strain tensor calculation script for HDF5
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#!/usr/bin/env python2.7
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# -*- coding: UTF-8 no BOM -*-
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import os
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import sys
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import damask
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import numpy as np
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from optparse import OptionParser
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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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# ----- Helper functions ----- #
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def operator(stretch, strain, eigenvalues):
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# Albrecht Bertram: Elasticity and Plasticity of Large Deformations
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# An Introduction (3rd Edition, 2012), p. 102
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return {'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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def calcEPS(defgrads, stretchType, strainType):
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"""calculate specific type of strain tensor"""
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eps = np.zeros(defgrads.shape) # initialize container
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# TODO:
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# this loop can use some performance boost
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# (multi-threading?)
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for ri in xrange(defgrads.shape[0]):
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f = defgrads[ri, :, :].reshape(3, 3)
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U, S, Vh = np.lingalg.svd(f)
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R = np.dot(U, Vh) # rotation of polar decomposition
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if stretchType == 'U':
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stretch = np.dot(np.linalg.inv(R), f) # F = RU
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elif stretchType == 'V':
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stretch = np.dot(f, np.linalg.inv(R)) # F = VR
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# kill nasty noisy data
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stretch = np.where(abs(stretch) < 1e-12, 0, stretch)
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(D, V) = np.linalg.eig(stretch)
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# flip principal component with negative Eigen values
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neg = np.where(D < 0.0)
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D[neg] *= -1.
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V[:, neg] *= -1.
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# check each vector for orthogonality
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# --> brutal force enforcing orthogonal base
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# and re-normalize
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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:
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V[:, (i+1) % 3] = np.cross(V[:, (i+2) % 3], V[:, i])
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V[:, (i+1) % 3] /= np.sqrt(np.dot(V[:, (i+1) % 3],
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V[:, (i+1) % 3].conj()))
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# calculate requested version of strain tensor
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d = operator(stretchType, strainType, D)
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eps[ri] = (np.dot(V, np.dot(np.diag(d), V.T)).real).reshape(9)
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return eps
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# --------------------------------------------------------------------
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# MAIN
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# --------------------------------------------------------------------
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desp = "Add column(s) containing given strains based on given stretches"
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parser = OptionParser(option_class=damask.extendableOption,
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usage='%prog options [file[s]]',
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description=desp,
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version=scriptID)
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msg = 'material strains based on right Cauchy-Green deformation, i.e., C and U'
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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=msg)
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msg = 'spatial strains based on left Cauchy--Green deformation, i.e., B and V'
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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=msg)
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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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msg = 'heading(s) of columns containing deformation tensor values'
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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=msg)
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parser.set_defaults(right=False, left=False,
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logarithmic=False, biot=False, green=False,
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defgrad=['f'])
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(options, filenames) = parser.parse_args()
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stretches = []
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strains = []
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if options.right:
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stretches.append('U')
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if options.left:
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stretches.append('V')
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if options.logarithmic:
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strains.append('ln')
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if options.biot:
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strains.append('Biot')
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if options.green:
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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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for name in filenames:
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try:
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h5f = damask.H5Table(name, new_file=False)
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except:
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continue
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damask.util.report(scriptName, name)
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# extract defgrads from HDF5 storage
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F = h5f.get_data(options.defgrads)
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# allow calculate multiple types of strain within the
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# same cmd call
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for stretchType in stretches:
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for strainType in strains:
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# calculate strain tensor for this type
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eps = calcEPS(F, stretchType, strainType)
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# compose labels/headers for this strain tensor
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labelsStrain = strainType + stretchType
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# prepare log info
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cmd_log = scriptID + '\t' + ' '.join(sys.argv[1:])
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# write data to HDF5 file
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h5f.add_data(labelsStrain, eps, cmd_log=cmd_log)
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