.5*np.sqrt(2), 0.0, 0.5*np.sqrt(2), 0.0 ],
[-0.5*np.sqrt(2), 0.0, -0.5*np.sqrt(2), 0.0 ],
[-0.5*np.sqrt(2), 0.5*np.sqrt(2), 0.0, 0.0 ],
[-0.5*np.sqrt(2),-0.5*np.sqrt(2), 0.0, 0.0 ],
]
elif self.lattice == 'hexagonal':
symQuats = [
[ 1.0, 0.0, 0.0, 0.0 ],
[-0.5*np.sqrt(3), 0.0, 0.0, -0.5 ],
[ 0.5, 0.0, 0.0, 0.5*np.sqrt(3) ],
[ 0.0, 0.0, 0.0, 1.0 ],
[-0.5, 0.0, 0.0, 0.5*np.sqrt(3) ],
[-0.5*np.sqrt(3), 0.0, 0.0, 0.5 ],
[ 0.0, 1.0, 0.0, 0.0 ],
[ 0.0, -0.5*np.sqrt(3), 0.5, 0.0 ],
[ 0.0, 0.5, -0.5*np.sqrt(3), 0.0 ],
[ 0.0, 0.0, 1.0, 0.0 ],
[ 0.0, -0.5, -0.5*np.sqrt(3), 0.0 ],
[ 0.0, 0.5*np.sqrt(3), 0.5, 0.0 ],
]
elif self.lattice == 'tetragonal':
symQuats = [
[ 1.0, 0.0, 0.0, 0.0 ],
[ 0.0, 1.0, 0.0, 0.0 ],
[ 0.0, 0.0, 1.0, 0.0 ],
[ 0.0, 0.0, 0.0, 1.0 ],
[ 0.0, 0.5*np.sqrt(2), 0.5*np.sqrt(2), 0.0 ],
[ 0.0, -0.5*np.sqrt(2), 0.5*np.sqrt(2), 0.0 ],
[ 0.5*np.sqrt(2), 0.0, 0.0, 0.5*np.sqrt(2) ],
[-0.5*np.sqrt(2), 0.0, 0.0, 0.5*np.sqrt(2) ],
]
elif self.lattice == 'orthorhombic':
symQuats = [
[ 1.0,0.0,0.0,0.0 ],
[ 0.0,1.0,0.0,0.0 ],
[ 0.0,0.0,1.0,0.0 ],
[ 0.0,0.0,0.0,1.0 ],
]
else:
symQuats = [
[ 1.0,0.0,0.0,0.0 ],
]
symOps = list(map(Rotation,
np.array(symQuats)[np.atleast_1d(members) if members != [] else range(len(symQuats))]))
try:
iter(members) # asking for (even empty) list of members?
except TypeError:
return symOps[0] # no, return rotation object
else:
return symOps # yes, return list of rotations
def inFZ(self,rodrigues):
"""
Check whether given Rodrigues-Frank vector falls into fundamental zone of own symmetry.
Fundamental zone in Rodrigues space is point symmetric around origin.
"""
if (len(rodrigues) != 3):
raise ValueError('Input is not a Rodrigues-Frank vector.\n')
if np.any(rodrigues == np.inf): return False
Rabs = abs(rodrigues)
if self.lattice == 'cubic':
return np.sqrt(2.0)-1.0 >= Rabs[0] \
and np.sqrt(2.0)-1.0 >= Rabs[1] \
and np.sqrt(2.0)-1.0 >= Rabs[2] \
and 1.0 >= Rabs[0] + Rabs[1] + Rabs[2]
elif self.lattice == 'hexagonal':
return 1.0 >= Rabs[0] and 1.0 >= Rabs[1] and 1.0 >= Rabs[2] \
and 2.0 >= np.sqrt(3)*Rabs[0] + Rabs[1] \
and 2.0 >= np.sqrt(3)*Rabs[1] + Rabs[0] \
and 2.0 >= np.sqrt(3) + Rabs[2]
elif self.lattice == 'tetragonal':
return 1.0 >= Rabs[0] and 1.0 >= Rabs[1] \
and np.sqrt(2.0) >= Rabs[0] + Rabs[1] \
and np.sqrt(2.0) >= Rabs[2] + 1.0
elif self.lattice == 'orthorhombic':
return 1.0 >= Rabs[0] and 1.0 >= Rabs[1] and 1.0 >= Rabs[2]
else:
return True
def inDisorientationSST(self,rodrigues):
"""
Check whether given Rodrigues-Frank vector (of misorientation) falls into standard stereographic triangle of own symmetry.
References
----------
A. Heinz and P. Neumann, Acta Crystallographica Section A 47:780-789, 1991
https://doi.org/10.1107/S0108767391006864
"""
if (len(rodrigues) != 3):
raise ValueError('Input is not a Rodrigues-Frank vector.\n')
R = rodrigues
epsilon = 0.0
if self.lattice == 'cubic':
return R[0] >= R[1]+epsilon and R[1] >= R[2]+epsilon and R[2] >= epsilon
elif self.lattice == 'hexagonal':
return R[0] >= np.sqrt(3)*(R[1]-epsilon) and R[1] >= epsilon and R[2] >= epsilon
elif self.lattice == 'tetragonal':
return R[0] >= R[1]-epsilon and R[1] >= epsilon and R[2] >= epsilon
elif self.lattice == 'orthorhombic':
return R[0] >= epsilon and R[1] >= epsilon and R[2] >= epsilon
else:
return True
def inSST(self,
vector,
proper = False,
color = False):
"""
Check whether given vector falls into standard stereographic triangle of own symmetry.
proper considers only vectors with z >= 0, hence uses two neighboring SSTs.
Return inverse pole figure color if requested.
Bases are computed from
basis = {'cubic' : np.linalg.inv(np.array([[0.,0.,1.], # direction of red
[1.,0.,1.]/np.sqrt(2.), # direction of green
[1.,1.,1.]/np.sqrt(3.)]).T), # direction of blue
'hexagonal' : np.linalg.inv(np.array([[0.,0.,1.], # direction of red
[1.,0.,0.], # direction of green
[np.sqrt(3.),1.,0.]/np.sqrt(4.)]).T), # direction of blue
'tetragonal' : np.linalg.inv(np.array([[0.,0.,1.], # direction of red
[1.,0.,0.], # direction of green
[1.,1.,0.]/np.sqrt(2.)]).T), # direction of blue
'orthorhombic' : np.linalg.inv(np.array([[0.,0.,1.], # direction of red
[1.,0.,0.], # direction of green
[0.,1.,0.]]).T), # direction of blue
}
"""
if self.lattice == 'cubic':
basis = {'improper':np.array([ [-1. , 0. , 1. ],
[ np.sqrt(2.) , -np.sqrt(2.) , 0. ],
[ 0. , np.sqrt(3.) , 0. ] ]),
'proper':np.array([ [ 0. , -1. , 1. ],
[-np.sqrt(2.) , np.sqrt(2.) , 0. ],
[ np.sqrt(3.) , 0. , 0. ] ]),
}
elif self.lattice == 'hexagonal':
basis = {'improper':np.array([ [ 0. , 0. , 1. ],
[ 1. , -np.sqrt(3.) , 0. ],
[ 0. , 2. , 0. ] ]),
'proper':np.array([ [ 0. , 0. , 1. ],
[-1. , np.sqrt(3.) , 0. ],
[ np.sqrt(3.) , -1. , 0. ] ]),
}
elif self.lattice == 'tetragonal':
basis = {'improper':np.array([ [ 0. , 0. , 1. ],
[ 1. , -1. , 0. ],
[ 0. , np.sqrt(2.) , 0. ] ]),
'proper':np.array([ [ 0. , 0. , 1. ],
[-1. , 1. , 0. ],
[ np.sqrt(2.) , 0. , 0. ] ]),
}
elif self.lattice == 'orthorhombic':
basis = {'improper':np.array([ [ 0., 0., 1.],
[ 1., 0., 0.],
[ 0., 1., 0.] ]),
'proper':np.array([ [ 0., 0., 1.],
[-1., 0., 0.],
[ 0., 1., 0.] ]),
}
else: # direct exit for unspecified symmetry
if color:
return (True,np.zeros(3,'d'))
else:
return True
v = np.array(vector,dtype=float)
if proper: # check both improper ...
theComponents = np.around(np.dot(basis['improper'],v),12)
inSST = np.all(theComponents >= 0.0)
if not inSST: # ... and proper SST
theComponents = np.around(np.dot(basis['proper'],v),12)
inSST = np.all(theComponents >= 0.0)
else:
v[2] = abs(v[2]) # z component projects identical
theComponents = np.around(np.dot(basis['improper'],v),12) # for positive and negative values
inSST = np.all(theComponents >= 0.0)
if color: # have to return color array
if inSST:
rgb = np.power(theComponents/np.linalg.norm(theComponents),0.5) # smoothen color ramps
rgb = np.minimum(np.ones(3,dtype=float),rgb) # limit to maximum intensity
rgb /= max(rgb) # normalize to (HS)V = 1
else:
rgb = np.zeros(3,dtype=float)
return (inSST,rgb)
else:
return inSST
# code derived from https://github.com/ezag/pyeuclid
# suggested reading: http://web.mit.edu/2.998/www/QuaternionReport1.pdf
# ******************************************************************************************
class Lattice:
"""
Lattice system.
Currently, this contains only a mapping from Bravais lattice to symmetry
and orientation relationships. It could include twin and slip systems.
References
----------
https://en.wikipedia.org/wiki/Bravais_lattice
"""
lattices = {
'triclinic':{'symmetry':None},
'bct':{'symmetry':'tetragonal'},
'hex':{'symmetry':'hexagonal'},
'fcc':{'symmetry':'cubic','c/a':1.0},
'bcc':{'symmetry':'cubic','c/a':1.0},
}
def __init__(self, lattice):
"""
New lattice of given type.
Parameters
----------
lattice : str
Bravais lattice.
"""
self.lattice = lattice
self.symmetry = Symmetry(self.lattices[lattice]['symmetry'])
def __repr__(self):
"""Report basic lattice information."""
return 'Bravais lattice {} ({} symmetry)'.format(self.lattice,self.symmetry)
# Kurdjomov--Sachs orientation relationship for fcc <-> bcc transformation
# from S. Morito et al., Journal of Alloys and Compounds 577:s587-s592, 2013
# also see K. Kitahara et al., Acta Materialia 54:1279-1288, 2006
KS = {'mapping':{'fcc':0,'bcc':1},
'planes': np.array([
[[ 1, 1, 1],[ 0, 1, 1]],
[[ 1, 1, 1],[ 0, 1, 1]],
[[ 1, 1, 1],[ 0, 1, 1]],
[[ 1, 1, 1],[ 0, 1, 1]],
[[ 1, 1, 1],[ 0, 1, 1]],
[[ 1, 1, 1],[ 0, 1, 1]],
[[ 1, -1, 1],[ 0, 1, 1]],
[[ 1, -1, 1],[ 0, 1, 1]],
[[ 1, -1, 1],[ 0, 1, 1]],
[[ 1, -1, 1],[ 0, 1, 1]],
[[ 1, -1, 1],[ 0, 1, 1]],
[[ 1, -1, 1],[ 0, 1, 1]],
[[ -1, 1, 1],[ 0, 1, 1]],
[[ -1, 1, 1],[ 0, 1, 1]],
[[ -1, 1, 1],[ 0, 1, 1]],
[[ -1, 1, 1],[ 0, 1, 1]],
[[ -1, 1, 1],[ 0, 1, 1]],
[[ -1, 1, 1],[ 0, 1, 1]],
[[ 1, 1, -1],[ 0, 1, 1]],
[[ 1, 1, -1],[ 0, 1, 1]],
[[ 1, 1, -1],[ 0, 1, 1]],
[[ 1, 1, -1],[ 0, 1, 1]],
[[ 1, 1, -1],[ 0, 1, 1]],
[[ 1, 1, -1],[ 0, 1, 1]]],dtype='float'),
'directions': np.array([
[[ -1, 0, 1],[ -1, -1, 1]],
[[ -1, 0, 1],[ -1, 1, -1]],
[[ 0, 1, -1],[ -1, -1, 1]],
[[ 0, 1, -1],[ -1, 1, -1]],
[[ 1, -1, 0],[ -1, -1, 1]],
[[ 1, -1, 0],[ -1, 1, -1]],
[[ 1, 0, -1],[ -1, -1, 1]],
[[ 1, 0, -1],[ -1, 1, -1]],
[[ -1, -1, 0],[ -1, -1, 1]],
[[ -1, -1, 0],[ -1, 1, -1]],
[[ 0, 1, 1],[ -1, -1, 1]],
[[ 0, 1, 1],[ -1, 1, -1]],
[[ 0, -1, 1],[ -1, -1, 1]],
[[ 0, -1, 1],[ -1, 1, -1]],
[[ -1, 0, -1],[ -1, -1, 1]],
[[ -1, 0, -1],[ -1, 1, -1]],
[[ 1, 1, 0],[ -1, -1, 1]],
[[ 1, 1, 0],[ -1, 1, -1]],
[[ -1, 1, 0],[ -1, -1, 1]],
[[ -1, 1, 0],[ -1, 1, -1]],
[[ 0, -1, -1],[ -1, -1, 1]],
[[ 0, -1, -1],[ -1, 1, -1]],
[[ 1, 0, 1],[ -1, -1, 1]],
[[ 1, 0, 1],[ -1, 1, -1]]],dtype='float')}
# Greninger--Troiano orientation relationship for fcc <-> bcc transformation
# from Y. He et al., Journal of Applied Crystallography 39:72-81, 2006
GT = {'mapping':{'fcc':0,'bcc':1},
'planes': np.array([
[[ 1, 1, 1],[ 1, 0, 1]],
[[ 1, 1, 1],[ 1, 1, 0]],
[[ 1, 1, 1],[ 0, 1, 1]],
[[ -1, -1, 1],[ -1, 0, 1]],
[[ -1, -1, 1],[ -1, -1, 0]],
[[ -1, -1, 1],[ 0, -1, 1]],
[[ -1, 1, 1],[ -1, 0, 1]],
[[ -1, 1, 1],[ -1, 1, 0]],
[[ -1, 1, 1],[ 0, 1, 1]],
[[ 1, -1, 1],[ 1, 0, 1]],
[[ 1, -1, 1],[ 1, -1, 0]],
[[ 1, -1, 1],[ 0, -1, 1]],
[[ 1, 1, 1],[ 1, 1, 0]],
[[ 1, 1, 1],[ 0, 1, 1]],
[[ 1, 1, 1],[ 1, 0, 1]],
[[ -1, -1, 1],[ -1, -1, 0]],
[[ -1, -1, 1],[ 0, -1, 1]],
[[ -1, -1, 1],[ -1, 0, 1]],
[[ -1, 1, 1],[ -1, 1, 0]],
[[ -1, 1, 1],[ 0, 1, 1]],
[[ -1, 1, 1],[ -1, 0, 1]],
[[ 1, -1, 1],[ 1, -1, 0]],
[[ 1, -1, 1],[ 0, -1, 1]],
[[ 1, -1, 1],[ 1, 0, 1]]],dtype='float'),
'directions': np.array([
[[ -5,-12, 17],[-17, -7, 17]],
[[ 17, -5,-12],[ 17,-17, -7]],
[[-12, 17, -5],[ -7, 17,-17]],
[[ 5, 12, 17],[ 17, 7, 17]],
[[-17, 5,-12],[-17, 17, -7]],
[[ 12,-17, -5],[ 7,-17,-17]],
[[ -5, 12,-17],[-17, 7,-17]],
[[ 17, 5, 12],[ 17, 17, 7]],
[[-12,-17, 5],[ -7,-17, 17]],
[[ 5,-12,-17],[ 17, -7,-17]],
[[-17, -5, 12],[-17,-17, 7]],
[[ 12, 17, 5],[ 7, 17, 17]],
[[ -5, 17,-12],[-17, 17, -7]],
[[-12, -5, 17],[ -7,-17, 17]],
[[ 17,-12, -5],[ 17, -7,-17]],
[[ 5,-17,-12],[ 17,-17, -7]],
[[ 12, 5, 17],[ 7, 17, 17]],
[[-17, 12, -5],[-17, 7,-17]],
[[ -5,-17, 12],[-17,-17, 7]],
[[-12, 5,-17],[ -7, 17,-17]],
[[ 17, 12, 5],[ 17, 7, 17]],
[[ 5, 17, 12],[ 17, 17, 7]],
[[ 12, -5,-17],[ 7,-17,-17]],
[[-17,-12, 5],[-17,-7, 17]]],dtype='float')}
# Greninger--Troiano' orientation relationship for fcc <-> bcc transformation
# from Y. He et al., Journal of Applied Crystallography 39:72-81, 2006
GTprime = {'mapping':{'fcc':0,'bcc':1},
'planes': np.array([
[[ 7, 17, 17],[ 12, 5, 17]],
[[ 17, 7, 17],[ 17, 12, 5]],
[[ 17, 17, 7],[ 5, 17, 12]],
[[ -7,-17, 17],[-12, -5, 17]],
[[-17, -7, 17],[-17,-12, 5]],
[[-17,-17, 7],[ -5,-17, 12]],
[[ 7,-17,-17],[ 12, -5,-17]],
[[ 17, -7,-17],[ 17,-12, -5]],
[[ 17,-17, -7],[ 5,-17,-12]],
[[ -7, 17,-17],[-12, 5,-17]],
[[-17, 7,-17],[-17, 12, -5]],
[[-17, 17, -7],[ -5, 17,-12]],
[[ 7, 17, 17],[ 12, 17, 5]],
[[ 17, 7, 17],[ 5, 12, 17]],
[[ 17, 17, 7],[ 17, 5, 12]],
[[ -7,-17, 17],[-12,-17, 5]],
[[-17, -7, 17],[ -5,-12, 17]],
[[-17,-17, 7],[-17, -5, 12]],
[[ 7,-17,-17],[ 12,-17, -5]],
[[ 17, -7,-17],[ 5, -12,-17]],
[[ 17,-17, -7],[ 17, -5,-12]],
[[ -7, 17,-17],[-12, 17, -5]],
[[-17, 7,-17],[ -5, 12,-17]],
[[-17, 17, -7],[-17, 5,-12]]],dtype='float'),
'directions': np.array([
[[ 0, 1, -1],[ 1, 1, -1]],
[[ -1, 0, 1],[ -1, 1, 1]],
[[ 1, -1, 0],[ 1, -1, 1]],
[[ 0, -1, -1],[ -1, -1, -1]],
[[ 1, 0, 1],[ 1, -1, 1]],
[[ 1, -1, 0],[ 1, -1, -1]],
[[ 0, 1, -1],[ -1, 1, -1]],
[[ 1, 0, 1],[ 1, 1, 1]],
[[ -1, -1, 0],[ -1, -1, 1]],
[[ 0, -1, -1],[ 1, -1, -1]],
[[ -1, 0, 1],[ -1, -1, 1]],
[[ -1, -1, 0],[ -1, -1, -1]],
[[ 0, -1, 1],[ 1, -1, 1]],
[[ 1, 0, -1],[ 1, 1, -1]],
[[ -1, 1, 0],[ -1, 1, 1]],
[[ 0, 1, 1],[ -1, 1, 1]],
[[ -1, 0, -1],[ -1, -1, -1]],
[[ -1, 1, 0],[ -1, 1, -1]],
[[ 0, -1, 1],[ -1, -1, 1]],
[[ -1, 0, -1],[ -1, 1, -1]],
[[ 1, 1, 0],[ 1, 1, 1]],
[[ 0, 1, 1],[ 1, 1, 1]],
[[ 1, 0, -1],[ 1, -1, -1]],
[[ 1, 1, 0],[ 1, 1, -1]]],dtype='float')}
# Nishiyama--Wassermann orientation relationship for fcc <-> bcc transformation
# from H. Kitahara et al., Materials Characterization 54:378-386, 2005
NW = {'mapping':{'fcc':0,'bcc':1},
'planes': np.array([
[[ 1, 1, 1],[ 0, 1, 1]],
[[ 1, 1, 1],[ 0, 1, 1]],
[[ 1, 1, 1],[ 0, 1, 1]],
[[ -1, 1, 1],[ 0, 1, 1]],
[[ -1, 1, 1],[ 0, 1, 1]],
[[ -1, 1, 1],[ 0, 1, 1]],
[[ 1, -1, 1],[ 0, 1, 1]],
[[ 1, -1, 1],[ 0, 1, 1]],
[[ 1, -1, 1],[ 0, 1, 1]],
[[ -1, -1, 1],[ 0, 1, 1]],
[[ -1, -1, 1],[ 0, 1, 1]],
[[ -1, -1, 1],[ 0, 1, 1]]],dtype='float'),
'directions': np.array([
[[ 2, -1, -1],[ 0, -1, 1]],
[[ -1, 2, -1],[ 0, -1, 1]],
[[ -1, -1, 2],[ 0, -1, 1]],
[[ -2, -1, -1],[ 0, -1, 1]],
[[ 1, 2, -1],[ 0, -1, 1]],
[[ 1, -1, 2],[ 0, -1, 1]],
[[ 2, 1, -1],[ 0, -1, 1]],
[[ -1, -2, -1],[ 0, -1, 1]],
[[ -1, 1, 2],[ 0, -1, 1]],
[[ 2, -1, 1],[ 0, -1, 1]], #It is wrong in the paper, but matrix is correct
[[ -1, 2, 1],[ 0, -1, 1]],
[[ -1, -1, -2],[ 0, -1, 1]]],dtype='float')}
# Pitsch orientation relationship for fcc <-> bcc transformation
# from Y. He et al., Acta Materialia 53:1179-1190, 2005
Pitsch = {'mapping':{'fcc':0,'bcc':1},
'planes': np.array([
[[ 0, 1, 0],[ -1, 0, 1]],
[[ 0, 0, 1],[ 1, -1, 0]],
[[ 1, 0, 0],[ 0, 1, -1]],
[[ 1, 0, 0],[ 0, -1, -1]],
[[ 0, 1, 0],[ -1, 0, -1]],
[[ 0, 0, 1],[ -1, -1, 0]],
[[ 0, 1, 0],[ -1, 0, -1]],
[[ 0, 0, 1],[ -1, -1, 0]],
[[ 1, 0, 0],[ 0, -1, -1]],
[[ 1, 0, 0],[ 0, -1, 1]],
[[ 0, 1, 0],[ 1, 0, -1]],
[[ 0, 0, 1],[ -1, 1, 0]]],dtype='float'),
'directions': np.array([
[[ 1, 0, 1],[ 1, -1, 1]],
[[ 1, 1, 0],[ 1, 1, -1]],
[[ 0, 1, 1],[ -1, 1, 1]],
[[ 0, 1, -1],[ -1, 1, -1]],
[[ -1, 0, 1],[ -1, -1, 1]],
[[ 1, -1, 0],[ 1, -1, -1]],
[[ 1, 0, -1],[ 1, -1, -1]],
[[ -1, 1, 0],[ -1, 1, -1]],
[[ 0, -1, 1],[ -1, -1, 1]],
[[ 0, 1, 1],[ -1, 1, 1]],
[[ 1, 0, 1],[ 1, -1, 1]],
[[ 1, 1, 0],[ 1, 1, -1]]],dtype='float')}
# Bain orientation relationship for fcc <-> bcc transformation
# from Y. He et al., Journal of Applied Crystallography 39:72-81, 2006
Bain = {'mapping':{'fcc':0,'bcc':1},
'planes': np.array([
[[ 1, 0, 0],[ 1, 0, 0]],
[[ 0, 1, 0],[ 0, 1, 0]],
[[ 0, 0, 1],[ 0, 0, 1]]],dtype='float'),
'directions': np.array([
[[ 0, 1, 0],[ 0, 1, 1]],
[[ 0, 0, 1],[ 1, 0, 1]],
[[ 1, 0, 0],[ 1, 1, 0]]],dtype='float')}
def relationOperations(self,model):
"""
Crystallographic orientation relationships for phase transformations.
References
----------
S. Morito et al., Journal of Alloys and Compounds 577:s587-s592, 2013
https://doi.org/10.1016/j.jallcom.2012.02.004
K. Kitahara et al., Acta Materialia 54(5):1279-1288, 2006
https://doi.org/10.1016/j.actamat.2005.11.001
Y. He et al., Journal of Applied Crystallography 39:72-81, 2006
https://doi.org/10.1107/S0021889805038276
H. Kitahara et al., Materials Characterization 54(4-5):378-386, 2005
https://doi.org/10.1016/j.matchar.2004.12.015
Y. He et al., Acta Materialia 53(4):1179-1190, 2005
https://doi.org/10.1016/j.actamat.2004.11.021
"""
models={'KS':self.KS, 'GT':self.GT, 'GT_prime':self.GTprime,
'NW':self.NW, 'Pitsch': self.Pitsch, 'Bain':self.Bain}
try:
relationship = models[model]
except KeyError :
raise KeyError('Orientation relationship "{}" is unknown'.format(model))
if self.lattice not in relationship['mapping']:
raise ValueError('Relationship "{}" not supported for lattice "{}"'.format(model,self.lattice))
r = {'lattice':Lattice((set(relationship['mapping'])-{self.lattice}).pop()), # target lattice
'rotations':[] }
myPlane_id = relationship['mapping'][self.lattice]
otherPlane_id = (myPlane_id+1)%2
myDir_id = myPlane_id +2
otherDir_id = otherPlane_id +2
for miller in np.hstack((relationship['planes'],relationship['directions'])):
myPlane = miller[myPlane_id]/ np.linalg.norm(miller[myPlane_id])
myDir = miller[myDir_id]/ np.linalg.norm(miller[myDir_id])
myMatrix = np.array([myDir,np.cross(myPlane,myDir),myPlane])
otherPlane = miller[otherPlane_id]/ np.linalg.norm(miller[otherPlane_id])
otherDir = miller[otherDir_id]/ np.linalg.norm(miller[otherDir_id])
otherMatrix = np.array([otherDir,np.cross(otherPlane,otherDir),otherPlane])
r['rotations'].append(Rotation.fromMatrix(np.dot(otherMatrix.T,myMatrix)))
return r

95
python/damask/mechanics.py
View File

@ -21,21 +21,21 @@ def Cauchy(P,F):
return symmetric(sigma)
def deviatoric_part(x):
def deviatoric_part(T):
"""
Return deviatoric part of a tensor.
Parameters
----------
x : numpy.array of shape (:,3,3) or (3,3)
T : numpy.array of shape (:,3,3) or (3,3)
Tensor of which the deviatoric part is computed.
"""
return x - np.eye(3)*spherical_part(x) if np.shape(x) == (3,3) else \
x - np.einsum('ijk,i->ijk',np.broadcast_to(np.eye(3),[x.shape[0],3,3]),spherical_part(x))
return T - np.eye(3)*spherical_part(T) if np.shape(T) == (3,3) else \
T - np.einsum('ijk,i->ijk',np.broadcast_to(np.eye(3),[T.shape[0],3,3]),spherical_part(T))
def eigenvalues(x):
def eigenvalues(T_sym):
"""
Return the eigenvalues, i.e. principal components, of a symmetric tensor.
@ -44,14 +44,14 @@ def eigenvalues(x):
Parameters
----------
x : numpy.array of shape (:,3,3) or (3,3)
T_sym : numpy.array of shape (:,3,3) or (3,3)
Symmetric tensor of which the eigenvalues are computed.
"""
return np.linalg.eigvalsh(symmetric(x))
return np.linalg.eigvalsh(symmetric(T_sym))
def eigenvectors(x,RHS=False):
def eigenvectors(T_sym,RHS=False):
"""
Return eigenvectors of a symmetric tensor.
@ -59,47 +59,47 @@ def eigenvectors(x,RHS=False):
Parameters
----------
x : numpy.array of shape (:,3,3) or (3,3)
T_sym : numpy.array of shape (:,3,3) or (3,3)
Symmetric tensor of which the eigenvectors are computed.
RHS: bool, optional
Enforce right-handed coordinate system. Default is False.
"""
(u,v) = np.linalg.eigh(symmetric(x))
(u,v) = np.linalg.eigh(symmetric(T_sym))
if RHS:
if np.shape(x) == (3,3):
if np.shape(T_sym) == (3,3):
if np.linalg.det(v) < 0.0: v[:,2] *= -1.0
else:
v[np.linalg.det(v) < 0.0,:,2] *= -1.0
return v
def left_stretch(x):
def left_stretch(T):
"""
Return the left stretch of a tensor.
Parameters
----------
x : numpy.array of shape (:,3,3) or (3,3)
T : numpy.array of shape (:,3,3) or (3,3)
Tensor of which the left stretch is computed.
"""
return __polar_decomposition(x,'V')[0]
return __polar_decomposition(T,'V')[0]
def maximum_shear(x):
def maximum_shear(T_sym):
"""
Return the maximum shear component of a symmetric tensor.
Parameters
----------
x : numpy.array of shape (:,3,3) or (3,3)
T_sym : numpy.array of shape (:,3,3) or (3,3)
Symmetric tensor of which the maximum shear is computed.
"""
w = eigenvalues(x)
return (w[0] - w[2])*0.5 if np.shape(x) == (3,3) else \
w = eigenvalues(T_sym)
return (w[0] - w[2])*0.5 if np.shape(T_sym) == (3,3) else \
(w[:,0] - w[:,2])*0.5
@ -147,53 +147,54 @@ def PK2(P,F):
S = np.einsum('ijk,ikl->ijl',np.linalg.inv(F),P)
return symmetric(S)
def right_stretch(x):
def right_stretch(T):
"""
Return the right stretch of a tensor.
Parameters
----------
x : numpy.array of shape (:,3,3) or (3,3)
T : numpy.array of shape (:,3,3) or (3,3)
Tensor of which the right stretch is computed.
"""
return __polar_decomposition(x,'U')[0]
return __polar_decomposition(T,'U')[0]
def rotational_part(x):
def rotational_part(T):
"""
Return the rotational part of a tensor.
Parameters
----------
x : numpy.array of shape (:,3,3) or (3,3)
T : numpy.array of shape (:,3,3) or (3,3)
Tensor of which the rotational part is computed.
"""
return __polar_decomposition(x,'R')[0]
return __polar_decomposition(T,'R')[0]
def spherical_part(x,tensor=False):
def spherical_part(T,tensor=False):
"""
Return spherical (hydrostatic) part of a tensor.
Parameters
----------
x : numpy.array of shape (:,3,3) or (3,3)
T : numpy.array of shape (:,3,3) or (3,3)
Tensor of which the hydrostatic part is computed.
tensor : bool, optional
Map spherical part onto identity tensor. Default is false
"""
if x.shape == (3,3):
sph = np.trace(x)/3.0
if T.shape == (3,3):
sph = np.trace(T)/3.0
return sph if not tensor else np.eye(3)*sph
else:
sph = np.trace(x,axis1=1,axis2=2)/3.0
sph = np.trace(T,axis1=1,axis2=2)/3.0
if not tensor:
return sph
else:
return np.einsum('ijk,i->ijk',np.broadcast_to(np.eye(3),(x.shape[0],3,3)),sph)
return np.einsum('ijk,i->ijk',np.broadcast_to(np.eye(3),(T.shape[0],3,3)),sph)
def strain_tensor(F,t,m):
@ -234,73 +235,73 @@ def strain_tensor(F,t,m):
eps
def symmetric(x):
def symmetric(T):
"""
Return the symmetrized tensor.
Parameters
----------
x : numpy.array of shape (:,3,3) or (3,3)
T : numpy.array of shape (:,3,3) or (3,3)
Tensor of which the symmetrized values are computed.
"""
return (x+transpose(x))*0.5
return (T+transpose(T))*0.5
def transpose(x):
def transpose(T):
"""
Return the transpose of a tensor.
Parameters
----------
x : numpy.array of shape (:,3,3) or (3,3)
T : numpy.array of shape (:,3,3) or (3,3)
Tensor of which the transpose is computed.
"""
return x.T if np.shape(x) == (3,3) else \
np.transpose(x,(0,2,1))
return T.T if np.shape(T) == (3,3) else \
np.transpose(T,(0,2,1))
def __polar_decomposition(x,requested):
def __polar_decomposition(T,requested):
"""
Singular value decomposition.
Parameters
----------
x : numpy.array of shape (:,3,3) or (3,3)
T : numpy.array of shape (:,3,3) or (3,3)
Tensor of which the singular values are computed.
requested : iterable of str
Requested outputs: ‘R’ for the rotation tensor,
‘V’ for left stretch tensor and ‘U’ for right stretch tensor.
"""
u, s, vh = np.linalg.svd(x)
R = np.dot(u,vh) if np.shape(x) == (3,3) else \
u, s, vh = np.linalg.svd(T)
R = np.dot(u,vh) if np.shape(T) == (3,3) else \
np.einsum('ijk,ikl->ijl',u,vh)
output = []
if 'R' in requested:
output.append(R)
if 'V' in requested:
output.append(np.dot(x,R.T) if np.shape(x) == (3,3) else np.einsum('ijk,ilk->ijl',x,R))
output.append(np.dot(T,R.T) if np.shape(T) == (3,3) else np.einsum('ijk,ilk->ijl',T,R))
if 'U' in requested:
output.append(np.dot(R.T,x) if np.shape(x) == (3,3) else np.einsum('ikj,ikl->ijl',R,x))
output.append(np.dot(R.T,T) if np.shape(T) == (3,3) else np.einsum('ikj,ikl->ijl',R,T))
return tuple(output)
def __Mises(x,s):
def __Mises(T_sym,s):
"""
Base equation for Mises equivalent of a stres or strain tensor.
Parameters
----------
x : numpy.array of shape (:,3,3) or (3,3)
T_sym : numpy.array of shape (:,3,3) or (3,3)
Symmetric tensor of which the von Mises equivalent is computed.
s : float
Scaling factor (2/3 for strain, 3/2 for stress).
"""
d = deviatoric_part(x)
return np.sqrt(s*(np.sum(d**2.0))) if np.shape(x) == (3,3) else \
d = deviatoric_part(T_sym)
return np.sqrt(s*(np.sum(d**2.0))) if np.shape(T_sym) == (3,3) else \
np.sqrt(s*np.einsum('ijk->i',d**2.0))

1497
python/damask/orientation.py
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1139
python/damask/result.py Normal file
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837
python/damask/rotation.py Normal file
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@ -0,0 +1,837 @@
import numpy as np
from . import Lambert
P = -1
def iszero(a):
return np.isclose(a,0.0,atol=1.0e-12,rtol=0.0)
class Rotation:
u"""
Orientation stored with functionality for conversion to different representations.
References
----------
D. Rowenhorst et al., Modelling and Simulation in Materials Science and Engineering 23:083501, 2015
https://doi.org/10.1088/0965-0393/23/8/083501
Conventions
-----------
Convention 1: Coordinate frames are right-handed.
Convention 2: A rotation angle ω is taken to be positive for a counterclockwise rotation
when viewing from the end point of the rotation axis towards the origin.
Convention 3: Rotations will be interpreted in the passive sense.
Convention 4: Euler angle triplets are implemented using the Bunge convention,
with the angular ranges as [0, 2π],[0, π],[0, 2π].
Convention 5: The rotation angle ω is limited to the interval [0, π].
Convention 6: the real part of a quaternion is positive, Re(q) > 0
Convention 7: P = -1 (as default).
Usage
-----
Vector "a" (defined in coordinate system "A") is passively rotated
resulting in new coordinates "b" when expressed in system "B".
b = Q * a
b = np.dot(Q.asMatrix(),a)
"""
__slots__ = ['quaternion']
def __init__(self,quaternion = np.array([1.0,0.0,0.0,0.0])):
"""
Initializes to identity unless specified.
Parameters
----------
quaternion : numpy.ndarray, optional
Unit quaternion that follows the conventions. Use .fromQuaternion to perform a sanity check.
"""
self.quaternion = quaternion.copy()
def __copy__(self):
"""Copy."""
return self.__class__(self.quaternion)
copy = __copy__
def __repr__(self):
"""Orientation displayed as unit quaternion, rotation matrix, and Bunge-Euler angles."""
return '\n'.join([
'Quaternion: (real={:.3f}, imag=<{:+.3f}, {:+.3f}, {:+.3f}>)'.format(*(self.quaternion)),
'Matrix:\n{}'.format(self.asMatrix()),
'Bunge Eulers / deg: ({:3.2f}, {:3.2f}, {:3.2f})'.format(*self.asEulers(degrees=True)),
])
def __mul__(self, other):
"""
Multiplication.
Parameters
----------
other : numpy.ndarray or Rotation
Vector, second or fourth order tensor, or rotation object that is rotated.
Todo
----
Document details active/passive)
considere rotation of (3,3,3,3)-matrix
"""
if isinstance(other, Rotation): # rotate a rotation
self_q = self.quaternion[0]
self_p = self.quaternion[1:]
other_q = other.quaternion[0]
other_p = other.quaternion[1:]
R = self.__class__(np.append(self_q*other_q - np.dot(self_p,other_p),
self_q*other_p + other_q*self_p + P * np.cross(self_p,other_p)))
return R.standardize()
elif isinstance(other, (tuple,np.ndarray)):
if isinstance(other,tuple) or other.shape == (3,): # rotate a single (3)-vector or meshgrid
A = self.quaternion[0]**2.0 - np.dot(self.quaternion[1:],self.quaternion[1:])
B = 2.0 * ( self.quaternion[1]*other[0]
+ self.quaternion[2]*other[1]
+ self.quaternion[3]*other[2])
C = 2.0 * P*self.quaternion[0]
return np.array([
A*other[0] + B*self.quaternion[1] + C*(self.quaternion[2]*other[2] - self.quaternion[3]*other[1]),
A*other[1] + B*self.quaternion[2] + C*(self.quaternion[3]*other[0] - self.quaternion[1]*other[2]),
A*other[2] + B*self.quaternion[3] + C*(self.quaternion[1]*other[1] - self.quaternion[2]*other[0]),
])
elif other.shape == (3,3,): # rotate a single (3x3)-matrix
return np.dot(self.asMatrix(),np.dot(other,self.asMatrix().T))
elif other.shape == (3,3,3,3,):
raise NotImplementedError
else:
return NotImplemented
else:
return NotImplemented
def inverse(self):
"""In-place inverse rotation/backward rotation."""
self.quaternion[1:] *= -1
return self
def inversed(self):
"""Inverse rotation/backward rotation."""
return self.copy().inverse()
def standardize(self):
"""In-place quaternion representation with positive q."""
if self.quaternion[0] < 0.0: self.quaternion*=-1
return self
def standardized(self):
"""Quaternion representation with positive q."""
return self.copy().standardize()
def misorientation(self,other):
"""
Get Misorientation.
Parameters
----------
other : Rotation
Rotation to which the misorientation is computed.
"""
return other*self.inversed()
def average(self,other):
"""
Calculate the average rotation.
Parameters
----------
other : Rotation
Rotation from which the average is rotated.
"""
return Rotation.fromAverage([self,other])
################################################################################################
# convert to different orientation representations (numpy arrays)
def asQuaternion(self):
"""
Unit quaternion [q, p_1, p_2, p_3] unless quaternion == True: damask.quaternion object.
Parameters
----------
quaternion : bool, optional
return quaternion as DAMASK object.
"""
return self.quaternion
def asEulers(self,
degrees = False):
"""
Bunge-Euler angles: (φ_1, ϕ, φ_2).
Parameters
----------
degrees : bool, optional
return angles in degrees.
"""
eu = Rotation.qu2eu(self.quaternion)
if degrees: eu = np.degrees(eu)
return eu
def asAxisAngle(self,
degrees = False,
pair = False):
"""
Axis angle representation [n_1, n_2, n_3, ω] unless pair == True: ([n_1, n_2, n_3], ω).
Parameters
----------
degrees : bool, optional
return rotation angle in degrees.
pair : bool, optional
return tuple of axis and angle.
"""
ax = Rotation.qu2ax(self.quaternion)
if degrees: ax[3] = np.degrees(ax[3])
return (ax[:3],np.degrees(ax[3])) if pair else ax
def asMatrix(self):
"""Rotation matrix."""
return Rotation.qu2om(self.quaternion)
def asRodrigues(self,
vector = False):
"""
Rodrigues-Frank vector representation [n_1, n_2, n_3, tan(ω/2)] unless vector == True: [n_1, n_2, n_3] * tan(ω/2).
Parameters
----------
vector : bool, optional
return as actual Rodrigues--Frank vector, i.e. rotation axis scaled by tan(ω/2).
"""
ro = Rotation.qu2ro(self.quaternion)
return ro[:3]*ro[3] if vector else ro
def asHomochoric(self):
"""Homochoric vector: (h_1, h_2, h_3)."""
return Rotation.qu2ho(self.quaternion)
def asCubochoric(self):
"""Cubochoric vector: (c_1, c_2, c_3)."""
return Rotation.qu2cu(self.quaternion)
def asM(self):
"""
Intermediate representation supporting quaternion averaging.
References
----------
F. Landis Markley et al., Journal of Guidance, Control, and Dynamics 30(4):1193-1197, 2007
https://doi.org/10.2514/1.28949
"""
return np.outer(self.quaternion,self.quaternion)
################################################################################################
# static constructors. The input data needs to follow the convention, options allow to
# relax these convections
@staticmethod
def fromQuaternion(quaternion,
acceptHomomorph = False,
P = -1):
qu = quaternion if isinstance(quaternion,np.ndarray) and quaternion.dtype == np.dtype(float) \
else np.array(quaternion,dtype=float)
if P > 0: qu[1:4] *= -1 # convert from P=1 to P=-1
if qu[0] < 0.0:
if acceptHomomorph:
qu *= -1.
else:
raise ValueError('Quaternion has negative first component.\n{}'.format(qu[0]))
if not np.isclose(np.linalg.norm(qu), 1.0):
raise ValueError('Quaternion is not of unit length.\n{} {} {} {}'.format(*qu))
return Rotation(qu)
@staticmethod
def fromEulers(eulers,
degrees = False):
eu = eulers if isinstance(eulers, np.ndarray) and eulers.dtype == np.dtype(float) \
else np.array(eulers,dtype=float)
eu = np.radians(eu) if degrees else eu
if np.any(eu < 0.0) or np.any(eu > 2.0*np.pi) or eu[1] > np.pi:
raise ValueError('Euler angles outside of [0..2π],[0..π],[0..2π].\n{} {} {}.'.format(*eu))
return Rotation(Rotation.eu2qu(eu))
@staticmethod
def fromAxisAngle(angleAxis,
degrees = False,
normalise = False,
P = -1):
ax = angleAxis if isinstance(angleAxis, np.ndarray) and angleAxis.dtype == np.dtype(float) \
else np.array(angleAxis,dtype=float)
if P > 0: ax[0:3] *= -1 # convert from P=1 to P=-1
if degrees: ax[ 3] = np.radians(ax[3])
if normalise: ax[0:3] /= np.linalg.norm(ax[0:3])
if ax[3] < 0.0 or ax[3] > np.pi:
raise ValueError('Axis angle rotation angle outside of [0..π].\n'.format(ax[3]))
if not np.isclose(np.linalg.norm(ax[0:3]), 1.0):
raise ValueError('Axis angle rotation axis is not of unit length.\n{} {} {}'.format(*ax[0:3]))
return Rotation(Rotation.ax2qu(ax))
@staticmethod
def fromBasis(basis,
orthonormal = True,
reciprocal = False,
):
om = basis if isinstance(basis, np.ndarray) else np.array(basis).reshape((3,3))
if reciprocal:
om = np.linalg.inv(om.T/np.pi) # transform reciprocal basis set
orthonormal = False # contains stretch
if not orthonormal:
(U,S,Vh) = np.linalg.svd(om) # singular value decomposition
om = np.dot(U,Vh)
if not np.isclose(np.linalg.det(om),1.0):
raise ValueError('matrix is not a proper rotation.\n{}'.format(om))
if not np.isclose(np.dot(om[0],om[1]), 0.0) \
or not np.isclose(np.dot(om[1],om[2]), 0.0) \
or not np.isclose(np.dot(om[2],om[0]), 0.0):
raise ValueError('matrix is not orthogonal.\n{}'.format(om))
return Rotation(Rotation.om2qu(om))
@staticmethod
def fromMatrix(om,
):
return Rotation.fromBasis(om)
@staticmethod
def fromRodrigues(rodrigues,
normalise = False,
P = -1):
ro = rodrigues if isinstance(rodrigues, np.ndarray) and rodrigues.dtype == np.dtype(float) \
else np.array(rodrigues,dtype=float)
if P > 0: ro[0:3] *= -1 # convert from P=1 to P=-1
if normalise: ro[0:3] /= np.linalg.norm(ro[0:3])
if not np.isclose(np.linalg.norm(ro[0:3]), 1.0):
raise ValueError('Rodrigues rotation axis is not of unit length.\n{} {} {}'.format(*ro[0:3]))
if ro[3] < 0.0:
raise ValueError('Rodriques rotation angle not positive.\n'.format(ro[3]))
return Rotation(Rotation.ro2qu(ro))
@staticmethod
def fromHomochoric(homochoric,
P = -1):
ho = homochoric if isinstance(homochoric, np.ndarray) and homochoric.dtype == np.dtype(float) \
else np.array(homochoric,dtype=float)
if P > 0: ho *= -1 # convert from P=1 to P=-1
return Rotation(Rotation.ho2qu(ho))
@staticmethod
def fromCubochoric(cubochoric,
P = -1):
cu = cubochoric if isinstance(cubochoric, np.ndarray) and cubochoric.dtype == np.dtype(float) \
else np.array(cubochoric,dtype=float)
ho = Rotation.cu2ho(cu)
if P > 0: ho *= -1 # convert from P=1 to P=-1
return Rotation(Rotation.ho2qu(ho))
@staticmethod
def fromAverage(rotations,
weights = []):
"""
Average rotation.
References
----------
F. Landis Markley et al., Journal of Guidance, Control, and Dynamics 30(4):1193-1197, 2007
https://doi.org/10.2514/1.28949
Parameters
----------
rotations : list of Rotations
Rotations to average from
weights : list of floats, optional
Weights for each rotation used for averaging
"""
if not all(isinstance(item, Rotation) for item in rotations):
raise TypeError("Only instances of Rotation can be averaged.")
N = len(rotations)
if weights == [] or not weights:
weights = np.ones(N,dtype='i')
for i,(r,n) in enumerate(zip(rotations,weights)):
M = r.asM() * n if i == 0 \
else M + r.asM() * n # noqa add (multiples) of this rotation to average noqa
eig, vec = np.linalg.eig(M/N)
return Rotation.fromQuaternion(np.real(vec.T[eig.argmax()]),acceptHomomorph = True)
@staticmethod
def fromRandom():
r = np.random.random(3)
A = np.sqrt(r[2])
B = np.sqrt(1.0-r[2])
return Rotation(np.array([np.cos(2.0*np.pi*r[0])*A,
np.sin(2.0*np.pi*r[1])*B,
np.cos(2.0*np.pi*r[1])*B,
np.sin(2.0*np.pi*r[0])*A])).standardize()
####################################################################################################
# Code below available according to the following conditions on https://github.com/MarDiehl/3Drotations
####################################################################################################
# Copyright (c) 2017-2019, Martin Diehl/Max-Planck-Institut für Eisenforschung GmbH
# Copyright (c) 2013-2014, Marc De Graef/Carnegie Mellon University
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without modification, are
# permitted provided that the following conditions are met:
#
# - Redistributions of source code must retain the above copyright notice, this list
# of conditions and the following disclaimer.
# - Redistributions in binary form must reproduce the above copyright notice, this
# list of conditions and the following disclaimer in the documentation and/or
# other materials provided with the distribution.
# - Neither the names of Marc De Graef, Carnegie Mellon University nor the names
# of its contributors may be used to endorse or promote products derived from
# this software without specific prior written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
# ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
# LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
# SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
# CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
# OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
# USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
####################################################################################################
#---------- Quaternion ----------
@staticmethod
def qu2om(qu):
"""Quaternion to rotation matrix."""
qq = qu[0]**2-(qu[1]**2 + qu[2]**2 + qu[3]**2)
om = np.diag(qq + 2.0*np.array([qu[1],qu[2],qu[3]])**2)
om[1,0] = 2.0*(qu[2]*qu[1]+qu[0]*qu[3])
om[0,1] = 2.0*(qu[1]*qu[2]-qu[0]*qu[3])
om[2,1] = 2.0*(qu[3]*qu[2]+qu[0]*qu[1])
om[1,2] = 2.0*(qu[2]*qu[3]-qu[0]*qu[1])
om[0,2] = 2.0*(qu[1]*qu[3]+qu[0]*qu[2])
om[2,0] = 2.0*(qu[3]*qu[1]-qu[0]*qu[2])
return om if P > 0.0 else om.T
@staticmethod
def qu2eu(qu):
"""Quaternion to Bunge-Euler angles."""
q03 = qu[0]**2+qu[3]**2
q12 = qu[1]**2+qu[2]**2
chi = np.sqrt(q03*q12)
if iszero(chi):
eu = np.array([np.arctan2(-P*2.0*qu[0]*qu[3],qu[0]**2-qu[3]**2), 0.0, 0.0]) if iszero(q12) else \
np.array([np.arctan2(2.0*qu[1]*qu[2],qu[1]**2-qu[2]**2), np.pi, 0.0])
else:
eu = np.array([np.arctan2((-P*qu[0]*qu[2]+qu[1]*qu[3])*chi, (-P*qu[0]*qu[1]-qu[2]*qu[3])*chi ),
np.arctan2( 2.0*chi, q03-q12 ),
np.arctan2(( P*qu[0]*qu[2]+qu[1]*qu[3])*chi, (-P*qu[0]*qu[1]+qu[2]*qu[3])*chi )])
# reduce Euler angles to definition range, i.e a lower limit of 0.0
eu = np.where(eu<0, (eu+2.0*np.pi)%np.array([2.0*np.pi,np.pi,2.0*np.pi]),eu)
return eu
@staticmethod
def qu2ax(qu):
"""
Quaternion to axis angle pair.
Modified version of the original formulation, should be numerically more stable
"""
if iszero(qu[1]**2+qu[2]**2+qu[3]**2): # set axis to [001] if the angle is 0/360
ax = [ 0.0, 0.0, 1.0, 0.0 ]
elif not iszero(qu[0]):
s = np.sign(qu[0])/np.sqrt(qu[1]**2+qu[2]**2+qu[3]**2)
omega = 2.0 * np.arccos(np.clip(qu[0],-1.0,1.0))
ax = [ qu[1]*s, qu[2]*s, qu[3]*s, omega ]
else:
ax = [ qu[1], qu[2], qu[3], np.pi]
return np.array(ax)
@staticmethod
def qu2ro(qu):
"""Quaternion to Rodriques-Frank vector."""
if iszero(qu[0]):
ro = [qu[1], qu[2], qu[3], np.inf]
else:
s = np.linalg.norm([qu[1],qu[2],qu[3]])
ro = [0.0,0.0,P,0.0] if iszero(s) else \
[ qu[1]/s, qu[2]/s, qu[3]/s, np.tan(np.arccos(np.clip(qu[0],-1.0,1.0)))]
return np.array(ro)
@staticmethod
def qu2ho(qu):
"""Quaternion to homochoric vector."""
omega = 2.0 * np.arccos(np.clip(qu[0],-1.0,1.0))
if iszero(omega):
ho = np.array([ 0.0, 0.0, 0.0 ])
else:
ho = np.array([qu[1], qu[2], qu[3]])
f = 0.75 * ( omega - np.sin(omega) )
ho = ho/np.linalg.norm(ho) * f**(1./3.)
return ho
@staticmethod
def qu2cu(qu):
"""Quaternion to cubochoric vector."""
return Rotation.ho2cu(Rotation.qu2ho(qu))
#---------- Rotation matrix ----------
@staticmethod
def om2qu(om):
"""
Rotation matrix to quaternion.
The original formulation (direct conversion) had (numerical?) issues
"""
return Rotation.eu2qu(Rotation.om2eu(om))
@staticmethod
def om2eu(om):
"""Rotation matrix to Bunge-Euler angles."""
if abs(om[2,2]) < 1.0:
zeta = 1.0/np.sqrt(1.0-om[2,2]**2)
eu = np.array([np.arctan2(om[2,0]*zeta,-om[2,1]*zeta),
np.arccos(om[2,2]),
np.arctan2(om[0,2]*zeta, om[1,2]*zeta)])
else:
eu = np.array([np.arctan2( om[0,1],om[0,0]), np.pi*0.5*(1-om[2,2]),0.0]) # following the paper, not the reference implementation
# reduce Euler angles to definition range, i.e a lower limit of 0.0
eu = np.where(eu<0, (eu+2.0*np.pi)%np.array([2.0*np.pi,np.pi,2.0*np.pi]),eu)
return eu
@staticmethod
def om2ax(om):
"""Rotation matrix to axis angle pair."""
ax=np.empty(4)
# first get the rotation angle
t = 0.5*(om.trace() -1.0)
ax[3] = np.arccos(np.clip(t,-1.0,1.0))
if iszero(ax[3]):
ax = [ 0.0, 0.0, 1.0, 0.0]
else:
w,vr = np.linalg.eig(om)
# next, find the eigenvalue (1,0j)
i = np.where(np.isclose(w,1.0+0.0j))[0][0]
ax[0:3] = np.real(vr[0:3,i])
diagDelta = np.array([om[1,2]-om[2,1],om[2,0]-om[0,2],om[0,1]-om[1,0]])
ax[0:3] = np.where(iszero(diagDelta), ax[0:3],np.abs(ax[0:3])*np.sign(-P*diagDelta))
return np.array(ax)
@staticmethod
def om2ro(om):
"""Rotation matrix to Rodriques-Frank vector."""
return Rotation.eu2ro(Rotation.om2eu(om))
@staticmethod
def om2ho(om):
"""Rotation matrix to homochoric vector."""
return Rotation.ax2ho(Rotation.om2ax(om))
@staticmethod
def om2cu(om):
"""Rotation matrix to cubochoric vector."""
return Rotation.ho2cu(Rotation.om2ho(om))
#---------- Bunge-Euler angles ----------
@staticmethod
def eu2qu(eu):
"""Bunge-Euler angles to quaternion."""
ee = 0.5*eu
cPhi = np.cos(ee[1])
sPhi = np.sin(ee[1])
qu = np.array([ cPhi*np.cos(ee[0]+ee[2]),
-P*sPhi*np.cos(ee[0]-ee[2]),
-P*sPhi*np.sin(ee[0]-ee[2]),
-P*cPhi*np.sin(ee[0]+ee[2]) ])
if qu[0] < 0.0: qu*=-1
return qu
@staticmethod
def eu2om(eu):
"""Bunge-Euler angles to rotation matrix."""
c = np.cos(eu)
s = np.sin(eu)
om = np.array([[+c[0]*c[2]-s[0]*s[2]*c[1], +s[0]*c[2]+c[0]*s[2]*c[1], +s[2]*s[1]],
[-c[0]*s[2]-s[0]*c[2]*c[1], -s[0]*s[2]+c[0]*c[2]*c[1], +c[2]*s[1]],
[+s[0]*s[1], -c[0]*s[1], +c[1] ]])
om[np.where(iszero(om))] = 0.0
return om
@staticmethod
def eu2ax(eu):
"""Bunge-Euler angles to axis angle pair."""
t = np.tan(eu[1]*0.5)
sigma = 0.5*(eu[0]+eu[2])
delta = 0.5*(eu[0]-eu[2])
tau = np.linalg.norm([t,np.sin(sigma)])
alpha = np.pi if iszero(np.cos(sigma)) else \
2.0*np.arctan(tau/np.cos(sigma))
if iszero(alpha):
ax = np.array([ 0.0, 0.0, 1.0, 0.0 ])
else:
ax = -P/tau * np.array([ t*np.cos(delta), t*np.sin(delta), np.sin(sigma) ]) # passive axis angle pair so a minus sign in front
ax = np.append(ax,alpha)
if alpha < 0.0: ax *= -1.0 # ensure alpha is positive
return ax
@staticmethod
def eu2ro(eu):
"""Bunge-Euler angles to Rodriques-Frank vector."""
ro = Rotation.eu2ax(eu) # convert to axis angle pair representation
if ro[3] >= np.pi: # Differs from original implementation. check convention 5
ro[3] = np.inf
elif iszero(ro[3]):
ro = np.array([ 0.0, 0.0, P, 0.0 ])
else:
ro[3] = np.tan(ro[3]*0.5)
return ro
@staticmethod
def eu2ho(eu):
"""Bunge-Euler angles to homochoric vector."""
return Rotation.ax2ho(Rotation.eu2ax(eu))
@staticmethod
def eu2cu(eu):
"""Bunge-Euler angles to cubochoric vector."""
return Rotation.ho2cu(Rotation.eu2ho(eu))
#---------- Axis angle pair ----------
@staticmethod
def ax2qu(ax):
"""Axis angle pair to quaternion."""
if iszero(ax[3]):
qu = np.array([ 1.0, 0.0, 0.0, 0.0 ])
else:
c = np.cos(ax[3]*0.5)
s = np.sin(ax[3]*0.5)
qu = np.array([ c, ax[0]*s, ax[1]*s, ax[2]*s ])
return qu
@staticmethod
def ax2om(ax):
"""Axis angle pair to rotation matrix."""
c = np.cos(ax[3])
s = np.sin(ax[3])
omc = 1.0-c
om=np.diag(ax[0:3]**2*omc + c)
for idx in [[0,1,2],[1,2,0],[2,0,1]]:
q = omc*ax[idx[0]] * ax[idx[1]]
om[idx[0],idx[1]] = q + s*ax[idx[2]]
om[idx[1],idx[0]] = q - s*ax[idx[2]]
return om if P < 0.0 else om.T
@staticmethod
def ax2eu(ax):
"""Rotation matrix to Bunge Euler angles."""
return Rotation.om2eu(Rotation.ax2om(ax))
@staticmethod
def ax2ro(ax):
"""Axis angle pair to Rodriques-Frank vector."""
if iszero(ax[3]):
ro = [ 0.0, 0.0, P, 0.0 ]
else:
ro = [ax[0], ax[1], ax[2]]
# 180 degree case
ro += [np.inf] if np.isclose(ax[3],np.pi,atol=1.0e-15,rtol=0.0) else \
[np.tan(ax[3]*0.5)]
return np.array(ro)
@staticmethod
def ax2ho(ax):
"""Axis angle pair to homochoric vector."""
f = (0.75 * ( ax[3] - np.sin(ax[3]) ))**(1.0/3.0)
ho = ax[0:3] * f
return ho
@staticmethod
def ax2cu(ax):
"""Axis angle pair to cubochoric vector."""
return Rotation.ho2cu(Rotation.ax2ho(ax))
#---------- Rodrigues-Frank vector ----------
@staticmethod
def ro2qu(ro):
"""Rodriques-Frank vector to quaternion."""
return Rotation.ax2qu(Rotation.ro2ax(ro))
@staticmethod
def ro2om(ro):
"""Rodgrigues-Frank vector to rotation matrix."""
return Rotation.ax2om(Rotation.ro2ax(ro))
@staticmethod
def ro2eu(ro):
"""Rodriques-Frank vector to Bunge-Euler angles."""
return Rotation.om2eu(Rotation.ro2om(ro))
@staticmethod
def ro2ax(ro):
"""Rodriques-Frank vector to axis angle pair."""
ta = ro[3]
if iszero(ta):
ax = [ 0.0, 0.0, 1.0, 0.0 ]
elif not np.isfinite(ta):
ax = [ ro[0], ro[1], ro[2], np.pi ]
else:
angle = 2.0*np.arctan(ta)
ta = 1.0/np.linalg.norm(ro[0:3])
ax = [ ro[0]/ta, ro[1]/ta, ro[2]/ta, angle ]
return np.array(ax)
@staticmethod
def ro2ho(ro):
"""Rodriques-Frank vector to homochoric vector."""
if iszero(np.sum(ro[0:3]**2.0)):
ho = [ 0.0, 0.0, 0.0 ]
else:
f = 2.0*np.arctan(ro[3]) -np.sin(2.0*np.arctan(ro[3])) if np.isfinite(ro[3]) else np.pi
ho = ro[0:3] * (0.75*f)**(1.0/3.0)
return np.array(ho)
@staticmethod
def ro2cu(ro):
"""Rodriques-Frank vector to cubochoric vector."""
return Rotation.ho2cu(Rotation.ro2ho(ro))
#---------- Homochoric vector----------
@staticmethod
def ho2qu(ho):
"""Homochoric vector to quaternion."""
return Rotation.ax2qu(Rotation.ho2ax(ho))
@staticmethod
def ho2om(ho):
"""Homochoric vector to rotation matrix."""
return Rotation.ax2om(Rotation.ho2ax(ho))
@staticmethod
def ho2eu(ho):
"""Homochoric vector to Bunge-Euler angles."""
return Rotation.ax2eu(Rotation.ho2ax(ho))
@staticmethod
def ho2ax(ho):
"""Homochoric vector to axis angle pair."""
tfit = np.array([+1.0000000000018852, -0.5000000002194847,
-0.024999992127593126, -0.003928701544781374,
-0.0008152701535450438, -0.0002009500426119712,
-0.00002397986776071756, -0.00008202868926605841,
+0.00012448715042090092, -0.0001749114214822577,
+0.0001703481934140054, -0.00012062065004116828,
+0.000059719705868660826, -0.00001980756723965647,
+0.000003953714684212874, -0.00000036555001439719544])
# normalize h and store the magnitude
hmag_squared = np.sum(ho**2.)
if iszero(hmag_squared):
ax = np.array([ 0.0, 0.0, 1.0, 0.0 ])
else:
hm = hmag_squared
# convert the magnitude to the rotation angle
s = tfit[0] + tfit[1] * hmag_squared
for i in range(2,16):
hm *= hmag_squared
s += tfit[i] * hm
ax = np.append(ho/np.sqrt(hmag_squared),2.0*np.arccos(np.clip(s,-1.0,1.0)))
return ax
@staticmethod
def ho2ro(ho):
"""Axis angle pair to Rodriques-Frank vector."""
return Rotation.ax2ro(Rotation.ho2ax(ho))
@staticmethod
def ho2cu(ho):
"""Homochoric vector to cubochoric vector."""
return Lambert.BallToCube(ho)
#---------- Cubochoric ----------
@staticmethod
def cu2qu(cu):
"""Cubochoric vector to quaternion."""
return Rotation.ho2qu(Rotation.cu2ho(cu))
@staticmethod
def cu2om(cu):
"""Cubochoric vector to rotation matrix."""
return Rotation.ho2om(Rotation.cu2ho(cu))
@staticmethod
def cu2eu(cu):
"""Cubochoric vector to Bunge-Euler angles."""
return Rotation.ho2eu(Rotation.cu2ho(cu))
@staticmethod
def cu2ax(cu):
"""Cubochoric vector to axis angle pair."""
return Rotation.ho2ax(Rotation.cu2ho(cu))
@staticmethod
def cu2ro(cu):
"""Cubochoric vector to Rodriques-Frank vector."""
return Rotation.ho2ro(Rotation.cu2ho(cu))
@staticmethod
def cu2ho(cu):
"""Cubochoric vector to homochoric vector."""
return Lambert.CubeToBall(cu)

6
python/damask/table.py
View File

@ -32,7 +32,7 @@ class Table():
"""Label data individually, e.g. v v v ==> 1_v 2_v 3_v."""
labels = []
for label,shape in self.shapes.items():
size = np.prod(shape)
size = int(np.prod(shape))
labels += ['{}{}'.format('' if size == 1 else '{}_'.format(i+1),label) for i in range(size)]
self.data.columns = labels
@ -41,14 +41,14 @@ class Table():
"""Label data condensed, e.g. 1_v 2_v 3_v ==> v v v."""
labels = []
for label,shape in self.shapes.items():
labels += [label] * np.prod(shape)
labels += [label] * int(np.prod(shape))
self.data.columns = labels
def __add_comment(self,label,shape,info):
if info is not None:
self.comments.append('{}{}: {}'.format(label,
' '+str(shape) if np.prod(shape) > 1 else '',
' '+str(shape) if np.prod(shape,dtype=int) > 1 else '',
info))

148
python/damask/util.py
View File

@ -6,8 +6,6 @@ import shlex
from fractions import Fraction
from functools import reduce
from optparse import Option
from queue import Queue
from threading import Thread
import numpy as np
@ -42,55 +40,92 @@ class bcolors:
self.CROSSOUT = ''
# -----------------------------
def srepr(arg,glue = '\n'):
"""Joins arguments as individual lines."""
r"""
Join arguments as individual lines.
Parameters
----------
arg : iterable
Items to join.
glue : str, optional
Defaults to \n.
"""
if (not hasattr(arg, "strip") and
(hasattr(arg, "__getitem__") or
hasattr(arg, "__iter__"))):
return glue.join(str(x) for x in arg)
return arg if isinstance(arg,str) else repr(arg)
# -----------------------------
def croak(what, newline = True):
"""Writes formated to stderr."""
if what is not None:
"""
Write formated to stderr.
Parameters
----------
what : str or iterable
Content to be displayed
newline : bool, optional
Separate items of what by newline. Defaults to True.
"""
if not what:
sys.stderr.write(srepr(what,glue = '\n') + ('\n' if newline else ''))
sys.stderr.flush()
# -----------------------------
def report(who = None,
what = None):
"""Reports script and file name."""
"""
Reports script and file name.
DEPRECATED
"""
croak( (emph(who)+': ' if who is not None else '') + (what if what is not None else '') + '\n' )
# -----------------------------
def emph(what):
"""Formats string with emphasis."""
return bcolors.BOLD+srepr(what)+bcolors.ENDC
# -----------------------------
def deemph(what):
"""Formats string with deemphasis."""
return bcolors.DIM+srepr(what)+bcolors.ENDC
# -----------------------------
def delete(what):
"""Formats string as deleted."""
return bcolors.DIM+srepr(what)+bcolors.ENDC
# -----------------------------
def strikeout(what):
"""Formats string as strikeout."""
return bcolors.CROSSOUT+srepr(what)+bcolors.ENDC
# -----------------------------
def execute(cmd,
streamIn = None,
wd = './',
env = None):
"""Executes a command in given directory and returns stdout and stderr for optional stdin."""
"""
Execute command.
Parameters
----------
cmd : str
Command to be executed.
streanIn :, optional
Input (via pipe) for executed process.
wd : str, optional
Working directory of process. Defaults to ./ .
env :
Environment
"""
initialPath = os.getcwd()
os.chdir(wd)
myEnv = os.environ if env is None else env
@ -104,15 +139,17 @@ def execute(cmd,
out = out.decode('utf-8').replace('\x08','')
error = error.decode('utf-8').replace('\x08','')
os.chdir(initialPath)
if process.returncode != 0: raise RuntimeError('{} failed with returncode {}'.format(cmd,process.returncode))
if process.returncode != 0:
raise RuntimeError('{} failed with returncode {}'.format(cmd,process.returncode))
return out,error
# -----------------------------
class extendableOption(Option):
"""
Used for definition of new option parser action 'extend', which enables to take multiple option arguments.
Adopted from online tutorial http://docs.python.org/library/optparse.html
DEPRECATED
"""
ACTIONS = Option.ACTIONS + ("extend",)
@ -127,17 +164,24 @@ class extendableOption(Option):
else:
Option.take_action(self, action, dest, opt, value, values, parser)
# Print iterations progress
# from https://gist.github.com/aubricus/f91fb55dc6ba5557fbab06119420dd6a
def progressBar(iteration, total, prefix='', bar_length=50):
"""
Call in a loop to create terminal progress bar.
@params:
iteration - Required : current iteration (Int)
total - Required : total iterations (Int)
prefix - Optional : prefix string (Str)
bar_length - Optional : character length of bar (Int)
From https://gist.github.com/aubricus/f91fb55dc6ba5557fbab06119420dd6a
Parameters
----------
iteration : int
Current iteration.
total : int
Total iterations.
prefix : str, optional
Prefix string.
bar_length : int, optional
Character length of bar. Defaults to 50.
"""
fraction = iteration / float(total)
if not hasattr(progressBar, "last_fraction"): # first call to function
@ -161,7 +205,8 @@ def progressBar(iteration, total, prefix='', bar_length=50):
sys.stderr.write('\r{} {} {}'.format(prefix, bar, remaining_time)),
if iteration == total: sys.stderr.write('\n')
if iteration == total:
sys.stderr.write('\n')
sys.stderr.flush()
@ -202,56 +247,3 @@ class return_message():
"""Return message suitable for interactive shells."""
return srepr(self.message)
class ThreadPool:
"""Pool of threads consuming tasks from a queue."""
class Worker(Thread):
"""Thread executing tasks from a given tasks queue."""
def __init__(self, tasks):
"""Worker for tasks."""
Thread.__init__(self)
self.tasks = tasks
self.daemon = True
self.start()
def run(self):
while True:
func, args, kargs = self.tasks.get()
try:
func(*args, **kargs)
except Exception as e:
# An exception happened in this thread
print(e)
finally:
# Mark this task as done, whether an exception happened or not
self.tasks.task_done()
def __init__(self, num_threads):
"""
Thread pool.
Parameters
----------
num_threads : int
number of threads
"""
self.tasks = Queue(num_threads)
for _ in range(num_threads):
self.Worker(self.tasks)
def add_task(self, func, *args, **kargs):
"""Add a task to the queue."""
self.tasks.put((func, args, kargs))
def map(self, func, args_list):
"""Add a list of tasks to the queue."""
for args in args_list:
self.add_task(func, args)
def wait_completion(self):
"""Wait for completion of all the tasks in the queue."""
self.tasks.join()

0
python/tests/reference/DADF5/12grains6x7x8.geom → python/tests/reference/Result/12grains6x7x8.geom
View File

0
python/tests/reference/DADF5/12grains6x7x8_tensionY.hdf5 → python/tests/reference/Result/12grains6x7x8_tensionY.hdf5
View File

0
python/tests/reference/DADF5/material.config → python/tests/reference/Result/material.config
View File

0
python/tests/reference/DADF5/tensionY.load → python/tests/reference/Result/tensionY.load
View File

65
python/tests/test_Orientation.py Normal file
View File

@ -0,0 +1,65 @@
import os
from itertools import permutations
import pytest
import numpy as np
import damask
from damask import Rotation
from damask import Orientation
from damask import Lattice
n = 1000
@pytest.fixture
def default():
"""A set of n random rotations."""
return [Rotation.fromRandom() for r in range(n)]
@pytest.fixture
def reference_dir(reference_dir_base):
"""Directory containing reference results."""
return os.path.join(reference_dir_base,'Rotation')
class TestOrientation:
@pytest.mark.parametrize('color',[{'label':'red', 'RGB':[1,0,0],'direction':[0,0,1]},
{'label':'green','RGB':[0,1,0],'direction':[0,1,1]},
{'label':'blue', 'RGB':[0,0,1],'direction':[1,1,1]}])
@pytest.mark.parametrize('lattice',['fcc','bcc'])
def test_IPF_cubic(self,default,color,lattice):
cube = damask.Orientation(damask.Rotation(),lattice)
for direction in set(permutations(np.array(color['direction']))):
assert np.allclose(cube.IPFcolor(direction),np.array(color['RGB']))
@pytest.mark.parametrize('lattice',Lattice.lattices)
def test_IPF(self,lattice):
direction = np.random.random(3)*2.0-1
for rot in [Rotation.fromRandom() for r in range(n//100)]:
R = damask.Orientation(rot,lattice)
color = R.IPFcolor(direction)
for equivalent in R.equivalentOrientations():
assert np.allclose(color,R.IPFcolor(direction))
@pytest.mark.parametrize('model',['Bain','KS','GT','GT_prime','NW','Pitsch'])
@pytest.mark.parametrize('lattice',['fcc','bcc'])
def test_relationship_forward_backward(self,model,lattice):
ori = Orientation(Rotation.fromRandom(),lattice)
for i,r in enumerate(ori.relatedOrientations(model)):
ori2 = r.relatedOrientations(model)[i]
misorientation = ori.rotation.misorientation(ori2.rotation)
assert misorientation.asAxisAngle(degrees=True)[3]<1.0e-5
@pytest.mark.parametrize('model',['Bain','KS','GT','GT_prime','NW','Pitsch'])
@pytest.mark.parametrize('lattice',['fcc','bcc'])
def test_relationship_reference(self,update,reference_dir,model,lattice):
reference = os.path.join(reference_dir,'{}_{}.txt'.format(lattice,model))
ori = Orientation(Rotation(),lattice)
eu = np.array([o.rotation.asEulers(degrees=True) for o in ori.relatedOrientations(model)])
if update:
coords = np.array([(1,i+1) for i,x in enumerate(eu)])
table = damask.Table(eu,{'Eulers':(3,)})
table.add('pos',coords)
table.to_ASCII(reference)
assert np.allclose(eu,damask.Table.from_ASCII(reference).get('Eulers'))

10
python/tests/test_DADF5.py → python/tests/test_Result.py
View File

@ -4,25 +4,25 @@ import os
import pytest
import numpy as np
from damask import DADF5
from damask import Result
from damask import mechanics
@pytest.fixture
def default(tmp_path,reference_dir):
"""Small DADF5 file in temp location for modification."""
"""Small Result file in temp location for modification."""
fname = '12grains6x7x8_tensionY.hdf5'
shutil.copy(os.path.join(reference_dir,fname),tmp_path)
f = DADF5(os.path.join(tmp_path,fname))
f = Result(os.path.join(tmp_path,fname))
f.set_by_time(20.0,20.0)
return f
@pytest.fixture
def reference_dir(reference_dir_base):
"""Directory containing reference results."""
return os.path.join(reference_dir_base,'DADF5')
return os.path.join(reference_dir_base,'Result')
class TestDADF5:
class TestResult:
def test_time_increments(self,default):
shape = default.read_dataset(default.get_dataset_location('F'),0).shape

45
python/tests/test_Rotation.py
View File

@ -1,13 +1,9 @@
import os
from itertools import permutations
import pytest
import numpy as np
import damask
from damask import Rotation
from damask import Orientation
from damask import Lattice
n = 1000
@ -58,44 +54,3 @@ class TestRotation:
for rot in default:
assert np.allclose(rot.asCubochoric(),
Rotation.fromQuaternion(rot.asQuaternion()).asCubochoric())
@pytest.mark.parametrize('color',[{'label':'red', 'RGB':[1,0,0],'direction':[0,0,1]},
{'label':'green','RGB':[0,1,0],'direction':[0,1,1]},
{'label':'blue', 'RGB':[0,0,1],'direction':[1,1,1]}])
@pytest.mark.parametrize('lattice',['fcc','bcc'])
def test_IPF_cubic(self,default,color,lattice):
cube = damask.Orientation(damask.Rotation(),lattice)
for direction in set(permutations(np.array(color['direction']))):
assert np.allclose(cube.IPFcolor(direction),np.array(color['RGB']))
@pytest.mark.parametrize('lattice',Lattice.lattices)
def test_IPF(self,lattice):
direction = np.random.random(3)*2.0-1
for rot in [Rotation.fromRandom() for r in range(n//100)]:
R = damask.Orientation(rot,lattice)
color = R.IPFcolor(direction)
for equivalent in R.equivalentOrientations():
assert np.allclose(color,R.IPFcolor(direction))
@pytest.mark.parametrize('model',['Bain','KS','GT','GT_prime','NW','Pitsch'])
@pytest.mark.parametrize('lattice',['fcc','bcc'])
def test_relationship_forward_backward(self,model,lattice):
ori = Orientation(Rotation.fromRandom(),lattice)
for i,r in enumerate(ori.relatedOrientations(model)):
ori2 = r.relatedOrientations(model)[i]
misorientation = ori.rotation.misorientation(ori2.rotation)
assert misorientation.asAxisAngle(degrees=True)[3]<1.0e-5
@pytest.mark.parametrize('model',['Bain','KS','GT','GT_prime','NW','Pitsch'])
@pytest.mark.parametrize('lattice',['fcc','bcc'])
def test_relationship_reference(self,update,reference_dir,model,lattice):
reference = os.path.join(reference_dir,'{}_{}.txt'.format(lattice,model))
ori = Orientation(Rotation(),lattice)
eu = np.array([o.rotation.asEulers(degrees=True) for o in ori.relatedOrientations(model)])
if update:
coords = np.array([(1,i+1) for i,x in enumerate(eu)])
table = damask.Table(eu,{'Eulers':(3,)})
table.add('pos',coords)
table.to_ASCII(reference)
assert np.allclose(eu,damask.Table.from_ASCII(reference).get('Eulers'))

49
src/CPFEM.f90
View File

@ -69,12 +69,13 @@ contains
!> @brief call (thread safe) all module initializations
!--------------------------------------------------------------------------------------------------
subroutine CPFEM_initAll(el,ip)
integer(pInt), intent(in) :: el, & !< FE el number
ip !< FE integration point number
!$OMP CRITICAL (init)
!$OMP CRITICAL(init)
if (.not. CPFEM_init_done) then
call DAMASK_interface_init ! Spectral and FEM interface to commandline
call DAMASK_interface_init
call prec_init
call IO_init
call numerics_init
@ -93,7 +94,7 @@ subroutine CPFEM_initAll(el,ip)
call CPFEM_init
CPFEM_init_done = .true.
endif
!$OMP END CRITICAL (init)
!$OMP END CRITICAL(init)
end subroutine CPFEM_initAll
@ -174,35 +175,7 @@ subroutine CPFEM_general(mode, parallelExecution, ffn, ffn1, temperature_inp, dt
CPFEM_dcsde = CPFEM_dcsde_knownGood
!*** age results
if (iand(mode, CPFEM_AGERESULTS) /= 0_pInt) then
crystallite_F0 = crystallite_partionedF ! crystallite deformation
crystallite_Fp0 = crystallite_Fp ! crystallite plastic deformation
crystallite_Lp0 = crystallite_Lp ! crystallite plastic velocity
crystallite_Fi0 = crystallite_Fi ! crystallite intermediate deformation
crystallite_Li0 = crystallite_Li ! crystallite intermediate velocity
crystallite_S0 = crystallite_S ! crystallite 2nd Piola Kirchhoff stress
forall (i = 1:size(plasticState)) plasticState(i)%state0 = plasticState(i)%state
do i = 1, size(sourceState)
do mySource = 1,phase_Nsources(i)
sourceState(i)%p(mySource)%state0 = sourceState(i)%p(mySource)%state
enddo; enddo
if (iand(debug_level(debug_CPFEM), debug_levelBasic) /= 0_pInt) then
write(6,'(a)') '<< CPFEM >> aging states'
if (debug_e <= discretization_nElem .and. debug_i <=discretization_nIP) then
write(6,'(a,1x,i8,1x,i2,1x,i4,/,(12x,6(e20.8,1x)),/)') &
'<< CPFEM >> aged state of elFE ip grain',debug_e, debug_i, 1, &
plasticState(material_phaseAt(1,debug_e))%state(:,material_phasememberAt(1,debug_i,debug_e))
endif
endif
do homog = 1_pInt, material_Nhomogenization
homogState (homog)%state0 = homogState (homog)%state
thermalState (homog)%state0 = thermalState (homog)%state
damageState (homog)%state0 = damageState (homog)%state
enddo
endif
if (iand(mode, CPFEM_AGERESULTS) /= 0_pInt) call CPFEM_forward
!*** collection of FEM input with returning of randomize odd stress and jacobian
@ -360,7 +333,17 @@ end subroutine CPFEM_general
!--------------------------------------------------------------------------------------------------
!> @brief triggers writing of the results
!> @brief Forward data for new time increment.
!--------------------------------------------------------------------------------------------------
subroutine CPFEM_forward
call crystallite_forward
end subroutine CPFEM_forward
!--------------------------------------------------------------------------------------------------
!> @brief Trigger writing of results.
!--------------------------------------------------------------------------------------------------
subroutine CPFEM_results(inc,time)

114
src/CPFEM2.f90
View File

@ -64,123 +64,37 @@ end subroutine CPFEM_initAll
!--------------------------------------------------------------------------------------------------
!> @brief allocate the arrays defined in module CPFEM and initialize them
!> @brief Read restart information if needed.
!--------------------------------------------------------------------------------------------------
subroutine CPFEM_init
integer :: i
integer(HID_T) :: fileHandle, groupHandle
character(len=pStringLen) :: fileName, datasetName
write(6,'(/,a)') ' <<<+- CPFEM init -+>>>'; flush(6)
if (interface_restartInc > 0) then
write(6,'(/,a,i0,a)') ' reading restart information of increment ', interface_restartInc, ' from file'
write(fileName,'(a,i0,a)') trim(getSolverJobName())//'_',worldrank,'.hdf5'
fileHandle = HDF5_openFile(fileName)
call HDF5_read(fileHandle,crystallite_F0, 'F')
call HDF5_read(fileHandle,crystallite_Fp0,'Fp')
call HDF5_read(fileHandle,crystallite_Fi0,'Fi')
call HDF5_read(fileHandle,crystallite_Lp0,'Lp')
call HDF5_read(fileHandle,crystallite_Li0,'Li')
call HDF5_read(fileHandle,crystallite_S0, 'S')
groupHandle = HDF5_openGroup(fileHandle,'constituent')
do i = 1,size(phase_plasticity)
write(datasetName,'(i0,a)') i,'_omega_plastic'
call HDF5_read(groupHandle,plasticState(i)%state0,datasetName)
enddo
call HDF5_closeGroup(groupHandle)
groupHandle = HDF5_openGroup(fileHandle,'materialpoint')
do i = 1, material_Nhomogenization
write(datasetName,'(i0,a)') i,'_omega_homogenization'
call HDF5_read(groupHandle,homogState(i)%state0,datasetName)
enddo
call HDF5_closeGroup(groupHandle)
call HDF5_closeFile(fileHandle)
endif
if (interface_restartInc > 0) call crystallite_restartRead
end subroutine CPFEM_init
!--------------------------------------------------------------------------------------------------
!> @brief Forward data after successful increment.
! ToDo: Any guessing for the current states possible?
!--------------------------------------------------------------------------------------------------
subroutine CPFEM_forward
integer :: i, j
if (iand(debug_level(debug_CPFEM), debug_levelBasic) /= 0) &
write(6,'(a)') '<< CPFEM >> aging states'
crystallite_F0 = crystallite_partionedF
crystallite_Fp0 = crystallite_Fp
crystallite_Lp0 = crystallite_Lp
crystallite_Fi0 = crystallite_Fi
crystallite_Li0 = crystallite_Li
crystallite_S0 = crystallite_S
do i = 1, size(plasticState)
plasticState(i)%state0 = plasticState(i)%state
enddo
do i = 1, size(sourceState)
do j = 1,phase_Nsources(i)
sourceState(i)%p(j)%state0 = sourceState(i)%p(j)%state
enddo; enddo
do i = 1, material_Nhomogenization
homogState (i)%state0 = homogState (i)%state
thermalState(i)%state0 = thermalState(i)%state
damageState (i)%state0 = damageState (i)%state
enddo
end subroutine CPFEM_forward
!--------------------------------------------------------------------------------------------------
!> @brief Write current restart information (Field and constitutive data) to file.
!> @brief Write restart information.
!--------------------------------------------------------------------------------------------------
subroutine CPFEM_restartWrite
integer :: i
integer(HID_T) :: fileHandle, groupHandle
character(len=pStringLen) :: fileName, datasetName
write(6,'(a)') ' writing field and constitutive data required for restart to file';flush(6)
write(fileName,'(a,i0,a)') trim(getSolverJobName())//'_',worldrank,'.hdf5'
fileHandle = HDF5_openFile(fileName,'a')
call HDF5_write(fileHandle,crystallite_partionedF,'F')
call HDF5_write(fileHandle,crystallite_Fp, 'Fp')
call HDF5_write(fileHandle,crystallite_Fi, 'Fi')
call HDF5_write(fileHandle,crystallite_Lp, 'Lp')
call HDF5_write(fileHandle,crystallite_Li, 'Li')
call HDF5_write(fileHandle,crystallite_S, 'S')
groupHandle = HDF5_addGroup(fileHandle,'constituent')
do i = 1,size(phase_plasticity)
write(datasetName,'(i0,a)') i,'_omega_plastic'
call HDF5_write(groupHandle,plasticState(i)%state,datasetName)
enddo
call HDF5_closeGroup(groupHandle)
groupHandle = HDF5_addGroup(fileHandle,'materialpoint')
do i = 1, material_Nhomogenization
write(datasetName,'(i0,a)') i,'_omega_homogenization'
call HDF5_write(groupHandle,homogState(i)%state,datasetName)
enddo
call HDF5_closeGroup(groupHandle)
call HDF5_closeFile(fileHandle)
call crystallite_restartWrite
end subroutine CPFEM_restartWrite
!--------------------------------------------------------------------------------------------------
!> @brief Forward data for new time increment.
!--------------------------------------------------------------------------------------------------
subroutine CPFEM_forward
call crystallite_forward
end subroutine CPFEM_forward
!--------------------------------------------------------------------------------------------------
!> @brief Trigger writing of results.
!--------------------------------------------------------------------------------------------------

188
src/crystallite.f90
View File

@ -11,6 +11,8 @@
module crystallite
use prec
use IO
use HDF5_utilities
use DAMASK_interface
use config
use debug
use numerics
@ -36,25 +38,25 @@ module crystallite
crystallite_orientation !< current orientation
real(pReal), dimension(:,:,:,:,:), allocatable, public, protected :: &
crystallite_Fe, & !< current "elastic" def grad (end of converged time step)
crystallite_P !< 1st Piola-Kirchhoff stress per grain
crystallite_P, & !< 1st Piola-Kirchhoff stress per grain
crystallite_S0, & !< 2nd Piola-Kirchhoff stress vector at start of FE inc
crystallite_Fp0, & !< plastic def grad at start of FE inc
crystallite_Fi0, & !< intermediate def grad at start of FE inc
crystallite_F0, & !< def grad at start of FE inc
crystallite_Lp0, & !< plastic velocitiy grad at start of FE inc
crystallite_Li0 !< intermediate velocitiy grad at start of FE inc
real(pReal), dimension(:,:,:,:,:), allocatable, public :: &
crystallite_S, & !< current 2nd Piola-Kirchhoff stress vector (end of converged time step)
crystallite_S0, & !< 2nd Piola-Kirchhoff stress vector at start of FE inc
crystallite_partionedS0, & !< 2nd Piola-Kirchhoff stress vector at start of homog inc
crystallite_Fp, & !< current plastic def grad (end of converged time step)
crystallite_Fp0, & !< plastic def grad at start of FE inc
crystallite_partionedFp0,& !< plastic def grad at start of homog inc
crystallite_Fi, & !< current intermediate def grad (end of converged time step)
crystallite_Fi0, & !< intermediate def grad at start of FE inc
crystallite_partionedFi0,& !< intermediate def grad at start of homog inc
crystallite_F0, & !< def grad at start of FE inc
crystallite_partionedF, & !< def grad to be reached at end of homog inc
crystallite_partionedF0, & !< def grad at start of homog inc
crystallite_Lp, & !< current plastic velocitiy grad (end of converged time step)
crystallite_Lp0, & !< plastic velocitiy grad at start of FE inc
crystallite_partionedLp0, & !< plastic velocity grad at start of homog inc
crystallite_Li, & !< current intermediate velocitiy grad (end of converged time step)
crystallite_Li0, & !< intermediate velocitiy grad at start of FE inc
crystallite_partionedLi0 !< intermediate velocity grad at start of homog inc
real(pReal), dimension(:,:,:,:,:), allocatable :: &
crystallite_subFp0,& !< plastic def grad at start of crystallite inc
@ -104,7 +106,10 @@ module crystallite
crystallite_stressTangent, &
crystallite_orientations, &
crystallite_push33ToRef, &
crystallite_results
crystallite_results, &
crystallite_restartWrite, &
crystallite_restartRead, &
crystallite_forward
contains
@ -130,38 +135,30 @@ subroutine crystallite_init
iMax = discretization_nIP
eMax = discretization_nElem
allocate(crystallite_S0(3,3,cMax,iMax,eMax), source=0.0_pReal)
allocate(crystallite_partionedS0(3,3,cMax,iMax,eMax), source=0.0_pReal)
allocate(crystallite_S(3,3,cMax,iMax,eMax), source=0.0_pReal)
allocate(crystallite_P(3,3,cMax,iMax,eMax), source=0.0_pReal)
allocate(crystallite_F0(3,3,cMax,iMax,eMax), source=0.0_pReal)
allocate(crystallite_partionedF0(3,3,cMax,iMax,eMax), source=0.0_pReal)
allocate(crystallite_partionedF(3,3,cMax,iMax,eMax), source=0.0_pReal)
allocate(crystallite_subF0(3,3,cMax,iMax,eMax), source=0.0_pReal)
allocate(crystallite_subF(3,3,cMax,iMax,eMax), source=0.0_pReal)
allocate(crystallite_Fp0(3,3,cMax,iMax,eMax), source=0.0_pReal)
allocate(crystallite_partionedFp0(3,3,cMax,iMax,eMax), source=0.0_pReal)
allocate(crystallite_subFp0(3,3,cMax,iMax,eMax), source=0.0_pReal)
allocate(crystallite_Fp(3,3,cMax,iMax,eMax), source=0.0_pReal)
allocate(crystallite_Fi0(3,3,cMax,iMax,eMax), source=0.0_pReal)
allocate(crystallite_partionedFi0(3,3,cMax,iMax,eMax), source=0.0_pReal)
allocate(crystallite_subFi0(3,3,cMax,iMax,eMax), source=0.0_pReal)
allocate(crystallite_Fi(3,3,cMax,iMax,eMax), source=0.0_pReal)
allocate(crystallite_Fe(3,3,cMax,iMax,eMax), source=0.0_pReal)
allocate(crystallite_Lp0(3,3,cMax,iMax,eMax), source=0.0_pReal)
allocate(crystallite_partionedLp0(3,3,cMax,iMax,eMax), source=0.0_pReal)
allocate(crystallite_subLp0(3,3,cMax,iMax,eMax), source=0.0_pReal)
allocate(crystallite_Lp(3,3,cMax,iMax,eMax), source=0.0_pReal)
allocate(crystallite_Li0(3,3,cMax,iMax,eMax), source=0.0_pReal)
allocate(crystallite_partionedLi0(3,3,cMax,iMax,eMax), source=0.0_pReal)
allocate(crystallite_subLi0(3,3,cMax,iMax,eMax), source=0.0_pReal)
allocate(crystallite_Li(3,3,cMax,iMax,eMax), source=0.0_pReal)
allocate(crystallite_dPdF(3,3,3,3,cMax,iMax,eMax), source=0.0_pReal)
allocate(crystallite_dt(cMax,iMax,eMax), source=0.0_pReal)
allocate(crystallite_subdt(cMax,iMax,eMax), source=0.0_pReal)
allocate(crystallite_subFrac(cMax,iMax,eMax), source=0.0_pReal)
allocate(crystallite_subStep(cMax,iMax,eMax), source=0.0_pReal)
allocate(crystallite_partionedF(3,3,cMax,iMax,eMax),source=0.0_pReal)
allocate(crystallite_S0, &
crystallite_F0, crystallite_Fi0,crystallite_Fp0, &
crystallite_Li0,crystallite_Lp0, &
crystallite_partionedS0, &
crystallite_partionedF0,crystallite_partionedFp0,crystallite_partionedFi0, &
crystallite_partionedLp0,crystallite_partionedLi0, &
crystallite_S,crystallite_P, &
crystallite_Fe,crystallite_Fi,crystallite_Fp, &
crystallite_Li,crystallite_Lp, &
crystallite_subF,crystallite_subF0, &
crystallite_subFp0,crystallite_subFi0, &
crystallite_subLi0,crystallite_subLp0, &
source = crystallite_partionedF)
allocate(crystallite_dPdF(3,3,3,3,cMax,iMax,eMax),source=0.0_pReal)
allocate(crystallite_dt(cMax,iMax,eMax),source=0.0_pReal)
allocate(crystallite_subdt,crystallite_subFrac,crystallite_subStep, &
source = crystallite_dt)
allocate(crystallite_orientation(cMax,iMax,eMax))
allocate(crystallite_localPlasticity(cMax,iMax,eMax), source=.true.)
allocate(crystallite_requested(cMax,iMax,eMax), source=.false.)
allocate(crystallite_todo(cMax,iMax,eMax), source=.false.)
@ -1844,4 +1841,117 @@ logical function stateJump(ipc,ip,el)
end function stateJump
!--------------------------------------------------------------------------------------------------
!> @brief Write current restart information (Field and constitutive data) to file.
! ToDo: Merge data into one file for MPI, move state to constitutive and homogenization, respectively
!--------------------------------------------------------------------------------------------------
subroutine crystallite_restartWrite
integer :: i
integer(HID_T) :: fileHandle, groupHandle
character(len=pStringLen) :: fileName, datasetName
write(6,'(a)') ' writing field and constitutive data required for restart to file';flush(6)
write(fileName,'(a,i0,a)') trim(getSolverJobName())//'_',worldrank,'.hdf5'
fileHandle = HDF5_openFile(fileName,'a')
call HDF5_write(fileHandle,crystallite_partionedF,'F')
call HDF5_write(fileHandle,crystallite_Fp, 'Fp')
call HDF5_write(fileHandle,crystallite_Fi, 'Fi')
call HDF5_write(fileHandle,crystallite_Lp, 'Lp')
call HDF5_write(fileHandle,crystallite_Li, 'Li')
call HDF5_write(fileHandle,crystallite_S, 'S')
groupHandle = HDF5_addGroup(fileHandle,'constituent')
do i = 1,size(phase_plasticity)
write(datasetName,'(i0,a)') i,'_omega_plastic'
call HDF5_write(groupHandle,plasticState(i)%state,datasetName)
enddo
call HDF5_closeGroup(groupHandle)
groupHandle = HDF5_addGroup(fileHandle,'materialpoint')
do i = 1, material_Nhomogenization
write(datasetName,'(i0,a)') i,'_omega_homogenization'
call HDF5_write(groupHandle,homogState(i)%state,datasetName)
enddo
call HDF5_closeGroup(groupHandle)
call HDF5_closeFile(fileHandle)
end subroutine crystallite_restartWrite
!--------------------------------------------------------------------------------------------------
!> @brief Read data for restart
! ToDo: Merge data into one file for MPI, move state to constitutive and homogenization, respectively
!--------------------------------------------------------------------------------------------------
subroutine crystallite_restartRead
integer :: i
integer(HID_T) :: fileHandle, groupHandle
character(len=pStringLen) :: fileName, datasetName
write(6,'(/,a,i0,a)') ' reading restart information of increment from file'
write(fileName,'(a,i0,a)') trim(getSolverJobName())//'_',worldrank,'.hdf5'
fileHandle = HDF5_openFile(fileName)
call HDF5_read(fileHandle,crystallite_F0, 'F')
call HDF5_read(fileHandle,crystallite_Fp0,'Fp')
call HDF5_read(fileHandle,crystallite_Fi0,'Fi')
call HDF5_read(fileHandle,crystallite_Lp0,'Lp')
call HDF5_read(fileHandle,crystallite_Li0,'Li')
call HDF5_read(fileHandle,crystallite_S0, 'S')
groupHandle = HDF5_openGroup(fileHandle,'constituent')
do i = 1,size(phase_plasticity)
write(datasetName,'(i0,a)') i,'_omega_plastic'
call HDF5_read(groupHandle,plasticState(i)%state0,datasetName)
enddo
call HDF5_closeGroup(groupHandle)
groupHandle = HDF5_openGroup(fileHandle,'materialpoint')
do i = 1, material_Nhomogenization
write(datasetName,'(i0,a)') i,'_omega_homogenization'
call HDF5_read(groupHandle,homogState(i)%state0,datasetName)
enddo
call HDF5_closeGroup(groupHandle)
call HDF5_closeFile(fileHandle)
end subroutine crystallite_restartRead
!--------------------------------------------------------------------------------------------------
!> @brief Forward data after successful increment.
! ToDo: Any guessing for the current states possible?
!--------------------------------------------------------------------------------------------------
subroutine crystallite_forward
integer :: i, j
crystallite_F0 = crystallite_partionedF
crystallite_Fp0 = crystallite_Fp
crystallite_Lp0 = crystallite_Lp
crystallite_Fi0 = crystallite_Fi
crystallite_Li0 = crystallite_Li
crystallite_S0 = crystallite_S
do i = 1, size(plasticState)
plasticState(i)%state0 = plasticState(i)%state
enddo
do i = 1, size(sourceState)
do j = 1,phase_Nsources(i)
sourceState(i)%p(j)%state0 = sourceState(i)%p(j)%state
enddo; enddo
do i = 1, material_Nhomogenization
homogState (i)%state0 = homogState (i)%state
thermalState(i)%state0 = thermalState(i)%state
damageState (i)%state0 = damageState (i)%state
enddo
end subroutine crystallite_forward
end module crystallite

4
src/homogenization_mech_RGC.f90
View File

@ -669,7 +669,7 @@ module procedure mech_RGC_updateState
nDef = 0.0_pReal
do i = 1,3; do j = 1,3
do k = 1,3; do l = 1,3
nDef(i,j) = nDef(i,j) - nVect(k)*gDef(i,l)*math_civita(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
enddo; enddo
nDefNorm = nDefNorm + nDef(i,j)**2.0_pReal ! compute the norm of the mismatch tensor
enddo; enddo
@ -689,7 +689,7 @@ module procedure mech_RGC_updateState
rPen(i,j,iGrain) = rPen(i,j,iGrain) + 0.5_pReal*(muGrain*bgGrain + muGNghb*bgGNghb)*prm%xiAlpha &
*surfCorr(abs(intFace(1)))/prm%dAlpha(abs(intFace(1))) &
*cosh(prm%ciAlpha*nDefNorm) &
*0.5_pReal*nVect(l)*nDef(i,k)/nDefNorm*math_civita(k,l,j) &
*0.5_pReal*nVect(l)*nDef(i,k)/nDefNorm*math_LeviCivita(k,l,j) &
*tanh(nDefNorm/xSmoo_RGC)
enddo; enddo;enddo; enddo
enddo interfaceLoop

70
src/math.f90
View File

@ -73,6 +73,11 @@ module math
3,3 &
],[2,9]) !< arrangement in Plain notation
interface math_mul33xx33
module procedure math_tensordot
end interface math_mul33xx33
!---------------------------------------------------------------------------------------------------
private :: &
unitTest
@ -266,31 +271,30 @@ end function math_identity4th
!--------------------------------------------------------------------------------------------------
!> @brief permutation tensor e_ijk used for computing cross product of two tensors
!> @brief permutation tensor e_ijk
! e_ijk = 1 if even permutation of ijk
! e_ijk = -1 if odd permutation of ijk
! e_ijk = 0 otherwise
!--------------------------------------------------------------------------------------------------
real(pReal) pure function math_civita(i,j,k)
real(pReal) pure function math_LeviCivita(i,j,k)
integer, intent(in) :: i,j,k
math_civita = 0.0_pReal
if (((i == 1).and.(j == 2).and.(k == 3)) .or. &
((i == 2).and.(j == 3).and.(k == 1)) .or. &
((i == 3).and.(j == 1).and.(k == 2))) math_civita = 1.0_pReal
if (((i == 1).and.(j == 3).and.(k == 2)) .or. &
((i == 2).and.(j == 1).and.(k == 3)) .or. &
((i == 3).and.(j == 2).and.(k == 1))) math_civita = -1.0_pReal
if (all([i,j,k] == [1,2,3]) .or. all([i,j,k] == [2,3,1]) .or. all([i,j,k] == [3,1,2])) then
math_LeviCivita = +1.0_pReal
elseif (all([i,j,k] == [3,2,1]) .or. all([i,j,k] == [2,1,3]) .or. all([i,j,k] == [1,3,2])) then
math_LeviCivita = -1.0_pReal
else
math_LeviCivita = 0.0_pReal
endif
end function math_civita
end function math_LeviCivita
!--------------------------------------------------------------------------------------------------
!> @brief kronecker delta function d_ij
! d_ij = 1 if i = j
! d_ij = 0 otherwise
! inspired by http://fortraninacworld.blogspot.de/2012/12/ternary-operator.html
!--------------------------------------------------------------------------------------------------
real(pReal) pure function math_delta(i,j)
@ -317,7 +321,7 @@ end function math_cross
!--------------------------------------------------------------------------------------------------
!> @brief outer product A \otimes B of arbitrary sized vectors A and B
!> @brief outer product of arbitrary sized vectors (A ⊗ B / i,j)
!--------------------------------------------------------------------------------------------------
pure function math_outer(A,B)
@ -333,7 +337,7 @@ end function math_outer
!--------------------------------------------------------------------------------------------------
!> @brief outer product A \otimes B of arbitrary sized vectors A and B
!> @brief inner product of arbitrary sized vectors (A · B / i,i)
!--------------------------------------------------------------------------------------------------
real(pReal) pure function math_inner(A,B)
@ -346,24 +350,19 @@ end function math_inner
!--------------------------------------------------------------------------------------------------
!> @brief matrix multiplication 33xx33 = 1 (double contraction --> ij * ij)
!> @brief double contraction of 3x3 matrices (A : B / ij,ij)
!--------------------------------------------------------------------------------------------------
real(pReal) pure function math_mul33xx33(A,B)
real(pReal) pure function math_tensordot(A,B)
real(pReal), dimension(3,3), intent(in) :: A,B
integer :: i,j
real(pReal), dimension(3,3) :: C
do i=1,3; do j=1,3
C(i,j) = A(i,j) * B(i,j)
enddo; enddo
math_mul33xx33 = sum(C)
math_tensordot = sum(A*B)
end function math_mul33xx33
end function math_tensordot
!--------------------------------------------------------------------------------------------------
!> @brief matrix multiplication 3333x33 = 33 (double contraction --> ijkl *kl = ij)
!> @brief matrix double contraction 3333x33 = 33 (ijkl,kl)
!--------------------------------------------------------------------------------------------------
pure function math_mul3333xx33(A,B)
@ -380,7 +379,7 @@ end function math_mul3333xx33
!--------------------------------------------------------------------------------------------------
!> @brief matrix multiplication 3333x3333 = 3333 (ijkl *klmn = ijmn)
!> @brief matrix multiplication 3333x3333 = 3333 (ijkl,klmn)
!--------------------------------------------------------------------------------------------------
pure function math_mul3333xx3333(A,B)
@ -404,6 +403,7 @@ pure function math_exp33(A,n)
real(pReal), dimension(3,3), intent(in) :: A
integer, intent(in), optional :: n
real(pReal), dimension(3,3) :: B, math_exp33
real(pReal) :: invFac
integer :: n_,i
@ -433,9 +433,10 @@ end function math_exp33
!--------------------------------------------------------------------------------------------------
pure function math_inv33(A)
real(pReal),dimension(3,3),intent(in) :: A
real(pReal), dimension(3,3), intent(in) :: A
real(pReal), dimension(3,3) :: math_inv33
real(pReal) :: DetA
real(pReal),dimension(3,3) :: math_inv33
logical :: error
call math_invert33(math_inv33,DetA,error,A)
@ -451,10 +452,10 @@ end function math_inv33
!--------------------------------------------------------------------------------------------------
pure subroutine math_invert33(InvA, DetA, error, A)
logical, intent(out) :: error
real(pReal),dimension(3,3),intent(in) :: A
real(pReal),dimension(3,3),intent(out) :: InvA
real(pReal), dimension(3,3), intent(out) :: InvA
real(pReal), intent(out) :: DetA
logical, intent(out) :: error
real(pReal), dimension(3,3), intent(in) :: A
InvA(1,1) = A(2,2) * A(3,3) - A(2,3) * A(3,2)
InvA(2,1) = -A(2,1) * A(3,3) + A(2,3) * A(3,1)
@ -1307,6 +1308,7 @@ subroutine unitTest
sort_out_ = reshape([-1,-1, +1,+5, +5,+6, +3,-2],[2,4])
integer, dimension(5) :: range_out_ = [1,2,3,4,5]
integer, dimension(3) :: ijk
real(pReal) :: det
real(pReal), dimension(3) :: v3_1,v3_2,v3_3,v3_4
@ -1423,6 +1425,16 @@ subroutine unitTest
if(math_binomial(49,6) /= 13983816) &
call IO_error(0,ext_msg='math_binomial')
ijk = cshift([1,2,3],int(r*1.0e2_pReal))
if(dNeq(math_LeviCivita(ijk(1),ijk(2),ijk(3)),+1.0_pReal)) &
call IO_error(0,ext_msg='math_LeviCivita(even)')
ijk = cshift([3,2,1],int(r*2.0e2_pReal))
if(dNeq(math_LeviCivita(ijk(1),ijk(2),ijk(3)),-1.0_pReal)) &
call IO_error(0,ext_msg='math_LeviCivita(odd)')
ijk = cshift([2,2,1],int(r*2.0e2_pReal))
if(dNeq0(math_LeviCivita(ijk(1),ijk(2),ijk(3))))&
call IO_error(0,ext_msg='math_LeviCivita')
end subroutine unitTest
end module math