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DAMASK_EICMD
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do not rely on singular value decomposition

This commit is contained in:
Martin Diehl 2019-12-23 09:52:42 +01:00
parent 93bc66d19f
commit d26005960c
1 changed files with 8 additions and 10 deletions
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18
processing/post/addStrainTensors.py
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@ -15,12 +15,12 @@ scriptID = ' '.join([scriptName,damask.version])
def operator(stretch,strain,eigenvalues): def operator(stretch,strain,eigenvalues):
"""Albrecht Bertram: Elasticity and Plasticity of Large Deformations An Introduction (3rd Edition, 2012), p. 102.""" """Albrecht Bertram: Elasticity and Plasticity of Large Deformations An Introduction (3rd Edition, 2012), p. 102."""
return { return {
'V#ln': np.log(eigenvalues) , 'V#ln': np.log(eigenvalues)*.5 ,
'U#ln': np.log(eigenvalues) , 'U#ln': np.log(eigenvalues)*.5 ,
'V#Biot': ( np.ones(3,'d') - eigenvalues**-1.0) , 'V#Biot': ( np.ones(3,'d') - eigenvalues**-0.5) ,
'U#Biot': ( eigenvalues**1.0 - np.ones(3,'d')) , 'U#Biot': ( eigenvalues**0.5 - np.ones(3,'d')) ,
'V#Green': ( np.ones(3,'d') - eigenvalues**-2.0)*0.5, 'V#Green': ( np.ones(3,'d') - eigenvalues**-1.0)*0.5,
'U#Green': ( eigenvalues**2.0 - np.ones(3,'d')) *0.5, 'U#Green': ( eigenvalues**1.0 - np.ones(3,'d')) *0.5,
}[stretch+'#'+strain] }[stretch+'#'+strain]
@ -135,10 +135,8 @@ for name in filenames:
while outputAlive and table.data_read(): # read next data line of ASCII table while outputAlive and table.data_read(): # read next data line of ASCII table
for column in items['tensor']['column']: # loop over all requested defgrads for column in items['tensor']['column']: # loop over all requested defgrads
F = np.array(list(map(float,table.data[column:column+items['tensor']['dim']])),'d').reshape(items['tensor']['shape']) F = np.array(list(map(float,table.data[column:column+items['tensor']['dim']])),'d').reshape(items['tensor']['shape'])
(U,S,Vh) = np.linalg.svd(F) # singular value decomposition stretch['V'] = np.dot(F,F.T) # F = VR
R_inv = np.dot(U,Vh).T # rotation of polar decomposition stretch['U'] = np.dot(F.T,F) # F = RU
stretch['V'] = np.dot(F,R_inv) # F = VR
stretch['U'] = np.dot(R_inv,F) # F = RU
for theStretch in stretches: for theStretch in stretches:
(D,V) = np.linalg.eigh((stretch[theStretch]+stretch[theStretch].T)*0.5) # eigen decomposition (of symmetric(ed) matrix) (D,V) = np.linalg.eigh((stretch[theStretch]+stretch[theStretch].T)*0.5) # eigen decomposition (of symmetric(ed) matrix)