DAMASK_EICMD/processing/post/addCompatibilityMismatch.py

198 lines
8.5 KiB
Python
Raw Normal View History

#!/usr/bin/env python3
2011-08-25 22:14:36 +05:30
import os
2019-12-21 19:42:01 +05:30
import sys
2019-12-21 22:49:54 +05:30
from io import StringIO
from optparse import OptionParser
import numpy as np
import damask
2011-08-25 22:14:36 +05:30
scriptName = os.path.splitext(os.path.basename(__file__))[0]
scriptID = ' '.join([scriptName,damask.version])
2011-08-25 22:14:36 +05:30
2016-03-24 18:49:00 +05:30
def volTetrahedron(coords):
2016-03-24 17:05:33 +05:30
"""
2016-04-15 04:02:30 +05:30
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
2016-03-24 17:05:33 +05:30
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
2016-03-24 18:49:00 +05:30
vertices = np.concatenate((coords[0],coords[1],coords[2],coords[3])).reshape([4,3])
2016-03-24 17:05:33 +05:30
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
2016-03-24 18:49:00 +05:30
return np.sqrt(np.linalg.det(M) / 288)
2016-03-24 17:05:33 +05:30
2016-03-24 18:49:00 +05:30
def volumeMismatch(size,F,nodes):
2016-03-24 17:05:33 +05:30
"""
2019-12-21 22:49:54 +05:30
Calculates the volume mismatch.
2016-04-15 04:02:30 +05:30
volume mismatch is defined as the difference between volume of reconstructed
2019-12-21 22:49:54 +05:30
(compatible) cube and determinant of deformation gradient at Fourier point.
2016-03-24 17:05:33 +05:30
"""
2016-03-24 18:49:00 +05:30
coords = np.empty([8,3])
vMismatch = np.empty(grid[::-1])
2016-03-24 18:49:00 +05:30
volInitial = size.prod()/grid.prod()
2016-03-24 17:05:33 +05:30
#--------------------------------------------------------------------------------------------------
# calculate actual volume and volume resulting from deformation gradient
2016-10-25 00:46:29 +05:30
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]])) \
2016-03-24 18:49:00 +05:30
+ 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])
2016-03-24 18:49:00 +05:30
return vMismatch/volInitial
def shapeMismatch(size,F,nodes,centres):
2016-03-24 17:05:33 +05:30
"""
2019-12-21 22:49:54 +05:30
Routine to calculate the shape mismatch.
2016-04-15 04:02:30 +05:30
shape mismatch is defined as difference between the vectors from the central point to
2016-03-24 17:05:33 +05:30
the corners of reconstructed (combatible) volume element and the vectors calculated by deforming
2019-12-21 22:49:54 +05:30
the initial volume element with the current deformation gradient.
2016-03-24 17:05:33 +05:30
"""
2016-03-24 18:49:00 +05:30
coordsInitial = np.empty([8,3])
sMismatch = np.empty(grid[::-1])
2016-03-24 17:05:33 +05:30
2016-03-24 18:49:00 +05:30
#--------------------------------------------------------------------------------------------------
# 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
2016-03-24 17:05:33 +05:30
2016-03-24 18:49:00 +05:30
#--------------------------------------------------------------------------------------------------
# compare deformed original and deformed positions to actual positions
2016-10-25 00:46:29 +05:30
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]))
2016-03-24 18:49:00 +05:30
return sMismatch
2016-03-24 17:05:33 +05:30
2011-08-25 22:14:36 +05:30
# --------------------------------------------------------------------
# MAIN
# --------------------------------------------------------------------
2019-02-16 22:11:56 +05:30
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.
2011-08-25 22:14:36 +05:30
""", version = scriptID)
2011-08-25 22:14:36 +05:30
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,
)
2011-08-25 22:14:36 +05:30
(options,filenames) = parser.parse_args()
if filenames == []: filenames = [None]
2019-12-21 19:42:01 +05:30
for name in filenames:
damask.util.report(scriptName,name)
2019-12-21 19:42:01 +05:30
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))
F = table.get(options.defgrad).reshape(grid[2],grid[1],grid[0],3,3)
nodes = damask.grid_filters.node_coord(size,F)
if options.shape:
centres = damask.grid_filters.cell_coord(size,F)
2019-12-21 19:42:01 +05:30
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:
2019-12-21 19:42:01 +05:30
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:]))
2019-12-21 19:42:01 +05:30
table.to_ASCII(sys.stdout if name is None else name)