DAMASK_EICMD/processing/post/addCompatibilityMismatch.py

254 lines
12 KiB
Python
Executable File

#!/usr/bin/env python3
import os
import math
import sys
from optparse import OptionParser
import numpy as np
import damask
scriptName = os.path.splitext(os.path.basename(__file__))[0]
scriptID = ' '.join([scriptName,damask.version])
#--------------------------------------------------------------------------------------------------
def deformationAvgFFT(F,grid,size,nodal=False,transformed=False):
"""Calculate average cell center (or nodal) deformation for deformation gradient field specified in each grid cell"""
if nodal:
x, y, z = np.meshgrid(np.linspace(0,size[2],1+grid[2]),
np.linspace(0,size[1],1+grid[1]),
np.linspace(0,size[0],1+grid[0]),
indexing = 'ij')
else:
x, y, z = np.meshgrid(np.linspace(size[2]/grid[2]/2.,size[2]-size[2]/grid[2]/2.,grid[2]),
np.linspace(size[1]/grid[1]/2.,size[1]-size[1]/grid[1]/2.,grid[1]),
np.linspace(size[0]/grid[0]/2.,size[0]-size[0]/grid[0]/2.,grid[0]),
indexing = 'ij')
origCoords = np.concatenate((z[:,:,:,None],y[:,:,:,None],x[:,:,:,None]),axis = 3)
F_fourier = F if transformed else np.fft.rfftn(F,axes=(0,1,2)) # transform or use provided data
Favg = np.real(F_fourier[0,0,0,:,:])/grid.prod() # take zero freq for average
avgDeformation = np.einsum('ml,ijkl->ijkm',Favg,origCoords) # dX = Favg.X
return avgDeformation
#--------------------------------------------------------------------------------------------------
def displacementFluctFFT(F,grid,size,nodal=False,transformed=False):
"""Calculate cell center (or nodal) displacement for deformation gradient field specified in each grid cell"""
integrator = 0.5j * size / math.pi
kk, kj, ki = np.meshgrid(np.where(np.arange(grid[2])>grid[2]//2,np.arange(grid[2])-grid[2],np.arange(grid[2])),
np.where(np.arange(grid[1])>grid[1]//2,np.arange(grid[1])-grid[1],np.arange(grid[1])),
np.arange(grid[0]//2+1),
indexing = 'ij')
k_s = np.concatenate((ki[:,:,:,None],kj[:,:,:,None],kk[:,:,:,None]),axis = 3)
k_sSquared = np.einsum('...l,...l',k_s,k_s)
k_sSquared[0,0,0] = 1.0 # ignore global average frequency
#--------------------------------------------------------------------------------------------------
# integration in Fourier space
displacement_fourier = -np.einsum('ijkml,ijkl,l->ijkm',
F if transformed else np.fft.rfftn(F,axes=(0,1,2)),
k_s,
integrator,
) / k_sSquared[...,np.newaxis]
#--------------------------------------------------------------------------------------------------
# backtransformation to real space
displacement = np.fft.irfftn(displacement_fourier,grid[::-1],axes=(0,1,2))
return damask.grid_filters.cell_2_node(displacement) if nodal else displacement
def volTetrahedron(coords):
"""
Return the volume of the tetrahedron with given vertices or sides.
Ifvertices are given they must be in a NumPy array with shape (4,3): the
position vectors of the 4 vertices in 3 dimensions; if the six sides are
given, they must be an array of length 6. If both are given, the sides
will be used in the calculation.
This method implements
Tartaglia's formula using the Cayley-Menger determinant:
|0 1 1 1 1 |
|1 0 s1^2 s2^2 s3^2|
288 V^2 = |1 s1^2 0 s4^2 s5^2|
|1 s2^2 s4^2 0 s6^2|
|1 s3^2 s5^2 s6^2 0 |
where s1, s2, ..., s6 are the tetrahedron side lengths.
from http://codereview.stackexchange.com/questions/77593/calculating-the-volume-of-a-tetrahedron
"""
# The indexes of rows in the vertices array corresponding to all
# possible pairs of vertices
vertex_pair_indexes = np.array(((0, 1), (0, 2), (0, 3),
(1, 2), (1, 3), (2, 3)))
# Get all the squares of all side lengths from the differences between
# the 6 different pairs of vertex positions
vertices = np.concatenate((coords[0],coords[1],coords[2],coords[3])).reshape([4,3])
vertex1, vertex2 = vertex_pair_indexes[:,0], vertex_pair_indexes[:,1]
sides_squared = np.sum((vertices[vertex1] - vertices[vertex2])**2,axis=-1)
# Set up the Cayley-Menger determinant
M = np.zeros((5,5))
# Fill in the upper triangle of the matrix
M[0,1:] = 1
# The squared-side length elements can be indexed using the vertex
# pair indices (compare with the determinant illustrated above)
M[tuple(zip(*(vertex_pair_indexes + 1)))] = sides_squared
# The matrix is symmetric, so we can fill in the lower triangle by
# adding the transpose
M = M + M.T
return np.sqrt(np.linalg.det(M) / 288)
def volumeMismatch(size,F,nodes):
"""
Calculates the volume mismatch
volume mismatch is defined as the difference between volume of reconstructed
(compatible) cube and determinant of defgrad at the FP
"""
coords = np.empty([8,3])
vMismatch = np.empty(grid[::-1])
volInitial = size.prod()/grid.prod()
#--------------------------------------------------------------------------------------------------
# calculate actual volume and volume resulting from deformation gradient
for k in range(grid[2]):
for j in range(grid[1]):
for i in range(grid[0]):
coords[0,0:3] = nodes[k, j, i ,0:3]
coords[1,0:3] = nodes[k ,j, i+1,0:3]
coords[2,0:3] = nodes[k ,j+1,i+1,0:3]
coords[3,0:3] = nodes[k, j+1,i ,0:3]
coords[4,0:3] = nodes[k+1,j, i ,0:3]
coords[5,0:3] = nodes[k+1,j, i+1,0:3]
coords[6,0:3] = nodes[k+1,j+1,i+1,0:3]
coords[7,0:3] = nodes[k+1,j+1,i ,0:3]
vMismatch[k,j,i] = \
( abs(volTetrahedron([coords[6,0:3],coords[0,0:3],coords[7,0:3],coords[3,0:3]])) \
+ abs(volTetrahedron([coords[6,0:3],coords[0,0:3],coords[7,0:3],coords[4,0:3]])) \
+ abs(volTetrahedron([coords[6,0:3],coords[0,0:3],coords[2,0:3],coords[3,0:3]])) \
+ abs(volTetrahedron([coords[6,0:3],coords[0,0:3],coords[2,0:3],coords[1,0:3]])) \
+ abs(volTetrahedron([coords[6,0:3],coords[4,0:3],coords[1,0:3],coords[5,0:3]])) \
+ abs(volTetrahedron([coords[6,0:3],coords[4,0:3],coords[1,0:3],coords[0,0:3]]))) \
/np.linalg.det(F[k,j,i,0:3,0:3])
return vMismatch/volInitial
def shapeMismatch(size,F,nodes,centres):
"""
Routine to calculate the shape mismatch
shape mismatch is defined as difference between the vectors from the central point to
the corners of reconstructed (combatible) volume element and the vectors calculated by deforming
the initial volume element with the current deformation gradient
"""
coordsInitial = np.empty([8,3])
sMismatch = np.empty(grid[::-1])
#--------------------------------------------------------------------------------------------------
# initial positions
coordsInitial[0,0:3] = [-size[0]/grid[0],-size[1]/grid[1],-size[2]/grid[2]]
coordsInitial[1,0:3] = [+size[0]/grid[0],-size[1]/grid[1],-size[2]/grid[2]]
coordsInitial[2,0:3] = [+size[0]/grid[0],+size[1]/grid[1],-size[2]/grid[2]]
coordsInitial[3,0:3] = [-size[0]/grid[0],+size[1]/grid[1],-size[2]/grid[2]]
coordsInitial[4,0:3] = [-size[0]/grid[0],-size[1]/grid[1],+size[2]/grid[2]]
coordsInitial[5,0:3] = [+size[0]/grid[0],-size[1]/grid[1],+size[2]/grid[2]]
coordsInitial[6,0:3] = [+size[0]/grid[0],+size[1]/grid[1],+size[2]/grid[2]]
coordsInitial[7,0:3] = [-size[0]/grid[0],+size[1]/grid[1],+size[2]/grid[2]]
coordsInitial = coordsInitial/2.0
#--------------------------------------------------------------------------------------------------
# compare deformed original and deformed positions to actual positions
for k in range(grid[2]):
for j in range(grid[1]):
for i in range(grid[0]):
sMismatch[k,j,i] = \
+ np.linalg.norm(nodes[k, j, i ,0:3] - centres[k,j,i,0:3] - np.dot(F[k,j,i,:,:], coordsInitial[0,0:3]))\
+ np.linalg.norm(nodes[k, j, i+1,0:3] - centres[k,j,i,0:3] - np.dot(F[k,j,i,:,:], coordsInitial[1,0:3]))\
+ np.linalg.norm(nodes[k, j+1,i+1,0:3] - centres[k,j,i,0:3] - np.dot(F[k,j,i,:,:], coordsInitial[2,0:3]))\
+ np.linalg.norm(nodes[k, j+1,i ,0:3] - centres[k,j,i,0:3] - np.dot(F[k,j,i,:,:], coordsInitial[3,0:3]))\
+ np.linalg.norm(nodes[k+1,j, i ,0:3] - centres[k,j,i,0:3] - np.dot(F[k,j,i,:,:], coordsInitial[4,0:3]))\
+ np.linalg.norm(nodes[k+1,j, i+1,0:3] - centres[k,j,i,0:3] - np.dot(F[k,j,i,:,:], coordsInitial[5,0:3]))\
+ np.linalg.norm(nodes[k+1,j+1,i+1,0:3] - centres[k,j,i,0:3] - np.dot(F[k,j,i,:,:], coordsInitial[6,0:3]))\
+ np.linalg.norm(nodes[k+1,j+1,i ,0:3] - centres[k,j,i,0:3] - np.dot(F[k,j,i,:,:], coordsInitial[7,0:3]))
return sMismatch
# --------------------------------------------------------------------
# MAIN
# --------------------------------------------------------------------
parser = OptionParser(option_class=damask.extendableOption, usage='%prog options [ASCIItable(s)]', description = """
Add column(s) containing the shape and volume mismatch resulting from given deformation gradient.
Operates on periodic three-dimensional x,y,z-ordered data sets.
""", version = scriptID)
parser.add_option('-c','--coordinates',
dest = 'pos',
type = 'string', metavar = 'string',
help = 'column heading of coordinates [%default]')
parser.add_option('-f','--defgrad',
dest = 'defgrad',
type = 'string', metavar = 'string ',
help = 'column heading of deformation gradient [%default]')
parser.add_option('--no-shape','-s',
dest = 'shape',
action = 'store_false',
help = 'omit shape mismatch')
parser.add_option('--no-volume','-v',
dest = 'volume',
action = 'store_false',
help = 'omit volume mismatch')
parser.set_defaults(pos = 'pos',
defgrad = 'f',
shape = True,
volume = True,
)
(options,filenames) = parser.parse_args()
if filenames == []: filenames = [None]
for name in filenames:
damask.util.report(scriptName,name)
table = damask.Table.from_ASCII(StringIO(''.join(sys.stdin.read())) if name is None else name)
grid,size,origin = damask.grid_filters.cell_coord0_2_DNA(table.get(options.pos))
N = grid.prod()
F_fourier = np.fft.rfftn(table.get(options.defgrad).reshape(grid[2],grid[1],grid[0],3,3),axes=(0,1,2)) # perform transform only once...
nodes = displacementFluctFFT(F_fourier,grid,size,True,transformed=True)\
+ deformationAvgFFT (F_fourier,grid,size,True,transformed=True)
if options.shape:
centres = displacementFluctFFT(F_fourier,grid,size,False,transformed=True)\
+ deformationAvgFFT (F_fourier,grid,size,False,transformed=True)
shapeMismatch = shapeMismatch( size,table.get(options.defgrad).reshape(grid[2],grid[1],grid[0],3,3),nodes,centres)
table.add('shapeMismatch(({}))'.format(options.defgrad),
shapeMismatch.reshape((-1,1)),
scriptID+' '+' '.join(sys.argv[1:]))
if options.volume:
volumeMismatch = volumeMismatch(size,table.get(options.defgrad).reshape(grid[2],grid[1],grid[0],3,3),nodes)
table.add('volMismatch(({}))'.format(options.defgrad),
volumeMismatch.reshape((-1,1)),
scriptID+' '+' '.join(sys.argv[1:]))
table.to_ASCII(sys.stdout if name is None else name)