volume mismatch is unreliable

the volume of a deformed hexahedron is not properly defined, the
approximation error is in the order of the deviation from 1.0 (for
typical crystal plasticity cases)
This commit is contained in:
Martin Diehl 2020-11-23 20:47:05 +01:00
parent 5d2d92ff6b
commit 198736a859
1 changed files with 0 additions and 89 deletions

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@ -13,85 +13,6 @@ import damask
scriptName = os.path.splitext(os.path.basename(__file__))[0] scriptName = os.path.splitext(os.path.basename(__file__))[0]
scriptID = ' '.join([scriptName,damask.version]) scriptID = ' '.join([scriptName,damask.version])
def volTetrahedron(coords):
"""
Return the volume of the tetrahedron with given vertices or sides.
If vertices 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 deformation gradient at Fourier point.
"""
coords = np.empty([8,3])
vMismatch = np.empty(F.shape[:3])
#--------------------------------------------------------------------------------------------------
# calculate actual volume and volume resulting from deformation gradient
for k in range(grid[0]):
for j in range(grid[1]):
for i in range(grid[2]):
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/(size.prod()/grid.prod())
def shapeMismatch(size,F,nodes,centres): def shapeMismatch(size,F,nodes,centres):
""" """
@ -155,10 +76,6 @@ parser.add_option('--no-shape','-s',
dest = 'shape', dest = 'shape',
action = 'store_false', action = 'store_false',
help = 'omit shape mismatch') help = 'omit shape mismatch')
parser.add_option('--no-volume','-v',
dest = 'volume',
action = 'store_false',
help = 'omit volume mismatch')
parser.set_defaults(pos = 'pos', parser.set_defaults(pos = 'pos',
defgrad = 'f', defgrad = 'f',
shape = True, shape = True,
@ -185,10 +102,4 @@ for name in filenames:
shapeMismatch.reshape(-1,1,order='F'), shapeMismatch.reshape(-1,1,order='F'),
scriptID+' '+' '.join(sys.argv[1:])) scriptID+' '+' '.join(sys.argv[1:]))
if options.volume:
volumeMismatch = volumeMismatch(size,F,nodes)
table = table.add('volMismatch(({}))'.format(options.defgrad),
volumeMismatch.reshape(-1,1,order='F'),
scriptID+' '+' '.join(sys.argv[1:]))
table.save((sys.stdout if name is None else name), legacy=True) table.save((sys.stdout if name is None else name), legacy=True)