166 lines
7.5 KiB
Python
Executable File
166 lines
7.5 KiB
Python
Executable File
#!/usr/bin/env python3
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import os
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import sys
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from optparse import OptionParser
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import numpy as np
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import damask
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scriptName = os.path.splitext(os.path.basename(__file__))[0]
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scriptID = ' '.join([scriptName,damask.version])
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def operator(stretch,strain,eigenvalues):
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"""Albrecht Bertram: Elasticity and Plasticity of Large Deformations An Introduction (3rd Edition, 2012), p. 102"""
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return {
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'V#ln': np.log(eigenvalues) ,
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'U#ln': np.log(eigenvalues) ,
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'V#Biot': ( np.ones(3,'d') - 1.0/eigenvalues ) ,
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'U#Biot': ( eigenvalues - np.ones(3,'d') ) ,
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'V#Green': ( np.ones(3,'d') - 1.0/eigenvalues/eigenvalues) *0.5,
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'U#Green': ( eigenvalues*eigenvalues - np.ones(3,'d')) *0.5,
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}[stretch+'#'+strain]
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# --------------------------------------------------------------------
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# MAIN
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# --------------------------------------------------------------------
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parser = OptionParser(option_class=damask.extendableOption, usage='%prog options [ASCIItable(s)]', description = """
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Add column(s) containing given strains based on given stretches of requested deformation gradient column(s).
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""", version = scriptID)
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parser.add_option('-u','--right',
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dest = 'right',
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action = 'store_true',
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help = 'material strains based on right Cauchy--Green deformation, i.e., C and U')
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parser.add_option('-v','--left',
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dest = 'left',
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action = 'store_true',
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help = 'spatial strains based on left Cauchy--Green deformation, i.e., B and V')
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parser.add_option('-0','--logarithmic',
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dest = 'logarithmic',
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action = 'store_true',
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help = 'calculate logarithmic strain tensor')
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parser.add_option('-1','--biot',
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dest = 'biot',
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action = 'store_true',
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help = 'calculate biot strain tensor')
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parser.add_option('-2','--green',
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dest = 'green',
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action = 'store_true',
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help = 'calculate green strain tensor')
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parser.add_option('-f','--defgrad',
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dest = 'defgrad',
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action = 'extend',
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metavar = '<string LIST>',
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help = 'heading(s) of columns containing deformation tensor values [%default]')
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parser.set_defaults(
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defgrad = ['f'],
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)
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(options,filenames) = parser.parse_args()
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if len(options.defgrad) > 1:
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options.defgrad = options.defgrad[1:]
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stretches = []
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strains = []
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if options.right: stretches.append('U')
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if options.left: stretches.append('V')
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if options.logarithmic: strains.append('ln')
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if options.biot: strains.append('Biot')
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if options.green: strains.append('Green')
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if options.defgrad is None:
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parser.error('no data column specified.')
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# --- loop over input files -------------------------------------------------------------------------
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if filenames == []: filenames = [None]
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for name in filenames:
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try:
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table = damask.ASCIItable(name = name,
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buffered = False)
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except: continue
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damask.util.report(scriptName,name)
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# ------------------------------------------ read header ------------------------------------------
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table.head_read()
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# ------------------------------------------ sanity checks ----------------------------------------
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items = {
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'tensor': {'dim': 9, 'shape': [3,3], 'labels':options.defgrad, 'column': []},
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}
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errors = []
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remarks = []
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for type, data in items.items():
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for what in data['labels']:
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dim = table.label_dimension(what)
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if dim != data['dim']: remarks.append('column {} is not a {}...'.format(what,type))
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else:
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items[type]['column'].append(table.label_index(what))
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for theStretch in stretches:
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for theStrain in strains:
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table.labels_append(['{}_{}({}){}'.format(i+1, # extend ASCII header with new labels
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theStrain,
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theStretch,
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what if what != 'f' else '') for i in range(9)])
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if remarks != []: damask.util.croak(remarks)
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if errors != []:
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damask.util.croak(errors)
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table.close(dismiss = True)
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continue
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# ------------------------------------------ assemble header --------------------------------------
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table.info_append(scriptID + '\t' + ' '.join(sys.argv[1:]))
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table.head_write()
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# ------------------------------------------ process data ------------------------------------------
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stretch = {}
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outputAlive = True
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while outputAlive and table.data_read(): # read next data line of ASCII table
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for column in items['tensor']['column']: # loop over all requested defgrads
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F = np.array(list(map(float,table.data[column:column+items['tensor']['dim']])),'d').reshape(items['tensor']['shape'])
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(U,S,Vh) = np.linalg.svd(F) # singular value decomposition
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R_inv = np.dot(U,Vh).T # rotation of polar decomposition
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stretch['U'] = np.dot(R_inv,F) # F = RU
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stretch['V'] = np.dot(F,R_inv) # F = VR
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for theStretch in stretches:
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stretch[theStretch] = np.where(abs(stretch[theStretch]) < 1e-12, 0, stretch[theStretch]) # kill nasty noisy data
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(D,V) = np.linalg.eigh((stretch[theStretch]+stretch[theStretch].T)*0.5) # eigen decomposition (of symmetric(ed) matrix)
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neg = np.where(D < 0.0) # find negative eigenvalues ...
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D[neg] *= -1. # ... flip value ...
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V[:,neg] *= -1. # ... and vector
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for i,eigval in enumerate(D):
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if np.dot(V[:,i],V[:,(i+1)%3]) != 0.0: # check each vector for orthogonality
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V[:,(i+1)%3] = np.cross(V[:,(i+2)%3],V[:,i]) # correct next vector
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V[:,(i+1)%3] /= np.sqrt(np.dot(V[:,(i+1)%3],V[:,(i+1)%3])) # and renormalize (hyperphobic?)
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for theStrain in strains:
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d = operator(theStretch,theStrain,D) # operate on eigenvalues of U or V
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eps = np.dot(V,np.dot(np.diag(d),V.T)).reshape(9) # build tensor back from eigenvalue/vector basis
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table.data_append(list(eps))
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# ------------------------------------------ output result -----------------------------------------
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outputAlive = table.data_write() # output processed line
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# ------------------------------------------ output finalization -----------------------------------
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table.close() # close ASCII tables
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