1334 lines
56 KiB
Python
Executable File
1334 lines
56 KiB
Python
Executable File
#!/usr/bin/python
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# -*- coding: UTF-8 no BOM -*-
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import threading,time,os,subprocess,shlex,string
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import numpy as np
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from scipy.linalg import svd
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from optparse import OptionParser
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import damask
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from damask.util import leastsqBound
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scriptID = string.replace('$Id$','\n','\\n')
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scriptName = scriptID.split()[1][:-3]
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def execute(cmd,streamIn=None,wd='./'):
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'''
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executes a command in given directory and returns stdout and stderr for optional stdin
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'''
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initialPath=os.getcwd()
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os.chdir(wd)
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process = subprocess.Popen(shlex.split(cmd),stdout=subprocess.PIPE,stderr = subprocess.PIPE,stdin=subprocess.PIPE)
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if streamIn != None:
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out,error = process.communicate(streamIn.read())
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else:
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out,error = process.communicate()
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os.chdir(initialPath)
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return out,error
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def principalStresses(sigmas):
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'''
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computes principal stresses (i.e. eigenvalues) for a set of Cauchy stresses.
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sorted in descending order.
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'''
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lambdas=np.zeros(0,'d')
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for i in xrange(np.shape(sigmas)[1]):
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eigenvalues = np.linalg.eigvalsh(sym6to33(sigmas[:,i]))
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lambdas = np.append(lambdas,np.sort(eigenvalues)[::-1]) #append eigenvalues in descending order
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lambdas = np.transpose(lambdas.reshape(np.shape(sigmas)[1],3))
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return lambdas
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def stressInvariants(lambdas):
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'''
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computes stress invariants (i.e. eigenvalues) for a set of principal Cauchy stresses.
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'''
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Is=np.zeros(0,'d')
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for i in xrange(np.shape(lambdas)[1]):
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I = np.array([lambdas[0,i]+lambdas[1,i]+lambdas[2,i],\
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lambdas[0,i]*lambdas[1,i]+lambdas[1,i]*lambdas[2,i]+lambdas[2,i]*lambdas[0,i],\
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lambdas[0,i]*lambdas[1,i]*lambdas[2,i]])
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Is = np.append(Is,I)
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Is = Is.reshape(3,np.shape(lambdas)[1])
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return Is
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def formatOutput(n, type='%-14.6f'):
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return ''.join([type for i in xrange(n)])
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def sym6to33(sigma6):
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''' Shape the symmetric stress tensor(6,1) into (3,3) '''
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sigma33 = np.empty((3,3))
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sigma33[0,0] = sigma6[0]; sigma33[1,1] = sigma6[1]; sigma33[2,2] = sigma6[2];
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sigma33[0,1] = sigma6[3]; sigma33[1,0] = sigma6[3]
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sigma33[1,2] = sigma6[4]; sigma33[2,1] = sigma6[4]
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sigma33[2,0] = sigma6[5]; sigma33[0,2] = sigma6[5]
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return sigma33
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def array2tuple(array):
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'''transform numpy.array into tuple'''
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try:
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return tuple(array2tuple(i) for i in array)
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except TypeError:
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return array
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def get_weight(ndim):
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#more to do
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return np.ones(ndim)
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# ---------------------------------------------------------------------------------------------
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# isotropic yield surfaces
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# ---------------------------------------------------------------------------------------------
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class Tresca(object):
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'''
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residuum of Tresca yield criterion (eq. 2.26)
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'''
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def __init__(self, uniaxialStress):
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self.stress0 = uniaxialStress
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def fun(self,sigma0, ydata, sigmas):
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lambdas = principalStresses(sigmas)
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r = np.amax(np.array([abs(lambdas[2,:]-lambdas[1,:]),\
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abs(lambdas[1,:]-lambdas[0,:]),\
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abs(lambdas[0,:]-lambdas[2,:])]),0) - sigma0
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return r.ravel()
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def jac(self,sigma0, ydata, sigmas):
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return np.ones(len(ydata)) * (-1.0)
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class vonMises(object):
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'''
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residuum of Huber-Mises-Hencky yield criterion (eq. 2.37)
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'''
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def __init__(self, uniaxialStress):
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self.stress0 = uniaxialStress
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def fun(self, sigma0, ydata, sigmas):
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return HosfordBasis(sigma0, 1.0,1.0,1.0, 2.0, sigmas)
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def jac(self, sigma0, ydata, sigmas):
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return HosfordBasis(sigma0, 1.0,1.0,1.0, 2.0, sigmas, Jac=True, nParas=1)
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class Drucker(object):
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'''
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residuum of Drucker yield criterion (eq. 2.41, F = sigma0)
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'''
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def __init__(self, uniaxialStress):
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self.stress0 = uniaxialStress
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def fun(self, (sigma0, C_D), ydata, sigmas):
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return DruckerBasis(sigma0, C_D, 1.0, sigmas)
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def jac(self, (sigma0, C_D), ydata, sigmas):
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return DruckerBasis(sigma0, C_D, 1.0, sigmas, Jac=True, nParas=2)
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class generalDrucker(object):
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'''
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residuum of general Drucker yield criterion (eq. 2.42, F = sigma0)
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'''
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def __init__(self, uniaxialStress):
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self.stress0 = uniaxialStress
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def fun(self, (sigma0, C_D, p), ydata, sigmas):
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return DruckerBasis(sigma0, C_D, p, sigmas)
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def jac(self, (sigma0, C_D, p), ydata, sigmas):
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return DruckerBasis(sigma0, C_D, p, sigmas, Jac=True, nParas=3)
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class Hosford(object):
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'''
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residuum of Hershey yield criterion (eq. 2.43, Y = sigma0)
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'''
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def __init__(self, uniaxialStress):
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self.stress0 = uniaxialStress
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def fun(self, (sigma0, a), ydata, sigmas):
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return HosfordBasis(sigma0, 1.0,1.0,1.0, a, sigmas)
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def jac(self, (sigma0, a), ydata, sigmas):
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return HosfordBasis(sigma0, 1.0,1.0,1.0, a, sigmas, Jac=True, nParas=2)
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class Hill1948(object):
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'''
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residuum of Hill 1948 quadratic yield criterion (eq. 2.48)
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'''
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def __init__(self, uniaxialStress):
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self.stress0 = uniaxialStress
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def fun(self, (F,G,H,L,M,N), ydata, sigmas):
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r = F*(sigmas[1]-sigmas[2])**2.0 + G*(sigmas[2]-sigmas[0])**2.0 + H*(sigmas[0]-sigmas[1])**2.0\
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+ 2.0*L*sigmas[4]**2.0 + 2.0*M*sigmas[5]**2.0 + 2.0*N*sigmas[3]**2.0 - 1.0
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return r.ravel()/2.0
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def jac(self, (F,G,H,L,M,N), ydata, sigmas):
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jF=(sigmas[1]-sigmas[2])**2.0; jG=(sigmas[2]-sigmas[0])**2.0; jH=(sigmas[0]-sigmas[1])**2.0
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jL=2.0*sigmas[4]**2.0; jM=2.0*sigmas[5]**2.0; jN=2.0*sigmas[3]**2.0
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jaco = []
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for jacv in zip(jF, jG, jH, jL, jM, jN): jaco.append(jacv)
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return np.array(jaco)
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class Hill1979(object):
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'''
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residuum of Hill 1979 quadratic yield criterion (eq. 2.48)
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'''
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def __init__(self, uniaxialStress):
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self.stress0 = uniaxialStress
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def fun(self, (f,g,h,a,b,c,m), ydata, sigmas):
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return Hill1979Basis(self.stress0, f,g,h,a,b,c,m, sigmas)
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def jac(self, (f,g,h,a,b,c,m), ydata, sigmas):
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return Hill1979Basis(self.stress0, f,g,h,a,b,c,m, sigmas, Jac=True)
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class generalHosford(object):
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'''
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residuum of Hershey yield criterion (eq. 2.104, sigmas = sigma0)
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'''
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def __init__(self, uniaxialStress):
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self.stress0 = uniaxialStress
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def fun(self, (sigma0, F, G, H, a), ydata, sigmas, nParas=5):
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return HosfordBasis(sigma0, F, G, H, a, sigmas)
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def jac(self, (sigma0, F, G, H, a), ydata, sigmas):
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return HosfordBasis(sigma0, F,G,H, a, sigmas, Jac=True, nParas=5)
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class Barlat1991iso(object):
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'''
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residuum of isotropic Barlat 1991 yield criterion (eq. 2.37)
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'''
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def __init__(self, uniaxialStress):
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self.stress0 = uniaxialStress
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def fun(self, (sigma0, m), ydata, sigmas):
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return Barlat1991Basis(sigma0, 1.0,1.0,1.0,1.0,1.0,1.0, m, sigmas)
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def jac(self, (sigma0, m), ydata, sigmas):
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return Barlat1991Basis(sigma0, 1.0,1.0,1.0,1.0,1.0,1.0, m, sigmas, Jac=True, nParas=2)
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class Barlat1991aniso(object):
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'''
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residuum of anisotropic Barlat 1991 yield criterion (eq. 2.37)
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'''
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def __init__(self, uniaxialStress):
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self.stress0 = uniaxialStress
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def fun(self, (sigma0, a,b,c,f,g,h, m), ydata, sigmas):
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return Barlat1991Basis(sigma0, a,b,c,f,g,h, m, sigmas)
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def jac(self, (sigma0, a,b,c,f,g,h, m), ydata, sigmas):
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return Barlat1991Basis(sigma0, a,b,c,f,g,h, m, sigmas, Jac=True, nParas=8)
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class Yld200418p(object):
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'''
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residuum of anisotropic Barlat 1991 yield criterion (eq. 2.37)
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'''
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def __init__(self, uniaxialStress):
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self.stress0 = uniaxialStress
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def fun(self, (sigma0, c12,c21,c23,c32,c31,c13,c44,c55,c66,
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d12,d21,d23,d32,d31,d13,d44,d55,d66, m), ydata, sigmas):
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return Yld200418pBasis(sigma0, c12,c21,c23,c32,c31,c13,c44,c55,c66,
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d12,d21,d23,d32,d31,d13,d44,d55,d66, m, sigmas)
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def jac(self, (sigma0, c12,c21,c23,c32,c31,c13,c44,c55,c66,
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d12,d21,d23,d32,d31,d13,d44,d55,d66, m), ydata, sigmas):
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return Yld200418pBasis(sigma0, c12,c21,c23,c32,c31,c13,c44,c55,c66,
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d12,d21,d23,d32,d31,d13,d44,d55,d66, m, sigmas, Jac=True)
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class KarafillisBoyce(object):
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'''
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residuum of Karafillis-Boyce yield criterion
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'''
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def __init__(self, uniaxialStress):
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self.stress0 = uniaxialStress
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def fun(self, (c11,c12,c13,c14,c15,c16,c21,c22,c23,c24,c25,c26,
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b1, b2, a, alpha), ydata, sigmas):
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return KarafillisBoyceBasis(self.stress0, c11,c12,c13,c14,c15,c16,c21,c22,c23,c24,c25,c26,
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b1, b2, a, alpha, sigmas)
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def jac(self, (c11,c12,c13,c14,c15,c16,c21,c22,c23,c24,c25,c26,
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b1, b2, a, alpha), ydata, sigmas):
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return KarafillisBoyceBasis(self.stress0, c11,c12,c13,c14,c15,c16,c21,c22,c23,c24,c25,c26,
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b1, b2, a, alpha, sigmas, Jac=True)
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class BBC2003(object):
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'''
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residuum of anisotropic Barlat 1991 yield criterion (eq. 2.37)
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'''
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def __init__(self, uniaxialStress):
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self.stress0 = uniaxialStress
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def fun(self, (sigma0, a,b,c, d,e,f,g, k), ydata, sigmas):
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return BBC2003Basis(sigma0, a,b,c, d,e,f,g, k, sigmas)
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def jac(self, (sigma0, a,b,c, d,e,f,g, k), ydata, sigmas):
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return BBC2003Basis(sigma0, a,b,c, d,e,f,g, k, sigmas, Jac=True)
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class Cazacu_Barlat2D(object):
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'''
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'''
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def __init__(self, uniaxialStress):
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self.stress0 = uniaxialStress
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def fun(self, (a1,a2,a3,a4,b1,b2,b3,b4,b5,b10,c), ydata, sigmas):
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return Cazacu_Barlat2DBasis(a1,a2,a3,a4,b1,b2,b3,b4,b5,b10,c,
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self.stress0, sigmas)
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def jac(self, (a1,a2,a3,a4,b1,b2,b3,b4,b5,b10,c), ydata, sigmas):
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return Cazacu_Barlat2DBasis(a1,a2,a3,a4,b1,b2,b3,b4,b5,b10,c,
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self.stress0, sigmas,Jac=True)
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class Cazacu_Barlat3D(object):
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'''
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'''
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def __init__(self, uniaxialStress):
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self.stress0 = uniaxialStress
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def fun(self, (a1,a2,a3,a4,a5,a6,b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,c),ydata, sigmas):
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return Cazacu_Barlat3DBasis(a1,a2,a3,a4,a5,a6,b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,c,
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self.stress0, sigmas)
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def jac(self, (a1,a2,a3,a4,a5,a6,b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,c),ydata, sigmas):
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return Cazacu_Barlat3DBasis(a1,a2,a3,a4,a5,a6,b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,c,
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self.stress0, sigmas,Jac=True)
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def Cazacu_Barlat3DBasis(a1,a2,a3,a4,a5,a6,b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,c,
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sigma0,sigmas, Jac = False):
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'''
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residuum of the 3D Cazacu<63>Barlat (CZ) yield criterion
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'''
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s11 = sigmas[0]; s22 = sigmas[1]; s33 = sigmas[2]
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s12 = sigmas[3]; s23 = sigmas[4]; s31 = sigmas[5]
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s123, s321 = s11*s22*s33, s12*s23*s31
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s1_2, s2_2, s3_2 = s11**2, s22**2, s33**2
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s1_3, s2_3, s3_3 = s11*s1_2, s22*s2_2, s33*s3_2
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s12_2, s23_2, s31_2 = s12**2, s23**2, s31**2
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d12_2, d23_2, d31_2 = (s11-s22)**2, (s22-s33)**2, (s33-s11)**2
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J20 = ( a1*d12_2 + a2*d23_2 + a3*d31_2 )/6.0 + a4*s12_2 + a5*s23_2 + a6*s31_2
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J30 = ( (b1 +b2 )*s1_3 + (b3 +b4 )*s2_3 + ( b1+b4-b2 + b1+b4-b3 )*s3_3 )/27.0- \
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( (b1*s22+b2*s33)*s1_2 + (b3*s33+b4*s11)*s2_2 + ((b1+b4-b2)*s11 + (b1+b4-b3)*s22)*s3_2 )/9.0 + \
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( (b1+b4)*s123/9.0 + b11*s321 )*2.0 - \
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( ( 2.0*b9 *s22 - b8*s33 - (2.0*b9 -b8)*s11 )*s31_2 +
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( 2.0*b10*s33 - b5*s22 - (2.0*b10-b5)*s11 )*s12_2 +
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( (b6+b7)*s11 - b6*s22 - b7*s33 )*s23_2
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)/3.0
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f0 = (J20**3 - c*J30**2)/18.0
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r = f0**(1.0/6.0)*(3.0/sigma0)
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if not Jac:
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return (r - 1.0).ravel()
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else:
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drdf = r/f0/108.0
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dj2 = drdf*3.0*J20**2.0
|
||
dj3 = -drdf*2.0*J30*c
|
||
jc = -drdf*J30**2
|
||
|
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ja1,ja2,ja3 = dj2*d12_2/6.0, dj2*d23_2/6.0, dj2*d31_2/6.0
|
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ja4,ja5,ja6 = dj2*s12_2, dj2*s23_2, dj2*s31_2
|
||
jb1 = dj3*( (s1_3 + 2.0*s3_3)/27.0 - s22*s1_2/9.0 - (s11+s22)*s3_2/9.0 + s123/4.5 )
|
||
jb2 = dj3*( (s1_3 - s3_3)/27.0 - s33*s1_2/9.0 + s11 *s3_2/9.0 )
|
||
jb3 = dj3*( (s2_3 - s3_3)/27.0 - s33*s2_2/9.0 + s22 *s3_2/9.0 )
|
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jb4 = dj3*( (s2_3 + 2.0*s3_3)/27.0 - s11*s2_2/9.0 - (s11+s22)*s3_2/9.0 + s123/4.5 )
|
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|
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jb5, jb10 = dj3*(s22 - s11)*s12_2/3.0, dj3*(s11 - s33)*s12_2/3.0*2.0
|
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jb6, jb7 = dj3*(s22 - s11)*s23_2/3.0, dj3*(s33 - s11)*s23_2/3.0
|
||
jb8, jb9 = dj3*(s33 - s11)*s31_2/3.0, dj3*(s11 - s22)*s31_2/3.0*2.0
|
||
jb11 = dj3*s321*2.0
|
||
|
||
jaco = []
|
||
for jacv in zip(ja1,ja2,ja3,ja4,ja5,ja6,jb1,jb2,jb3,jb4,jb5,jb6,jb7,jb8,jb9,jb10,jb11,jc):
|
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jaco.append(jacv)
|
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return np.array(jaco)
|
||
|
||
def Cazacu_Barlat2DBasis(a1,a2,a3,a4,b1,b2,b3,b4,b5,b10,c,
|
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sigma0,sigmas, Jac = False):
|
||
'''
|
||
residuum of the 2D Cazacu<63>Barlat (CZ) yield criterion for plain stress
|
||
'''
|
||
s11 = sigmas[0]; s22 = sigmas[1]; s12 = sigmas[3]
|
||
s1_2, s2_2 = s11**2, s22**2
|
||
s1_3, s2_3 = s11*s1_2, s22*s2_2
|
||
s12_2 = s12**2
|
||
|
||
J20 = ( a1*(s11-s22)**2 + a2*s2_2 + a3*s1_2 )/6.0 + a4*s12_2
|
||
J30 = ( (b1+b2)*s1_3 + (b3+b4)*s2_3 )/27.0 - ( (b1*s11 + b4*s22)*s11*s22 )/9.0 + \
|
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( b5*s22 + (2*b10-b5)*s11 )*s12_2/3.0
|
||
|
||
f0 = (J20**3 - c*J30**2)/18.0
|
||
r = f0**(1.0/6.0)*(3.0/sigma0)
|
||
|
||
if not Jac:
|
||
return (r - 1.0).ravel()
|
||
else:
|
||
drdf = r/f0/108.0
|
||
dj2 = drdf*3.0*J20**2.0
|
||
dj3 = -drdf*2.0*J30*c
|
||
jc = -drdf*J30**2
|
||
|
||
ja1,ja2,ja3,ja4 = dj2*(s11-s22)**2/6.0, dj2*s2_2/6.0, dj2*s1_2/6.0, dj2*s12_2
|
||
jb1, jb2 = s1_3/27.0 - s1_2*s22/9.0, s1_3/27.0
|
||
jb4, jb3 = s2_3/27.0 - s2_2*s11/9.0, s2_3/27.0
|
||
jb5, jb10= -s12_2*(s11 - s22)/3.0, s12_2*s11*2.0/3.0
|
||
|
||
jaco = []
|
||
for jacv in zip(ja1,ja2,ja3,ja4,jb1,jb2,jb3,jb4,jb5,jb10,jc):
|
||
jaco.append(jacv)
|
||
return np.array(jaco)
|
||
|
||
def DruckerBasis(sigma0, C_D, p, sigmas, Jac=False, nParas=2):
|
||
s11 = sigmas[0]; s22 = sigmas[1]; s33 = sigmas[2]
|
||
s12 = sigmas[3]; s23 = sigmas[4]; s31 = sigmas[5]
|
||
I1 = s11 + s22 + s33
|
||
I2 = s11*s22 + s22*s33 + s33*s11 - s12**2 - s23**2 - s31**2
|
||
I3 = s11*s22*s33 + 2.0*s12*s23*s31 - s12**2*s33 - s23**2*s11 - s31**2*s22
|
||
J2 = I1**2/3.0 - I2
|
||
J3 = I1**3/13.5 - I1*I2/3.0 + I3
|
||
left= J2**(3.0*p) - C_D*J3**(2.0*p); right = 3.0**(0.5)/sigma0
|
||
expo= 1.0/(6.0*p)
|
||
|
||
if not Jac:
|
||
return (left**expo*right - 1.0).ravel()
|
||
else:
|
||
jaco = []
|
||
dfdl = expo*left**(expo-1.0)
|
||
js = -left**expo*right/sigma0
|
||
jC = -dfdl*J3**(2*p)*right
|
||
if nParas == 2:
|
||
for jacv in zip(js, jC): jaco.append(jacv)
|
||
return np.array(jaco)
|
||
else:
|
||
ln = lambda x : np.log(x + 1.0e-32)
|
||
dldp = 3.0*J2**(3.0*p)*ln(J2) - 2.0*C_D*J3**(2.0*p)*ln(J3)
|
||
|
||
jp = dfdl*dldp*right + (left**expo)*ln(left)*expo/(-p)*right
|
||
for jacv in zip(js, jC, jp): jaco.append(jacv)
|
||
return np.array(jaco)
|
||
|
||
def Hill1979Basis(sigma0, f,g,h,a,b,c,m, sigmas, Jac=False):
|
||
|
||
s1,s2,s3 = principalStresses(sigmas)
|
||
d23 = s2-s3; d123 = 2.0*s1 - s2 - s3
|
||
d31 = s3-s1; d231 = 2.0*s2 - s3 - s1
|
||
d12 = s1-s2; d312 = 2.0*s3 - s1 - s2
|
||
|
||
d23s = d23**2; d123s = d123**2
|
||
d31s = d31**2; d231s = d231**2
|
||
d12s = d12**2; d312s = d312**2
|
||
|
||
m2 = m/2.0; mi = 1.0/m
|
||
base = f* d23s**m2 + g* d31s**m2 + h* d12s**m2 + \
|
||
a*d123s**m2 + b*d231s**m2 + c*d312s**m2
|
||
left = base**mi
|
||
r = left/sigma0
|
||
|
||
if not Jac:
|
||
return (r-1.0).ravel()
|
||
else:
|
||
ln = lambda x : np.log(x + 1.0e-32)
|
||
drdb = r/base*mi
|
||
dbdm = ( f* d23s**m2*ln( d23s) + g* d31s**m2*ln( d31s) + h*d12s**m2*ln( d12s) +
|
||
a*d123s**m2*ln(d123s) + b*d231s**m2*ln(d231s) + c*d312s**m2*ln(d312s) )*0.5
|
||
jf = drdb*d23s**m2; ja = drdb*d123s**m2
|
||
jg = drdb*d31s**m2; jb = drdb*d231s**m2
|
||
jh = drdb*d12s**m2; jc = drdb*d312s**m2
|
||
jm = drdb*dbdm + r*ln(base)*(-mi*mi)
|
||
|
||
jaco = []
|
||
for jacv in zip(jf,jg,jh,ja,jb,jc,jm):
|
||
jaco.append(jacv)
|
||
return np.array(jaco)
|
||
|
||
def HosfordBasis(sigma0, F,G,H, a, sigmas, Jac=False, nParas=1):
|
||
'''
|
||
residuum of Hershey yield criterion (eq. 2.43, Y = sigma0)
|
||
'''
|
||
lambdas = principalStresses(sigmas)
|
||
diff23 = abs(lambdas[1,:] - lambdas[2,:])
|
||
diff31 = abs(lambdas[2,:] - lambdas[0,:])
|
||
diff12 = abs(lambdas[0,:] - lambdas[1,:])
|
||
base = F*diff23**a + G*diff31**a + H*diff12**a; expo = 1.0/a
|
||
left = base**expo
|
||
right = 2.0**expo*sigma0
|
||
|
||
if not Jac:
|
||
if nParas == 1: return (left - right).ravel()
|
||
else: return (left/right - 1.0).ravel()
|
||
else:
|
||
ones = np.ones(np.shape(sigmas)[1])
|
||
if nParas > 1:
|
||
ln = lambda x : np.log(x + 1.0e-32)
|
||
dbda = F*ln(diff23)*diff23**a + G*ln(diff31)*diff31**a + H*ln(diff12)*diff12**a
|
||
deda = -expo*expo
|
||
drda = sigma0*(2.0**expo)*ln(2.0)*deda
|
||
dldb = expo*left/base
|
||
jaco = []
|
||
|
||
if nParas == 1: # von Mises
|
||
return ones*(-2.0**0.5)
|
||
elif nParas == 2: # isotropic Hosford
|
||
js = ones*(-2.0**expo) # d[]/dsigma0
|
||
ja = dldb*dbda + left*ln(base)*deda - drda # d[]/da
|
||
for jacv in zip(js, ja):
|
||
jaco.append(jacv)
|
||
return np.array(jaco)
|
||
elif nParas == 5: # anisotropic Hosford
|
||
js = -left/right/sigma0 #ones*(-2.0**expo) # d[]/dsigma0
|
||
jF = dldb*diff23**a/right
|
||
jG = dldb*diff31**a/right
|
||
jH = dldb*diff12**a/right
|
||
ja =(dldb*dbda + left*ln(base)*deda)/right + left*(-right**(-2))*drda # d[]/da
|
||
for jacv in zip(js, jF,jG,jH,ja):
|
||
jaco.append(jacv)
|
||
return np.array(jaco)
|
||
|
||
def Barlat1991Basis(sigma0, a, b, c, f, g, h, m, sigmas, Jac=False, nParas=2):
|
||
'''
|
||
residuum of Barlat 1997 yield criterion
|
||
'''
|
||
cos = np.cos; sin = np.sin; pi = np.pi; abs = np.abs
|
||
dAda = sigmas[1] - sigmas[2]; A = a*dAda
|
||
dBdb = sigmas[2] - sigmas[0]; B = b*dBdb
|
||
dCdc = sigmas[0] - sigmas[1]; C = c*dCdc
|
||
dFdf = sigmas[4]; F = f*dFdf
|
||
dGdg = sigmas[5]; G = g*dGdg
|
||
dHdh = sigmas[3]; H = h*dHdh
|
||
|
||
I2 = (F*F + G*G + H*H)/3.0 + ((A-C)**2+(C-B)**2+(B-A)**2)/54.0
|
||
I3 = (C-B)*(A-C)*(B-A)/54.0 + F*G*H - \
|
||
( (C-B)*F*F + (A-C)*G*G + (B-A)*H*H )/6.0
|
||
theta = np.arccos(I3/I2**1.5)
|
||
phi1 = (2.0*theta + pi)/6.0
|
||
phi2 = (2.0*theta + pi*3.0)/6.0
|
||
phi3 = (2.0*theta + pi*5.0)/6.0
|
||
cos1 = 2.0*cos(phi1); absc1 = abs(cos1)
|
||
cos2 = 2.0*cos(phi2); absc2 = abs(cos2)
|
||
cos3 = 2.0*cos(phi3); absc3 = abs(cos3)
|
||
ratio= np.sqrt(3.0*I2)/sigma0; expo = 1.0/m
|
||
left = ( absc1**m + absc2**m + absc3**m )/2.0
|
||
leftNorm = left**expo
|
||
r = ratio*leftNorm - 1.0
|
||
|
||
if not Jac:
|
||
return r.ravel()
|
||
else:
|
||
ln = lambda x : np.log(x + 1.0e-32)
|
||
jaco = []
|
||
dfdl = expo*leftNorm/left
|
||
js = -(r + 1.0)/sigma0
|
||
jm = (r+1.0)*ln(left)*(-expo*expo) + ratio*dfdl*0.5*(
|
||
absc1**m*ln(absc1) + absc2**m*ln(absc2) + absc3**m*ln(absc3) )
|
||
if nParas == 2:
|
||
for jacv in zip(js, jm): jaco.append(jacv)
|
||
return np.array(jaco)
|
||
else:
|
||
dI2da = (2.0*A-B-C)*dAda/27.0
|
||
dI2db = (2.0*B-C-A)*dBdb/27.0
|
||
dI2dc = (2.0*C-A-B)*dCdc/27.0
|
||
dI2df = 2.0*F*dFdf/3.0
|
||
dI2dg = 2.0*G*dGdg/3.0
|
||
dI2dh = 2.0*H*dHdh/3.0
|
||
dI3da = dI2da*(B-C)/2.0 + (H**2 - G**2)*dAda/6.0
|
||
dI3db = dI2db*(C-A)/2.0 + (F**2 - H**2)*dBdb/6.0
|
||
dI3dc = dI2dc*(A-B)/2.0 + (G**2 - F**2)*dCdc/6.0
|
||
dI3df = ( (H*G + (B-C)) * F/3.0 )*dFdf
|
||
dI3dg = ( (F*H + (C-A)) * G/3.0 )*dGdg
|
||
dI3dh = ( (G*F + (A-B)) * H/3.0 )*dHdh
|
||
|
||
darccos = -(1.0 - I3**2/I2**3)**(-0.5)
|
||
dthedI2 = darccos*I3*(-1.5)*I2**(-2.5)
|
||
dthedI3 = darccos*I2**(-1.5)
|
||
dc1dthe = -sin(phi1)/3.0
|
||
dc2dthe = -sin(phi2)/3.0
|
||
dc3dthe = -sin(phi3)/3.0
|
||
dfdc = ratio * dfdl * 0.5 * m
|
||
dfdc1 = dfdc* absc1**(expo-1.0)*np.sign(cos1)
|
||
dfdc2 = dfdc* absc2**(expo-1.0)*np.sign(cos2)
|
||
dfdc3 = dfdc* absc3**(expo-1.0)*np.sign(cos3)
|
||
dfdthe= (dfdc1*dc1dthe + dfdc2*dc2dthe + dfdc2*dc2dthe)*2.0
|
||
dfdI2 = dfdthe*dthedI2; dfdI3 = dfdthe*dthedI3
|
||
ja = dfdI2*dI2da + dfdI3*dI3da
|
||
jb = dfdI2*dI2db + dfdI3*dI3db
|
||
jc = dfdI2*dI2dc + dfdI3*dI3dc
|
||
jf = dfdI2*dI2df + dfdI3*dI3df
|
||
jg = dfdI2*dI2dg + dfdI3*dI3dg
|
||
jh = dfdI2*dI2dh + dfdI3*dI3dh
|
||
|
||
for jacv in zip(js,ja,jb,jc,jf,jg,jh,jm):
|
||
jaco.append(jacv)
|
||
return np.array(jaco)
|
||
|
||
def BBC2003Basis(sigma0, a,b,c, d,e,f,g, k, sigmas, Jac=False):
|
||
'''
|
||
residuum of the BBC2003 yield criterion for plain stress
|
||
'''
|
||
s11 = sigmas[0]; s22 = sigmas[1]; s12 = sigmas[3]
|
||
k2 = 2.0*k
|
||
M = d+e; N = e+f; P = (d-e)/2.0; Q = (e-f)/2.0; R = g**2
|
||
Gamma = M*s11 + N*s22
|
||
Psi = ( (P*s11 + Q*s22)**2 + s12**2*R )**0.5
|
||
|
||
l1 = b*Gamma + c*Psi; l2 = b*Gamma - c*Psi; l3 = 2.0*c*Psi
|
||
l1s = l1**2; l2s = l2**2; l3s = l3**2
|
||
left = a*l1s**k + a*l2s**k + (1-a)*l3s**k
|
||
sBar = left**(1.0/k2); r = sBar/sigma0 - 1.0
|
||
if not Jac:
|
||
return r.ravel()
|
||
else:
|
||
temp = (P*s11 + Q*s22)/Psi
|
||
dPsidP = temp*s11; dPsidQ = temp*s22; dPsidR = 0.5*s12**2/Psi
|
||
ln = lambda x : np.log(x + 1.0e-32)
|
||
jaco = []
|
||
expo = 0.5/k; k1 = k-1.0
|
||
|
||
dsBardl = expo*sBar/left/sigma0
|
||
dsBarde = sBar*ln(left); dedk = expo/(-k)
|
||
dldl1 = a *k*(l1s**k1)*(2.0*l1)
|
||
dldl2 = a *k*(l2s**k1)*(2.0*l2)
|
||
dldl3 = (1-a)*k*(l3s**k1)*(2.0*l3)
|
||
|
||
dldGama = (dldl1 + dldl2)*b
|
||
dldPsi = (dldl1 - dldl2 + 2.0*dldl3)*c
|
||
|
||
dlda = l1s**k + l2s**k - l3s**k
|
||
dldb = dldl1*Gamma + dldl2*Gamma
|
||
dldc = dldl1*Psi - dldl2*Psi + dldl3*2.0*Psi
|
||
dldk = a*ln(l1s)*l1s**k + a*ln(l2s)*l2s**k + (1-a)*ln(l3s)*l3s**k
|
||
|
||
js = -(r + 1.0)/sigma0
|
||
ja = dsBardl * dlda
|
||
jb = dsBardl * dldb
|
||
jc = dsBardl * dldc
|
||
jd = dsBardl *(dldGama*s11 + dldPsi*dPsidP*0.5)
|
||
je = dsBardl *(dldGama*(s11+s22) + dldPsi*(dPsidP*(-0.5) + dPsidQ*0.5) )
|
||
jf = dsBardl *(dldGama*s22 + dldPsi*dPsidQ*(-0.5))
|
||
jg = dsBardl * dldPsi * dPsidR * 2.0*g
|
||
jk = dsBardl * dldk + dsBarde * dedk
|
||
|
||
for jacv in zip(js,ja,jb,jc,jd, je, jf,jg,jk):
|
||
jaco.append(jacv)
|
||
return np.array(jaco)
|
||
|
||
def principalStress(p):
|
||
sin = np.sin; cos = np.cos
|
||
s11 = p[0]; s22 = p[1]; s33 = p[2]
|
||
s12 = p[3]; s23 = p[4]; s31 = p[5]
|
||
I1 = s11 + s22 + s33
|
||
I2 = s11*s22 + s22*s33 + s33*s11 - s12**2 - s23**2 - s31**2
|
||
I3 = s11*s22*s33 + 2.0*s12*s23*s31 - s12**2*s33 - s23**2*s11 - s31**2*s22
|
||
|
||
third = 1.0/3.0
|
||
I1s3I2= (I1**2 - 3.0*I2)**0.5
|
||
numer = 2.0*I1**3 - 9.0*I1*I2 + 27.0*I3
|
||
denom = I1s3I2**(-3.0)
|
||
cs = 0.5*numer*denom
|
||
phi = np.arccos(cs)/3.0
|
||
t1 = I1/3.0; t2 = 2.0/3.0*I1s3I2
|
||
S1 = t1 + t2*cos(phi)
|
||
S2 = t1 + t2*cos(phi+np.pi*2.0/3.0)
|
||
S3 = t1 + t2*cos(phi+np.pi*4.0/3.0)
|
||
|
||
return np.array([S1,S2,S3]), np.array([I1,I2,I3])
|
||
|
||
def principalStrs_Der(p, Invariant, s1, s2, s3, s4, s5, s6, Karafillis=False):
|
||
sin = np.sin; cos = np.cos
|
||
I1 = Invariant[0,:]; I2 = Invariant[1,:]; I3 = Invariant[2,:]
|
||
|
||
third = 1.0/3.0
|
||
I1s3I2= (I1**2 - 3.0*I2)**0.5
|
||
numer = 2.0*I1**3 - 9.0*I1*I2 + 27.0*I3
|
||
denom = I1s3I2**(-3.0)
|
||
cs = 0.5*numer*denom
|
||
phi = np.arccos(cs)*third
|
||
|
||
dphidcs = -third/np.sqrt(1.0 - cs**2)
|
||
dcsddenom = 0.5*numer*(-1.5)*I1s3I2**(-5.0)
|
||
dcsdI1 = 0.5*(6.0*I1**2 - 9.0*I2)*denom + dcsddenom*(2.0*I1)
|
||
dcsdI2 = 0.5*( - 9.0*I1)*denom + dcsddenom*(-3.0)
|
||
dcsdI3 = 13.5*denom
|
||
dphidI1 = dphidcs*dcsdI1
|
||
dphidI2 = dphidcs*dcsdI2
|
||
dphidI3 = dphidcs*dcsdI3
|
||
|
||
dI1s3I2dI1= I1/I1s3I2; dI1s3I2dI2 = -1.5/I1s3I2
|
||
third2 = 2.0*third; tcoeff = third2*I1s3I2
|
||
|
||
theta = phi
|
||
dS1dI1 = third + tcoeff*(-sin(theta))*dphidI1 + third2*dI1s3I2dI1*cos(theta)
|
||
dS1dI2 = + tcoeff*(-sin(theta))*dphidI2 + third2*dI1s3I2dI2*cos(theta)
|
||
dS1dI3 = tcoeff*(-sin(theta))*dphidI3
|
||
|
||
theta = phi + np.pi*2.0/3.0
|
||
dS2dI1 = third + tcoeff*(-sin(theta))*dphidI1 + third2*dI1s3I2dI1*cos(theta)
|
||
dS2dI2 = + tcoeff*(-sin(theta))*dphidI2 + third2*dI1s3I2dI2*cos(theta)
|
||
dS2dI3 = tcoeff*(-sin(theta))*dphidI3
|
||
|
||
theta = phi + np.pi*4.0/3.0
|
||
dS3dI1 = third + tcoeff*(-sin(theta))*dphidI1 + third2*dI1s3I2dI1*cos(theta)
|
||
dS3dI2 = + tcoeff*(-sin(theta))*dphidI2 + third2*dI1s3I2dI2*cos(theta)
|
||
dS3dI3 = tcoeff*(-sin(theta))*dphidI3
|
||
|
||
# calculate the derivation of principal stress with regards to the anisotropic coefficients
|
||
dI1dp0 = dI1dp1 = dI1dp2 = 1.0
|
||
dI1dp3 = dI1dp4 = dI1dp5 = 0.0
|
||
dI2dp0 = p[1] + p[2]; dI2dp4 = -2.0*p[4]
|
||
dI2dp1 = p[2] + p[0]; dI2dp5 = -2.0*p[5]
|
||
dI2dp2 = p[0] + p[1]; dI2dp3 = -2.0*p[3]
|
||
|
||
dI3dp0 = p[1]*p[2] - p[4]**2; dI3dp4 = -2.0*p[4]*p[0] + 2.0*p[5]*p[3]
|
||
dI3dp1 = p[2]*p[0] - p[5]**2; dI3dp5 = -2.0*p[5]*p[1] + 2.0*p[3]*p[4]
|
||
dI3dp2 = p[0]*p[1] - p[3]**2; dI3dp3 = -2.0*p[3]*p[2] + 2.0*p[4]*p[5]
|
||
|
||
if Karafillis:
|
||
dS1dp0 = dS1dI1*dI1dp0 + dS1dI2*dI2dp0 + dS1dI3*dI3dp0
|
||
dS1dp1 = dS1dI1*dI1dp1 + dS1dI2*dI2dp1 + dS1dI3*dI3dp1
|
||
dS1dp2 = dS1dI1*dI1dp2 + dS1dI2*dI2dp2 + dS1dI3*dI3dp2
|
||
dS1dp3 = dS1dI1*dI1dp3 + dS1dI2*dI2dp3 + dS1dI3*dI3dp3
|
||
dS1dp4 = dS1dI1*dI1dp4 + dS1dI2*dI2dp4 + dS1dI3*dI3dp4
|
||
dS1dp5 = dS1dI1*dI1dp5 + dS1dI2*dI2dp5 + dS1dI3*dI3dp5
|
||
dS2dp0 = dS2dI1*dI1dp0 + dS2dI2*dI2dp0 + dS2dI3*dI3dp0
|
||
dS2dp1 = dS2dI1*dI1dp1 + dS2dI2*dI2dp1 + dS2dI3*dI3dp1
|
||
dS2dp2 = dS2dI1*dI1dp2 + dS2dI2*dI2dp2 + dS2dI3*dI3dp2
|
||
dS2dp3 = dS2dI1*dI1dp3 + dS2dI2*dI2dp3 + dS2dI3*dI3dp3
|
||
dS2dp4 = dS2dI1*dI1dp4 + dS2dI2*dI2dp4 + dS2dI3*dI3dp4
|
||
dS2dp5 = dS2dI1*dI1dp5 + dS2dI2*dI2dp5 + dS2dI3*dI3dp5
|
||
dS3dp0 = dS3dI1*dI1dp0 + dS3dI2*dI2dp0 + dS3dI3*dI3dp0
|
||
dS3dp1 = dS3dI1*dI1dp1 + dS3dI2*dI2dp1 + dS3dI3*dI3dp1
|
||
dS3dp2 = dS3dI1*dI1dp2 + dS3dI2*dI2dp2 + dS3dI3*dI3dp2
|
||
dS3dp3 = dS3dI1*dI1dp3 + dS3dI2*dI2dp3 + dS3dI3*dI3dp3
|
||
dS3dp4 = dS3dI1*dI1dp4 + dS3dI2*dI2dp4 + dS3dI3*dI3dp4
|
||
dS3dp5 = dS3dI1*dI1dp5 + dS3dI2*dI2dp5 + dS3dI3*dI3dp5
|
||
|
||
dS1dc1 = ( dS1dp0*0.0 + dS1dp1*(s2-s3) + dS1dp2*(s3-s2) )/3.0
|
||
dS1dc2 = ( dS1dp0*(s1-s3) + dS1dp1*0.0 + dS1dp2*(s3-s1) )/3.0
|
||
dS1dc3 = ( dS1dp0*(s1-s2) + dS1dp1*(s2-s1) + dS1dp2*0.0 )/3.0
|
||
dS2dc1 = ( dS2dp0*0.0 + dS2dp1*(s2-s3) + dS2dp2*(s3-s2) )/3.0
|
||
dS2dc2 = ( dS2dp0*(s1-s3) + dS2dp1*0.0 + dS2dp2*(s3-s1) )/3.0
|
||
dS2dc3 = ( dS2dp0*(s1-s2) + dS2dp1*(s2-s1) + dS2dp2*0.0 )/3.0
|
||
dS3dc1 = ( dS3dp0*0.0 + dS3dp1*(s2-s3) + dS3dp2*(s3-s2) )/3.0
|
||
dS3dc2 = ( dS3dp0*(s1-s3) + dS3dp1*0.0 + dS3dp2*(s3-s1) )/3.0
|
||
dS3dc3 = ( dS3dp0*(s1-s2) + dS3dp1*(s2-s1) + dS3dp2*0.0 )/3.0
|
||
dS1dc4 = dS1dp3*s4; dS1dc5 = dS1dp4*s5; dS1dc6 = dS1dp5*s6
|
||
dS2dc4 = dS2dp3*s4; dS2dc5 = dS2dp4*s5; dS2dc6 = dS2dp5*s6
|
||
dS3dc4 = dS3dp3*s4; dS3dc5 = dS3dp4*s5; dS3dc6 = dS3dp5*s6
|
||
|
||
return dS1dc1,dS1dc2,dS1dc3,dS1dc4,dS1dc5,dS1dc6,\
|
||
dS2dc1,dS2dc2,dS2dc3,dS2dc4,dS2dc5,dS2dc6,\
|
||
dS3dc1,dS3dc2,dS3dc3,dS3dc4,dS3dc5,dS3dc6
|
||
else:
|
||
dI1dc12 = dI1dp0*(-s2); dI2dc12 = dI2dp0*(-s2); dI3dc12 = dI3dp0*(-s2) # c12
|
||
dI1dc21 = dI1dp1*(-s1); dI2dc21 = dI2dp1*(-s1); dI3dc21 = dI3dp1*(-s1) # c21
|
||
dI1dc23 = dI1dp1*(-s3); dI2dc23 = dI2dp1*(-s3); dI3dc23 = dI3dp1*(-s3) # c23
|
||
dI1dc32 = dI1dp2*(-s2); dI2dc32 = dI2dp2*(-s2); dI3dc32 = dI3dp2*(-s2) # c32
|
||
dI1dc31 = dI1dp2*(-s1); dI2dc31 = dI2dp2*(-s1); dI3dc31 = dI3dp2*(-s1) # c31
|
||
dI1dc13 = dI1dp0*(-s3); dI2dc13 = dI2dp0*(-s3); dI3dc13 = dI3dp0*(-s3) # c13
|
||
dI1dc44 = dI1dp3* s4 ; dI2dc44 = dI2dp3* s4 ; dI3dc44 = dI3dp3* s4 # c44
|
||
dI1dc55 = dI1dp4* s5 ; dI2dc55 = dI2dp4* s5 ; dI3dc55 = dI3dp4* s5 # c55
|
||
dI1dc66 = dI1dp5* s6 ; dI2dc66 = dI2dp5* s6 ; dI3dc66 = dI3dp5* s6 # c66
|
||
|
||
dS1dc12 = dS1dI1 * dI1dc12 + dS1dI2 * dI2dc12 + dS1dI3 * dI3dc12
|
||
dS1dc21 = dS1dI1 * dI1dc21 + dS1dI2 * dI2dc21 + dS1dI3 * dI3dc21
|
||
dS1dc23 = dS1dI1 * dI1dc23 + dS1dI2 * dI2dc23 + dS1dI3 * dI3dc23
|
||
dS1dc32 = dS1dI1 * dI1dc32 + dS1dI2 * dI2dc32 + dS1dI3 * dI3dc32
|
||
dS1dc31 = dS1dI1 * dI1dc31 + dS1dI2 * dI2dc31 + dS1dI3 * dI3dc31
|
||
dS1dc13 = dS1dI1 * dI1dc13 + dS1dI2 * dI2dc13 + dS1dI3 * dI3dc13
|
||
dS1dc44 = dS1dI1 * dI1dc44 + dS1dI2 * dI2dc44 + dS1dI3 * dI3dc44
|
||
dS1dc55 = dS1dI1 * dI1dc55 + dS1dI2 * dI2dc55 + dS1dI3 * dI3dc55
|
||
dS1dc66 = dS1dI1 * dI1dc66 + dS1dI2 * dI2dc66 + dS1dI3 * dI3dc66
|
||
|
||
dS2dc12 = dS2dI1 * dI1dc12 + dS2dI2 * dI2dc12 + dS2dI3 * dI3dc12
|
||
dS2dc21 = dS2dI1 * dI1dc21 + dS2dI2 * dI2dc21 + dS2dI3 * dI3dc21
|
||
dS2dc23 = dS2dI1 * dI1dc23 + dS2dI2 * dI2dc23 + dS2dI3 * dI3dc23
|
||
dS2dc32 = dS2dI1 * dI1dc32 + dS2dI2 * dI2dc32 + dS2dI3 * dI3dc32
|
||
dS2dc31 = dS2dI1 * dI1dc31 + dS2dI2 * dI2dc31 + dS2dI3 * dI3dc31
|
||
dS2dc13 = dS2dI1 * dI1dc13 + dS2dI2 * dI2dc13 + dS2dI3 * dI3dc13
|
||
dS2dc44 = dS2dI1 * dI1dc44 + dS2dI2 * dI2dc44 + dS2dI3 * dI3dc44
|
||
dS2dc55 = dS2dI1 * dI1dc55 + dS2dI2 * dI2dc55 + dS2dI3 * dI3dc55
|
||
dS2dc66 = dS2dI1 * dI1dc66 + dS2dI2 * dI2dc66 + dS2dI3 * dI3dc66
|
||
|
||
dS3dc12 = dS3dI1 * dI1dc12 + dS3dI2 * dI2dc12 + dS3dI3 * dI3dc12
|
||
dS3dc21 = dS3dI1 * dI1dc21 + dS3dI2 * dI2dc21 + dS3dI3 * dI3dc21
|
||
dS3dc23 = dS3dI1 * dI1dc23 + dS3dI2 * dI2dc23 + dS3dI3 * dI3dc23
|
||
dS3dc32 = dS3dI1 * dI1dc32 + dS3dI2 * dI2dc32 + dS3dI3 * dI3dc32
|
||
dS3dc31 = dS3dI1 * dI1dc31 + dS3dI2 * dI2dc31 + dS3dI3 * dI3dc31
|
||
dS3dc13 = dS3dI1 * dI1dc13 + dS3dI2 * dI2dc13 + dS3dI3 * dI3dc13
|
||
dS3dc44 = dS3dI1 * dI1dc44 + dS3dI2 * dI2dc44 + dS3dI3 * dI3dc44
|
||
dS3dc55 = dS3dI1 * dI1dc55 + dS3dI2 * dI2dc55 + dS3dI3 * dI3dc55
|
||
dS3dc66 = dS3dI1 * dI1dc66 + dS3dI2 * dI2dc66 + dS3dI3 * dI3dc66
|
||
|
||
return dS1dc12, dS1dc21, dS1dc23, dS1dc32, dS1dc31, dS1dc13, dS1dc44, dS1dc55, dS1dc66, \
|
||
dS2dc12, dS2dc21, dS2dc23, dS2dc32, dS2dc31, dS2dc13, dS2dc44, dS2dc55, dS2dc66, \
|
||
dS3dc12, dS3dc21, dS3dc23, dS3dc32, dS3dc31, dS3dc13, dS3dc44, dS3dc55, dS3dc66
|
||
|
||
def Yld200418pBasis(sigma0, c12,c21,c23,c32,c31,c13,c44,c55,c66,
|
||
d12,d21,d23,d32,d31,d13,d44,d55,d66, m, sigmas, Jac=False):
|
||
|
||
sv = (sigmas[0] + sigmas[1] + sigmas[2])/3.0
|
||
s1 = sigmas[0]-sv; s2 = sigmas[1]-sv; s3 = sigmas[2]-sv
|
||
s4 = sigmas[3]; s5 = sigmas[4]; s6 = sigmas[5]
|
||
|
||
p = np.empty_like(sigmas); q = np.empty_like(sigmas)
|
||
p[0] = -c12*s2 - c13*s3
|
||
p[1] = -c21*s1 - c23*s3
|
||
p[2] = -c31*s1 - c32*s2
|
||
p[3] = c44*s4
|
||
p[4] = c55*s5
|
||
p[5] = c66*s6
|
||
|
||
q[0] = -d12*s2 - d13*s3
|
||
q[1] = -d21*s1 - d23*s3
|
||
q[2] = -d31*s1 - d32*s2
|
||
q[3] = d44*s4
|
||
q[4] = d55*s5
|
||
q[5] = d66*s6
|
||
|
||
plambdas, pInvariant = principalStress(p) # no sort
|
||
qlambdas, qInvariant = principalStress(q) # no sort
|
||
|
||
P1 = plambdas[0,:]; P2 = plambdas[1,:]; P3 = plambdas[2,:]
|
||
Q1 = qlambdas[0,:]; Q2 = qlambdas[1,:]; Q3 = qlambdas[2,:]
|
||
|
||
m2 = m/2.0; m1 = 1.0/m; m21 = m2-1.0
|
||
P1Q1s = (P1-Q1)**2; P1Q2s = (P1-Q2)**2; P1Q3s = (P1-Q3)**2
|
||
P2Q1s = (P2-Q1)**2; P2Q2s = (P2-Q2)**2; P2Q3s = (P2-Q3)**2
|
||
P3Q1s = (P3-Q1)**2; P3Q2s = (P3-Q2)**2; P3Q3s = (P3-Q3)**2
|
||
|
||
phi= P1Q1s**m2 + P1Q2s**m2 + P1Q3s**m2 + \
|
||
P2Q1s**m2 + P2Q2s**m2 + P2Q3s**m2 + \
|
||
P3Q1s**m2 + P3Q2s**m2 + P3Q3s**m2
|
||
r = (0.25*phi)**m1/sigma0 - 1.0
|
||
|
||
if not Jac:
|
||
return r.ravel()
|
||
else:
|
||
ln = lambda x : np.log(x + 1.0e-32)
|
||
|
||
drdphi = (r+1.0)*m1/phi
|
||
dphidm =( (P1Q1s**m2)*ln(P1Q1s) + (P1Q2s**m2)*ln(P1Q2s) + (P1Q3s**m2)*ln(P1Q3s) +
|
||
(P2Q1s**m2)*ln(P2Q1s) + (P2Q2s**m2)*ln(P2Q2s) + (P2Q3s**m2)*ln(P2Q3s) +
|
||
(P3Q1s**m2)*ln(P3Q1s) + (P3Q2s**m2)*ln(P3Q2s) + (P3Q3s**m2)*ln(P3Q3s)
|
||
)*0.5
|
||
js = -(r+1.0)/sigma0
|
||
jm = drdphi*dphidm + (r+1.0)*ln(0.25*phi)*(-m1*m1)
|
||
|
||
dP1dc12, dP1dc21, dP1dc23, dP1dc32, dP1dc31, dP1dc13, dP1dc44, dP1dc55, dP1dc66, \
|
||
dP2dc12, dP2dc21, dP2dc23, dP2dc32, dP2dc31, dP2dc13, dP2dc44, dP2dc55, dP2dc66, \
|
||
dP3dc12, dP3dc21, dP3dc23, dP3dc32, dP3dc31, dP3dc13, dP3dc44, dP3dc55, dP3dc66= \
|
||
principalStrs_Der(p, pInvariant, s1,s2,s3,s4,s5,s6)
|
||
|
||
dQ1dd12, dQ1dd21, dQ1dd23, dQ1dd32, dQ1dd31, dQ1dd13, dQ1dd44, dQ1dd55, dQ1dd66, \
|
||
dQ2dd12, dQ2dd21, dQ2dd23, dQ2dd32, dQ2dd31, dQ2dd13, dQ2dd44, dQ2dd55, dQ2dd66, \
|
||
dQ3dd12, dQ3dd21, dQ3dd23, dQ3dd32, dQ3dd31, dQ3dd13, dQ3dd44, dQ3dd55, dQ3dd66= \
|
||
principalStrs_Der(q, qInvariant, s1,s2,s3,s4,s5,s6)
|
||
|
||
dphidP1 = m*( P1Q1s**m21*(P1-Q1) + P1Q2s**m21*(P1-Q2) + P1Q3s**m21*(P1-Q3) )
|
||
dphidP2 = m*( P2Q1s**m21*(P2-Q1) + P2Q2s**m21*(P2-Q2) + P2Q3s**m21*(P2-Q3) )
|
||
dphidP3 = m*( P3Q1s**m21*(P3-Q1) + P3Q2s**m21*(P3-Q2) + P3Q3s**m21*(P3-Q3) )
|
||
|
||
dphidQ1 = m*( P1Q1s**m21*(Q1-P1) + P2Q1s**m21*(Q1-P2) + P3Q1s**m21*(Q1-P3) )
|
||
dphidQ2 = m*( P1Q2s**m21*(Q2-P1) + P2Q2s**m21*(Q2-P2) + P3Q2s**m21*(Q2-P3) )
|
||
dphidQ3 = m*( P1Q3s**m21*(Q3-P1) + P2Q3s**m21*(Q3-P2) + P3Q3s**m21*(Q3-P3) )
|
||
|
||
jc12 = drdphi*( dphidP1*dP1dc12 + dphidP2*dP2dc12 + dphidP3*dP3dc12 )
|
||
jc21 = drdphi*( dphidP1*dP1dc21 + dphidP2*dP2dc21 + dphidP3*dP3dc21 )
|
||
jc23 = drdphi*( dphidP1*dP1dc23 + dphidP2*dP2dc23 + dphidP3*dP3dc23 )
|
||
jc32 = drdphi*( dphidP1*dP1dc32 + dphidP2*dP2dc32 + dphidP3*dP3dc32 )
|
||
jc31 = drdphi*( dphidP1*dP1dc31 + dphidP2*dP2dc31 + dphidP3*dP3dc31 )
|
||
jc13 = drdphi*( dphidP1*dP1dc13 + dphidP2*dP2dc13 + dphidP3*dP3dc13 )
|
||
jc44 = drdphi*( dphidP1*dP1dc44 + dphidP2*dP2dc44 + dphidP3*dP3dc44 )
|
||
jc55 = drdphi*( dphidP1*dP1dc55 + dphidP2*dP2dc55 + dphidP3*dP3dc55 )
|
||
jc66 = drdphi*( dphidP1*dP1dc66 + dphidP2*dP2dc66 + dphidP3*dP3dc66 )
|
||
|
||
jd12 = drdphi*( dphidQ1*dQ1dd12 + dphidQ2*dQ2dd12 + dphidQ3*dQ3dd12 )
|
||
jd21 = drdphi*( dphidQ1*dQ1dd21 + dphidQ2*dQ2dd21 + dphidQ3*dQ3dd21 )
|
||
jd23 = drdphi*( dphidQ1*dQ1dd23 + dphidQ2*dQ2dd23 + dphidQ3*dQ3dd23 )
|
||
jd32 = drdphi*( dphidQ1*dQ1dd32 + dphidQ2*dQ2dd32 + dphidQ3*dQ3dd32 )
|
||
jd31 = drdphi*( dphidQ1*dQ1dd31 + dphidQ2*dQ2dd31 + dphidQ3*dQ3dd31 )
|
||
jd13 = drdphi*( dphidQ1*dQ1dd13 + dphidQ2*dQ2dd13 + dphidQ3*dQ3dd13 )
|
||
jd44 = drdphi*( dphidQ1*dQ1dd44 + dphidQ2*dQ2dd44 + dphidQ3*dQ3dd44 )
|
||
jd55 = drdphi*( dphidQ1*dQ1dd55 + dphidQ2*dQ2dd55 + dphidQ3*dQ3dd55 )
|
||
jd66 = drdphi*( dphidQ1*dQ1dd66 + dphidQ2*dQ2dd66 + dphidQ3*dQ3dd66 )
|
||
|
||
jaco = []
|
||
for jacv in zip(js,jc12,jc21,jc23,jc32,jc31,jc13,jc44,jc55,jc66,
|
||
jd12,jd21,jd23,jd32,jd31,jd13,jd44,jd55,jd66, jm):
|
||
jaco.append(jacv)
|
||
return np.array(jaco)
|
||
|
||
def KarafillisBoyceBasis(sigma0, c11,c12,c13,c14,c15,c16,c21,c22,c23,c24,c25,c26,
|
||
b1, b2, a, alpha , sigmas, Jac=False):
|
||
s1 = sigmas[0]; s2 = sigmas[1]; s3 = sigmas[2]
|
||
s4 = sigmas[3]; s5 = sigmas[4]; s6 = sigmas[5]
|
||
|
||
p = np.empty_like(sigmas); q = np.empty_like(sigmas)
|
||
p[0] = ( (c12+c13)*s1 - c13*s2 - c12*s3 )/3.0
|
||
p[1] = ( (c13+c11)*s2 - c13*s1 - c11*s3 )/3.0
|
||
p[2] = ( (c11+c12)*s3 - c12*s1 - c11*s2 )/3.0
|
||
p[3] = c14*s4
|
||
p[4] = c15*s5
|
||
p[5] = c16*s6
|
||
|
||
q[0] = ( (c22+c23)*s1 - c23*s2 - c22*s3 )/3.0
|
||
q[1] = ( (c23+c21)*s2 - c23*s1 - c21*s3 )/3.0
|
||
q[2] = ( (c21+c22)*s3 - c22*s1 - c21*s2 )/3.0
|
||
q[3] = c24*s4
|
||
q[4] = c25*s5
|
||
q[5] = c26*s6
|
||
|
||
plambdas, pInvariant = principalStress(p) # no sort
|
||
qlambdas, qInvariant = principalStress(q) # no sort
|
||
|
||
P1 = plambdas[0,:]; P2 = plambdas[1,:]; P3 = plambdas[2,:]
|
||
Q1 = qlambdas[0,:]; Q2 = qlambdas[1,:]; Q3 = qlambdas[2,:]
|
||
|
||
b1h = b1/2.0; b1h1 = b1h-1.0; b2h = b2/2.0; b2h1 = b2h-1.0
|
||
b1i = 1.0/b1; b2i = 1.0/b2
|
||
ai = 1.0/a
|
||
P2P3s = (P2-P3)**2; Q1s = Q1**2
|
||
P3P1s = (P3-P1)**2; Q2s = Q2**2
|
||
P1P2s = (P1-P2)**2; Q3s = Q3**2
|
||
|
||
phi10 = P2P3s**b1h + P3P1s**b1h + P1P2s**b1h
|
||
phi20 = Q1s**b2h+Q2s**b2h+Q3s**b2h; rb2 = 3.0**b2/(2.0**b2+2.0)
|
||
phi1 = (0.5*phi10)**b1i
|
||
phi2 = (rb2*phi20)**b2i
|
||
|
||
Stress = alpha*phi1**a + (1.0-alpha)*phi2**a; EqStress = Stress**ai
|
||
r = EqStress/sigma0 - 1.0
|
||
|
||
if not Jac:
|
||
return r.ravel()
|
||
else:
|
||
ln = lambda x : np.log(x + 1.0e-32)
|
||
|
||
drds = (r+1.0)*ai/Stress
|
||
drdphi1 = drds* alpha *a*phi1**(a-1.0)
|
||
drdphi2 = drds*(1.0-alpha)*a*phi2**(a-1.0)
|
||
dsda = alpha*phi1**a*ln(phi1) + (1.0-alpha)*phi2**a*ln(phi2)
|
||
|
||
dphi1dphi10 = phi1/phi10/b1; dphi2dphi20 = phi2/phi20/b2
|
||
dphi1dP1 = dphi1dphi10*b1*( P3P1s**b1h1*(P1-P3) + P1P2s**b1h1*(P1-P2))
|
||
dphi1dP2 = dphi1dphi10*b1*( P2P3s**b1h1*(P2-P3) + P1P2s**b1h1*(P2-P1))
|
||
dphi1dP3 = dphi1dphi10*b1*( P3P1s**b1h1*(P3-P1) + P2P3s**b1h1*(P3-P2))
|
||
|
||
dphi2dQ1 = dphi2dphi20*b2*Q1s*b2h1*Q1
|
||
dphi2dQ2 = dphi2dphi20*b2*Q2s*b2h1*Q2
|
||
dphi2dQ3 = dphi2dphi20*b2*Q3s*b2h1*Q3
|
||
|
||
dP1dc1,dP1dc2,dP1dc3,dP1dc4,dP1dc5,dP1dc6, \
|
||
dP2dc1,dP2dc2,dP2dc3,dP2dc4,dP2dc5,dP2dc6, \
|
||
dP3dc1,dP3dc2,dP3dc3,dP3dc4,dP3dc5,dP3dc6= \
|
||
principalStrs_Der(p, pInvariant, s1,s2,s3,s4,s5,s6, Karafillis=True)
|
||
dQ1dc1,dQ1dc2,dQ1dc3,dQ1dc4,dQ1dc5,dQ1dc6, \
|
||
dQ2dc1,dQ2dc2,dQ2dc3,dQ2dc4,dQ2dc5,dQ2dc6, \
|
||
dQ3dc1,dQ3dc2,dQ3dc3,dQ3dc4,dQ3dc5,dQ3dc6= \
|
||
principalStrs_Der(q, qInvariant, s1,s2,s3,s4,s5,s6, Karafillis=True)
|
||
|
||
dphi10db1 = ( (P2P3s**b1h)*ln(P2P3s)+(P3P1s**b1h)*ln(P3P1s)+(P1P2s**b1h)*ln(P1P2s) )*0.5
|
||
dphi20db2 = ( (P2P3s**b1h)*ln(P2P3s)+(P3P1s**b1h)*ln(P3P1s)+(P1P2s**b1h)*ln(P1P2s) )*0.5
|
||
drb2db2 = rb2*ln(3.0) - rb2*ln(2.0)/(1.0+2.0**(1.0-b2))
|
||
dphi1db1 = phi1*ln(phi10)*(-b1i*b1i) + b1i*phi1/(0.5*phi10)* 0.5*dphi10db1
|
||
dphi2db2 = phi2*ln(phi20)*(-b2i*b2i) + b2i*phi2/(rb2*phi20)*(rb2*dphi20db2 + drb2db2*phi20)
|
||
ja = drds*dsda - (r+1.0)*ln(Stress)/a/a #drda
|
||
jb1 = drds * ( alpha *a*phi1**(a-1)) * dphi1db1
|
||
jb2 = drds * ((1.0-alpha)*a*phi2**(a-1)) * dphi2db2
|
||
jalpha = drds * (phi1**a - phi2**a)
|
||
|
||
jc11 = drdphi1*( dphi1dP1*dP1dc1 + dphi1dP2*dP2dc1 + dphi1dP3*dP3dc1 )
|
||
jc12 = drdphi1*( dphi1dP1*dP1dc2 + dphi1dP2*dP2dc2 + dphi1dP3*dP3dc2 )
|
||
jc13 = drdphi1*( dphi1dP1*dP1dc3 + dphi1dP2*dP2dc3 + dphi1dP3*dP3dc3 )
|
||
jc14 = drdphi1*( dphi1dP1*dP1dc4 + dphi1dP2*dP2dc4 + dphi1dP3*dP3dc4 )
|
||
jc15 = drdphi1*( dphi1dP1*dP1dc5 + dphi1dP2*dP2dc5 + dphi1dP3*dP3dc5 )
|
||
jc16 = drdphi1*( dphi1dP1*dP1dc6 + dphi1dP2*dP2dc6 + dphi1dP3*dP3dc6 )
|
||
|
||
jc21 = drdphi2*( dphi2dQ1*dQ1dc1 + dphi2dQ2*dQ2dc1 + dphi2dQ3*dQ3dc1 )
|
||
jc22 = drdphi2*( dphi2dQ1*dQ1dc2 + dphi2dQ2*dQ2dc2 + dphi2dQ3*dQ3dc2 )
|
||
jc23 = drdphi2*( dphi2dQ1*dQ1dc3 + dphi2dQ2*dQ2dc3 + dphi2dQ3*dQ3dc3 )
|
||
jc24 = drdphi2*( dphi2dQ1*dQ1dc4 + dphi2dQ2*dQ2dc4 + dphi2dQ3*dQ3dc4 )
|
||
jc25 = drdphi2*( dphi2dQ1*dQ1dc5 + dphi2dQ2*dQ2dc5 + dphi2dQ3*dQ3dc5 )
|
||
jc26 = drdphi2*( dphi2dQ1*dQ1dc6 + dphi2dQ2*dQ2dc6 + dphi2dQ3*dQ3dc6 )
|
||
|
||
jaco = []
|
||
for jacv in zip(jc11,jc12,jc13,jc14,jc15,jc16,jc21,jc22,jc23,jc24,jc25,jc26,
|
||
jb1,jb2,ja,jalpha):
|
||
jaco.append(jacv)
|
||
return np.array(jaco)
|
||
|
||
|
||
fittingCriteria = {
|
||
'tresca' :{'func' : Tresca,
|
||
'num' : 1,'err':np.inf,
|
||
'name' : 'Tresca',
|
||
'paras': 'Initial yield stress:',
|
||
'text' : '\nCoefficient of Tresca criterion:\nsigma0: ',
|
||
'error': 'The standard deviation error is: '
|
||
},
|
||
'vonmises' :{'func' : vonMises,
|
||
'num' : 1,'err':np.inf,
|
||
'name' : 'Huber-Mises-Hencky(von Mises)',
|
||
'paras': 'Initial yield stress:',
|
||
'text' : '\nCoefficient of Huber-Mises-Hencky criterion:\nsigma0: ',
|
||
'error': 'The standard deviation error is: '
|
||
},
|
||
'hosfordiso' :{'func' : Hosford,
|
||
'num' : 2,'err':np.inf,
|
||
'name' : 'Gerenal isotropic Hosford',
|
||
'paras': 'Initial yield stress, a:',
|
||
'text' : '\nCoefficients of Hosford criterion:\nsigma0, a: ',
|
||
'error': 'The standard deviation errors are: '
|
||
},
|
||
'hosfordaniso' :{'func' : generalHosford,
|
||
'num' : 5,'err':np.inf,
|
||
'name' : 'Gerenal isotropic Hosford',
|
||
'paras': 'Initial yield stress, F, G, H, a:',
|
||
'text' : '\nCoefficients of Hosford criterion:\nsigma0, F, G, H, a: ',
|
||
'error': 'The standard deviation errors are: '
|
||
},
|
||
'hill1948' :{'func' : Hill1948,
|
||
'num' : 6,'err':np.inf,
|
||
'name' : 'Hill1948',
|
||
'paras': 'Normalized [F, G, H, L, M, N]:',
|
||
'text' : '\nCoefficients of Hill1948 criterion:\n[F, G, H, L, M, N]:'+' '*16,
|
||
'error': 'The standard deviation errors are: '
|
||
},
|
||
'hill1979' :{'func' : Hill1979,
|
||
'num' : 7,'err':np.inf,
|
||
'name' : 'Hill1979',
|
||
'paras': 'f,g,h,a,b,c,m:',
|
||
'text' : '\nCoefficients of Hill1979 criterion:\n f,g,h,a,b,c,m:\n',
|
||
'error': 'The standard deviation errors are: '
|
||
},
|
||
'drucker' :{'func' : Drucker,
|
||
'num' : 2,'err':np.inf,
|
||
'name' : 'Drucker',
|
||
'paras': 'Initial yield stress, C_D:',
|
||
'text' : '\nCoefficients of Drucker criterion:\nsigma0, C_D: ',
|
||
'error': 'The standard deviation errors are: '
|
||
},
|
||
'gdrucker' :{'func' : generalDrucker,
|
||
'num' : 3,'err':np.inf,
|
||
'name' : 'General Drucker',
|
||
'paras': 'Initial yield stress, C_D, p:',
|
||
'text' : '\nCoefficients of Drucker criterion:\nsigma0, C_D, p: ',
|
||
'error': 'The standard deviation errors are: '
|
||
},
|
||
'barlat1991iso' :{'func' : Barlat1991iso,
|
||
'num' : 2,'err':np.inf,
|
||
'name' : 'Barlat1991iso',
|
||
'paras': 'Initial yield stress, m:',
|
||
'text' : '\nCoefficients of isotropic Barlat 1991 criterion:\nsigma0, m:\n',
|
||
'error': 'The standard deviation errors are: '
|
||
},
|
||
'barlat1991aniso':{'func' : Barlat1991aniso,
|
||
'num' : 8,'err':np.inf,
|
||
'name' : 'Barlat1991aniso',
|
||
'paras': 'Initial yield stress, a, b, c, f, g, h, m:',
|
||
'text' : '\nCoefficients of anisotropic Barlat 1991 criterion:\nsigma0, a, b, c, f, g, h, m:\n',
|
||
'error': 'The standard deviation errors are: '
|
||
},
|
||
'bbc2003' :{'func' : BBC2003,
|
||
'num' : 9,'err':np.inf,
|
||
'name' : 'Banabic-Balan-Comsa 2003',
|
||
'paras': 'Initial yield stress, a, b, c, d, e, f, g, k:',
|
||
'text' : '\nCoefficients of anisotropic Barlat 1991 criterion:\nsigma0, a, b, c, d, e, f, g, k:\n',
|
||
'error': 'The standard deviation errors are: '
|
||
},
|
||
'Cazacu_Barlat2D':{'func' : Cazacu_Barlat2D,
|
||
'num' : 11,'err':np.inf,
|
||
'name' : 'Cazacu Barlat for plain stress',
|
||
'paras': 'a1,a2,a3,a6; b1,b2,b3,b4,b5,b10; c:',
|
||
'text' : '\nCoefficients of Cazacu Barlat yield criterion for plane stress: \
|
||
\n a1,a2,a3,a6; b1,b2,b3,b4,b5,b10; c:\n',
|
||
'error': 'The standard deviation errors are: '
|
||
},
|
||
'Cazacu_Barlat3D':{'func' : Cazacu_Barlat3D,
|
||
'num' : 18,'err':np.inf,
|
||
'name' : 'Cazacu Barlat',
|
||
'paras': 'a1,a2,a3,a4,a5,a6; b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11; c:',
|
||
'text' : '\nCoefficients of Cazacu Barlat yield criterion for plane stress: \
|
||
\n a1,a2,a3,a4,a5,a6; b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11; c\n',
|
||
'error': 'The standard deviation errors are: '
|
||
},
|
||
'yld200418p' :{'func' : Yld200418p,
|
||
'num' : 20,'err':np.inf,
|
||
'name' : 'Yld200418p',
|
||
'paras': 'Equivalent stress,c12,c21,c23,c32,c31,c13,c44,c55,c66,d12,d21,d23,d32,d31,d13,d44,d55,d66,m:',
|
||
'text' : '\nCoefficients of Yld2004-18p yield criterion: \
|
||
\n Y, c12,c21,c23,c32,c31,c13,c44,c55,c66,d12,d21,d23,d32,d31,d13,d44,d55,d66,m\n',
|
||
'error': 'The standard deviation errors are: '
|
||
},
|
||
'karafillis' :{'func' : KarafillisBoyce,
|
||
'num' : 16,'err':np.inf,
|
||
'name' : 'Yld200418p',
|
||
'paras': 'c11,c12,c13,c14,c15,c16,c21,c22,c23,c24,c25,c26,b1,b2,a,alpha',
|
||
'text' : '\nCoefficients of Karafillis-Boyce yield criterion: \
|
||
\n c11,c12,c13,c14,c15,c16,c21,c22,c23,c24,c25,c26,b1,b2,a,alpha\n',
|
||
'error': 'The standard deviation errors are: '
|
||
},
|
||
'worst' :{'err':np.inf},
|
||
'best' :{'err':np.inf}
|
||
}
|
||
|
||
for key in fittingCriteria.keys():
|
||
if 'num' in fittingCriteria[key].keys():
|
||
fittingCriteria[key]['bound']=[(None,None)]*fittingCriteria[key]['num']
|
||
fittingCriteria[key]['guess']=np.ones(fittingCriteria[key]['num'],'d')
|
||
|
||
thresholdParameter = ['totalshear','equivalentStrain']
|
||
|
||
#---------------------------------------------------------------------------------------------------
|
||
class Loadcase():
|
||
#---------------------------------------------------------------------------------------------------
|
||
'''
|
||
Class for generating load cases for the spectral solver
|
||
'''
|
||
|
||
# ------------------------------------------------------------------
|
||
def __init__(self,finalStrain,incs,time):
|
||
print('using the random load case generator')
|
||
self.finalStrain = finalStrain
|
||
self.incs = incs
|
||
self.time = time
|
||
|
||
def getLoadcase(self,N=0):
|
||
defgrad=['*']*9
|
||
stress =[0]*9
|
||
values=(np.random.random_sample(9)-.5)*self.finalStrain*2
|
||
|
||
main=np.array([0,4,8])
|
||
np.random.shuffle(main)
|
||
for i in main[:2]: # fill 2 out of 3 main entries
|
||
defgrad[i]=1.+values[i]
|
||
stress[i]='*'
|
||
for off in [[1,3,0],[2,6,0],[5,7,0]]: # fill 3 off-diagonal pairs of defgrad (1 or 2 entries)
|
||
off=np.array(off)
|
||
np.random.shuffle(off)
|
||
for i in off[0:2]:
|
||
if i != 0:
|
||
defgrad[i]=values[i]
|
||
stress[i]='*'
|
||
|
||
return 'f '+' '.join(str(c) for c in defgrad)+\
|
||
' p '+' '.join(str(c) for c in stress)+\
|
||
' incs %s'%self.incs+\
|
||
' time %s'%self.time
|
||
|
||
#---------------------------------------------------------------------------------------------------
|
||
class Criterion(object):
|
||
#---------------------------------------------------------------------------------------------------
|
||
'''
|
||
Fitting to certain criterion
|
||
'''
|
||
def __init__(self,name='worst'):
|
||
self.name = name
|
||
self.results = fittingCriteria
|
||
|
||
if self.name.lower() not in map(str.lower, self.results.keys()):
|
||
raise Exception('no suitable fitting criterion selected')
|
||
else:
|
||
print('fitting to the %s criterion'%name)
|
||
|
||
def fit(self,stress):
|
||
global fitResults
|
||
|
||
nameCriterion = self.name.lower()
|
||
criteriaClass = fittingCriteria[nameCriterion]['func']
|
||
numParas = fittingCriteria[nameCriterion]['num']
|
||
textParas = fittingCriteria[nameCriterion]['text'] + formatOutput(numParas)
|
||
textError = fittingCriteria[nameCriterion]['error']+ formatOutput(numParas,'%-14.8f')+'\n'
|
||
bounds = fittingCriteria[nameCriterion]['bound'] # Default bounds, no bound
|
||
guess0 = fittingCriteria[nameCriterion]['guess'] # Default initial guess, depends on bounds
|
||
criteria = criteriaClass(0.0)
|
||
if fitResults == [] : initialguess = guess0
|
||
else : initialguess = np.array(fitResults[-1])
|
||
weight = get_weight(np.shape(stress)[1])
|
||
ydata = np.zeros(np.shape(stress)[1])
|
||
try:
|
||
popt, pcov, infodict, errmsg, ierr = \
|
||
leastsqBound (criteria.fun, initialguess, args=(ydata,stress),
|
||
bounds=bounds, Dfun=criteria.jac, full_output=True)
|
||
if ierr not in [1, 2, 3, 4]:
|
||
raise RuntimeError("Optimal parameters not found: " + errmsg)
|
||
if (len(ydata) > len(initialguess)) and pcov is not None:
|
||
s_sq = (criteria.fun(popt, *(ydata,stress))**2).sum()/(len(ydata)-len(initialguess))
|
||
pcov = pcov * s_sq
|
||
perr = np.sqrt(np.diag(pcov))
|
||
fitResults.append(popt.tolist())
|
||
|
||
print (textParas%array2tuple(popt))
|
||
print (textError%array2tuple(perr))
|
||
print('Number of function calls =', infodict['nfev'])
|
||
except Exception as detail:
|
||
print detail
|
||
pass
|
||
|
||
|
||
#---------------------------------------------------------------------------------------------------
|
||
class myThread (threading.Thread):
|
||
#---------------------------------------------------------------------------------------------------
|
||
'''
|
||
Runner class
|
||
'''
|
||
def __init__(self, threadID):
|
||
threading.Thread.__init__(self)
|
||
self.threadID = threadID
|
||
def run(self):
|
||
s.acquire()
|
||
conv=converged()
|
||
s.release()
|
||
while not conv:
|
||
doSim(4.,self.name)
|
||
s.acquire()
|
||
conv=converged()
|
||
s.release()
|
||
|
||
def doSim(delay,thread):
|
||
|
||
s.acquire()
|
||
me=getLoadcase()
|
||
if not os.path.isfile('%s.load'%me):
|
||
print('generating loadcase for sim %s from %s'%(me,thread))
|
||
f=open('%s.load'%me,'w')
|
||
f.write(myLoad.getLoadcase(me))
|
||
f.close()
|
||
s.release()
|
||
else: s.release()
|
||
|
||
s.acquire()
|
||
if not os.path.isfile('%s_%i.spectralOut'%(options.geometry,me)):
|
||
print('starting simulation %s from %s'%(me,thread))
|
||
s.release()
|
||
execute('DAMASK_spectral -g %s -l %i'%(options.geometry,me))
|
||
else: s.release()
|
||
|
||
s.acquire()
|
||
if not os.path.isfile('./postProc/%s_%i.txt'%(options.geometry,me)):
|
||
print('starting post processing for sim %i from %s'%(me,thread))
|
||
s.release()
|
||
try:
|
||
execute('postResults --cr f,p --co totalshear %s_%i.spectralOut'%(options.geometry,me))
|
||
except:
|
||
execute('postResults --cr f,p %s_%i.spectralOut'%(options.geometry,me))
|
||
execute('addCauchy ./postProc/%s_%i.txt'%(options.geometry,me))
|
||
execute('addStrainTensors -l -v ./postProc/%s_%i.txt'%(options.geometry,me))
|
||
execute('addMises -s Cauchy -e ln(V) ./postProc/%s_%i.txt'%(options.geometry,me))
|
||
else: s.release()
|
||
|
||
s.acquire()
|
||
print('-'*10)
|
||
print('reading values for sim %i from %s'%(me,thread))
|
||
s.release()
|
||
|
||
refFile = open('./postProc/%s_%i.txt'%(options.geometry,me))
|
||
table = damask.ASCIItable(refFile)
|
||
table.head_read()
|
||
if options.fitting =='equivalentStrain':
|
||
thresholdKey = 'Mises(ln(V))'
|
||
elif options.fitting =='totalshear':
|
||
thresholdKey = 'totalshear'
|
||
s.acquire()
|
||
for l in [thresholdKey,'1_Cauchy']:
|
||
if l not in table.labels: print '%s not found'%l
|
||
s.release()
|
||
table.data_readArray(['%i_Cauchy'%(i+1) for i in xrange(9)]+[thresholdKey]+['%i_ln(V)'%(i+1) for i in xrange(9)])
|
||
|
||
line = 0
|
||
lines = np.shape(table.data)[0]
|
||
yieldStress = np.empty((int(options.yieldValue[2]),6),'d')
|
||
deformationRate = np.empty((int(options.yieldValue[2]),6),'d')
|
||
for i,threshold in enumerate(np.linspace(options.yieldValue[0],options.yieldValue[1],options.yieldValue[2])):
|
||
while line < lines:
|
||
if table.data[line,9]>= threshold:
|
||
upper,lower = table.data[line,9],table.data[line-1,9] # values for linear interpolation
|
||
stress = np.array(table.data[line-1,0:9] * (upper-threshold)/(upper-lower) + \
|
||
table.data[line ,0:9] * (threshold-lower)/(upper-lower)).reshape(3,3) # linear interpolation of stress values
|
||
dstrain= np.array(table.data[line,10:] - table.data[line-1,10:]).reshape(3,3)
|
||
|
||
yieldStress[i,0]= stress[0,0]; yieldStress[i,1]=stress[1,1]; yieldStress[i,2]=stress[2,2]
|
||
yieldStress[i,3]=(stress[0,1] + stress[1,0])/2.0 # 0 3 5
|
||
yieldStress[i,4]=(stress[1,2] + stress[2,1])/2.0 # * 1 4 yieldStress
|
||
yieldStress[i,5]=(stress[2,0] + stress[0,2])/2.0 # * * 2
|
||
|
||
# D*dt = 0.5(L+L^T)*dt = 0.5*d(lnF + lnF^T) = dlnV
|
||
deformationRate[i,0]= dstrain[0,0]; deformationRate[i,1]=dstrain[1,1]; deformationRate[i,2]=dstrain[2,2]
|
||
deformationRate[i,3]=(dstrain[0,1] + dstrain[1,0])/2.0 # 0 3 5
|
||
deformationRate[i,4]=(dstrain[1,2] + dstrain[2,1])/2.0 # * 1 4
|
||
deformationRate[i,5]=(dstrain[2,0] + dstrain[0,2])/2.0 # * * 2
|
||
break
|
||
else:
|
||
line+=1
|
||
|
||
s.acquire()
|
||
global stressAll, strainAll
|
||
print('number of yield points of sim %i: %i'%(me,len(yieldStress)))
|
||
print('starting fitting for sim %i from %s'%(me,thread))
|
||
try:
|
||
for i in xrange(int(options.yieldValue[2])):
|
||
stressAll[i]=np.append(stressAll[i], yieldStress[i]/unitGPa)
|
||
strainAll[i]=np.append(strainAll[i], deformationRate[i])
|
||
myFit.fit(stressAll[i].reshape(len(stressAll[i])//6,6).transpose())
|
||
except Exception as detail:
|
||
print('could not fit for sim %i from %s'%(me,thread))
|
||
print detail
|
||
s.release()
|
||
return
|
||
s.release()
|
||
|
||
def getLoadcase():
|
||
global N_simulations
|
||
N_simulations+=1
|
||
return N_simulations
|
||
|
||
def converged():
|
||
global N_simulations
|
||
if N_simulations < options.max:
|
||
return False
|
||
else:
|
||
return True
|
||
|
||
# --------------------------------------------------------------------
|
||
# MAIN
|
||
# --------------------------------------------------------------------
|
||
|
||
parser = OptionParser(option_class=damask.extendableOption, usage='%prog options [file[s]]', description = """
|
||
Performs calculations with various loads on given geometry file and fits yield surface.
|
||
|
||
""", version=string.replace(scriptID,'\n','\\n')
|
||
)
|
||
|
||
parser.add_option('-l','--load' , dest='load', type='float', nargs=3,
|
||
help='load: final strain; increments; time %default', metavar='float int float')
|
||
parser.add_option('-g','--geometry', dest='geometry', type='string',
|
||
help='name of the geometry file [%default]', metavar='string')
|
||
parser.add_option('-c','--criterion', dest='criterion', choices=fittingCriteria.keys(),
|
||
help='criterion for stopping simulations [%default]', metavar='string')
|
||
parser.add_option('-f','--fitting', dest='fitting', choices=thresholdParameter,
|
||
help='yield criterion [%default]', metavar='string')
|
||
parser.add_option('-y','--yieldvalue', dest='yieldValue', type='float', nargs=3,
|
||
help='yield points: start; end; count %default', metavar='float float int')
|
||
parser.add_option('--min', dest='min', type='int',
|
||
help='minimum number of simulations [%default]', metavar='int')
|
||
parser.add_option('--max', dest='max', type='int',
|
||
help='maximum number of iterations [%default]', metavar='int')
|
||
parser.add_option('-t','--threads', dest='threads', type='int',
|
||
help='number of parallel executions [%default]', metavar='int')
|
||
parser.set_defaults(min = 12)
|
||
parser.set_defaults(max = 30)
|
||
parser.set_defaults(threads = 4)
|
||
parser.set_defaults(yieldValue = (0.002,0.004,2))
|
||
parser.set_defaults(load = (0.010,100,100.0))
|
||
parser.set_defaults(criterion = 'worst')
|
||
parser.set_defaults(fitting = 'totalshear')
|
||
parser.set_defaults(geometry = '20grains16x16x16')
|
||
|
||
options = parser.parse_args()[0]
|
||
|
||
if not os.path.isfile(options.geometry+'.geom'):
|
||
parser.error('geometry file %s.geom not found'%options.geometry)
|
||
if not os.path.isfile('material.config'):
|
||
parser.error('material.config file not found')
|
||
if options.threads<1:
|
||
parser.error('invalid number of threads %i'%options.threads)
|
||
if options.min<0:
|
||
parser.error('invalid minimum number of simulations %i'%options.min)
|
||
if options.max<options.min:
|
||
parser.error('invalid maximum number of simulations (below minimum)')
|
||
if options.yieldValue[0]>options.yieldValue[1]:
|
||
parser.error('invalid yield start (below yield end)')
|
||
if options.yieldValue[2] != int(options.yieldValue[2]):
|
||
parser.error('count must be an integer')
|
||
if not os.path.isfile('numerics.config'):
|
||
print('numerics.config file not found')
|
||
|
||
if not os.path.isfile('material.config'):
|
||
print('material.config file not found')
|
||
|
||
unitGPa = 10.e8
|
||
N_simulations=0
|
||
fitResults = []
|
||
s=threading.Semaphore(1)
|
||
|
||
stressAll=[np.zeros(0,'d').reshape(0,0) for i in xrange(int(options.yieldValue[2]))]
|
||
strainAll=[np.zeros(0,'d').reshape(0,0) for i in xrange(int(options.yieldValue[2]))]
|
||
myLoad = Loadcase(options.load[0],options.load[1],options.load[2])
|
||
myFit = Criterion(options.criterion)
|
||
|
||
threads=[]
|
||
|
||
for i in range(options.threads):
|
||
threads.append(myThread(i))
|
||
threads[i].start()
|
||
|
||
for i in range(options.threads):
|
||
threads[i].join()
|
||
|
||
print 'finished fitting to yield criteria'
|