DAMASK_EICMD/processing/misc/yieldSurface.py

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#!/usr/bin/python
# -*- coding: UTF-8 no BOM -*-
import threading,time,os,subprocess,shlex,string
import numpy as np
from scipy.linalg import svd
from optparse import OptionParser
import damask
from damask.util import leastsqBound
scriptID = string.replace('$Id$','\n','\\n')
scriptName = scriptID.split()[1][:-3]
def execute(cmd,streamIn=None,wd='./'):
'''
executes a command in given directory and returns stdout and stderr for optional stdin
'''
initialPath=os.getcwd()
os.chdir(wd)
process = subprocess.Popen(shlex.split(cmd),stdout=subprocess.PIPE,stderr = subprocess.PIPE,stdin=subprocess.PIPE)
if streamIn != None:
out,error = process.communicate(streamIn.read())
else:
out,error = process.communicate()
os.chdir(initialPath)
return out,error
def principalStresses(sigmas):
'''
computes principal stresses (i.e. eigenvalues) for a set of Cauchy stresses.
sorted in descending order.
'''
lambdas=np.zeros(0,'d')
for i in xrange(np.shape(sigmas)[1]):
eigenvalues = np.linalg.eigvalsh(sym6to33(sigmas[:,i]))
lambdas = np.append(lambdas,np.sort(eigenvalues)[::-1]) #append eigenvalues in descending order
lambdas = np.transpose(lambdas.reshape(np.shape(sigmas)[1],3))
return lambdas
def invariant(sigmas):
s11,s22,s33,s12,s23,s31 = sigmas
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
return (I1,I2,I3)
def formatOutput(n, type='%-14.6f'):
return ''.join([type for i in xrange(n)])
def math_ln(x):
return np.log(x + 1.0e-32)
def sym6to33(sigma6):
''' Shape the symmetric stress tensor(6,1) into (3,3) '''
sigma33 = np.empty((3,3))
sigma33[0,0] = sigma6[0]; sigma33[1,1] = sigma6[1]; sigma33[2,2] = sigma6[2];
sigma33[0,1] = sigma6[3]; sigma33[1,0] = sigma6[3]
sigma33[1,2] = sigma6[4]; sigma33[2,1] = sigma6[4]
sigma33[2,0] = sigma6[5]; sigma33[0,2] = sigma6[5]
return sigma33
def array2tuple(array):
'''transform numpy.array into tuple'''
try:
return tuple(array2tuple(i) for i in array)
except TypeError:
return array
def get_weight(ndim):
#more to do
return np.ones(ndim)
# ---------------------------------------------------------------------------------------------
# isotropic yield surfaces
# ---------------------------------------------------------------------------------------------
class Tresca(object):
'''
residuum of Tresca yield criterion (eq. 2.26)
'''
def __init__(self, uniaxialStress):
self.stress0 = uniaxialStress
def fun(self,sigma0, ydata, sigmas):
lambdas = principalStresses(sigmas)
r = np.amax(np.array([abs(lambdas[2,:]-lambdas[1,:]),\
abs(lambdas[1,:]-lambdas[0,:]),\
abs(lambdas[0,:]-lambdas[2,:])]),0) - sigma0
return r.ravel()
def jac(self,sigma0, ydata, sigmas):
return np.ones(len(ydata)) * (-1.0)
class vonMises(object):
'''
residuum of Huber-Mises-Hencky yield criterion (eq. 2.37)
'''
def __init__(self, uniaxialStress):
self.stress0 = uniaxialStress
def fun(self, sigma0, ydata, sigmas):
return HosfordBasis(sigma0, (0.5,0.5,0.5), 2.0, sigmas)
def jac(self, sigma0, ydata, sigmas):
return HosfordBasis(sigma0, (0.5,0.5,0.5), 2.0, sigmas, Jac=True, nParas=1)
class Drucker(object):
'''
residuum of Drucker yield criterion (eq. 2.41, F = sigma0)
'''
def __init__(self, uniaxialStress):
self.stress0 = uniaxialStress
def fun(self, (sigma0, C_D), ydata, sigmas):
return DruckerBasis(sigma0, C_D, 1.0, sigmas)
def jac(self, (sigma0, C_D), ydata, sigmas):
return DruckerBasis(sigma0, C_D, 1.0, sigmas, Jac=True, nParas=2)
class generalDrucker(object):
'''
residuum of general Drucker yield criterion (eq. 2.42, F = sigma0)
'''
def __init__(self, uniaxialStress):
self.stress0 = uniaxialStress
def fun(self, (sigma0, C_D, p), ydata, sigmas):
return DruckerBasis(sigma0, C_D, p, sigmas)
def jac(self, (sigma0, C_D, p), ydata, sigmas):
return DruckerBasis(sigma0, C_D, p, sigmas, Jac=True, nParas=3)
class Hosford(object):
'''
residuum of Hershey yield criterion (eq. 2.43, Y = sigma0)
'''
def __init__(self, uniaxialStress):
self.stress0 = uniaxialStress
def fun(self, (sigma0, a), ydata, sigmas):
return HosfordBasis(sigma0, (0.5,0.5,0.5), a, sigmas)
def jac(self, (sigma0, a), ydata, sigmas):
return HosfordBasis(sigma0, (0.5,0.5,0.5), a, sigmas, Jac=True, nParas=2)
class Hill1948(object):
'''
residuum of Hill 1948 quadratic yield criterion (eq. 2.48) Right
'''
def __init__(self, uniaxialStress):
self.stress0 = uniaxialStress
def fun(self, (F,G,H,L,M,N), ydata, sigmas):
return Hill1948Basis((F,G,H,L,M,N),sigmas)
def jac(self, (F,G,H,L,M,N), ydata, sigmas):
return Hill1948Basis((F,G,H,L,M,N),sigmas, Jac=True)
class Hill1979(object):
'''
residuum of Hill 1979 non-quadratic yield criterion (eq. 2.48)
'''
def __init__(self, uniaxialStress):
self.stress0 = uniaxialStress
def fun(self, (f,g,h,a,b,c,m), ydata, sigmas):
return Hill1979Basis(self.stress0, (f,g,h,a,b,c),m, sigmas)
def jac(self, (f,g,h,a,b,c,m), ydata, sigmas):
return Hill1979Basis(self.stress0, (f,g,h,a,b,c),m, sigmas, Jac=True)
class generalHosford(object):
'''
residuum of Hershey yield criterion (eq. 2.104, sigmas = sigma0)
'''
def __init__(self, uniaxialStress):
self.stress0 = uniaxialStress
def fun(self, (F, G, H, a), ydata, sigmas, nParas=4):
return HosfordBasis(self.stress0, (F, G, H), a, sigmas)
def jac(self, (F, G, H, a), ydata, sigmas):
return HosfordBasis(self.stress0, (F, G, H), a, sigmas, Jac=True, nParas=4)
class Barlat1991iso(object):
'''
residuum of isotropic Barlat 1991 yield criterion (eq. 2.37)
'''
def __init__(self, uniaxialStress):
self.stress0 = uniaxialStress
def fun(self, (sigma0, m), ydata, sigmas):
return Barlat1991Basis(sigma0, np.ones(6), m, sigmas)
def jac(self, (sigma0, m), ydata, sigmas):
return Barlat1991Basis(sigma0, np.ones(6), m, sigmas, Jac=True, nParas=2)
class Barlat1991aniso(object):
'''
residuum of anisotropic Barlat 1991 yield criterion (eq. 2.37)
'''
def __init__(self, uniaxialStress):
self.stress0 = uniaxialStress
def fun(self, (a,b,c,f,g,h, m), ydata, sigmas):
return Barlat1991Basis(self.stress0, (a,b,c,f,g,h), m, sigmas)
def jac(self, (a,b,c,f,g,h, m), ydata, sigmas):
return Barlat1991Basis(self.stress0, (a,b,c,f,g,h), m, sigmas, Jac=True, nParas=7)
class Yld200418p(object):
'''
residuum of anisotropic Barlat 1991 yield criterion (eq. 2.37)
'''
def __init__(self, uniaxialStress):
self.stress0 = uniaxialStress
def fun(self, (c12,c21,c23,c32,c31,c13,c44,c55,c66,
d12,d21,d23,d32,d31,d13,d44,d55,d66, m), ydata, sigmas):
return Yld200418pBasis(self.stress0, (c12,c21,c23,c32,c31,c13,c44,c55,c66),
(d12,d21,d23,d32,d31,d13,d44,d55,d66), m, sigmas)
def jac(self, (c12,c21,c23,c32,c31,c13,c44,c55,c66,
d12,d21,d23,d32,d31,d13,d44,d55,d66, m), ydata, sigmas):
return Yld200418pBasis(self.stress0, (c12,c21,c23,c32,c31,c13,c44,c55,c66),
(d12,d21,d23,d32,d31,d13,d44,d55,d66), m, sigmas, Jac=True)
class KarafillisBoyce(object):
'''
residuum of Karafillis-Boyce yield criterion
'''
def __init__(self, uniaxialStress):
self.stress0 = uniaxialStress
def fun(self, (c11,c12,c13,c14,c15,c16,c21,c22,c23,c24,c25,c26,
b1, b2, a, alpha), ydata, sigmas):
return KarafillisBoyceBasis(self.stress0, (c11,c12,c13,c14,c15,c16),
(c21,c22,c23,c24,c25,c26), b1, b2, a, alpha, sigmas)
def jac(self, (c11,c12,c13,c14,c15,c16,c21,c22,c23,c24,c25,c26,
b1, b2, a, alpha), ydata, sigmas):
return KarafillisBoyceBasis(self.stress0, (c11,c12,c13,c14,c15,c16),
(c21,c22,c23,c24,c25,c26), b1, b2, a, alpha, sigmas, Jac=True)
class BBC2003(object):
'''
residuum of anisotropic Barlat 1991 yield criterion (eq. 2.37)
'''
def __init__(self, uniaxialStress):
self.stress0 = uniaxialStress
def fun(self, (a,b,c, d,e,f,g, k), ydata, sigmas):
return BBC2003Basis(self.stress0, a,b,c, d,e,f,g, k, sigmas)
def jac(self, (a,b,c, d,e,f,g, k), ydata, sigmas):
return BBC2003Basis(self.stress0, a,b,c, d,e,f,g, k, sigmas, Jac=True)
class BBC2005(object):
'''
residuum of anisotropic Barlat 1991 yield criterion (eq. 2.37)
'''
def __init__(self, uniaxialStress):
self.stress0 = uniaxialStress
def fun(self, (a,b,L, M, N, P, Q, R, k), ydata, sigmas):
return BBC2005Basis(self.stress0, a,b,L, M, N, P, Q, R, k, sigmas)
def jac(self, (a,b,L, M, N, P, Q, R, k), ydata, sigmas):
return BBC2005Basis(self.stress0, a,b,L, M, N, P, Q, R, k, sigmas, Jac=True)
class Cazacu_Barlat2D(object):
'''
'''
def __init__(self, uniaxialStress):
self.stress0 = uniaxialStress
def fun(self, (a1,a2,a3,a4,b1,b2,b3,b4,b5,b10,c), ydata, sigmas):
return Cazacu_BarlatBasis(self.stress0, (a1,a2,a3,a4),
(b1,b2,b3,b4,b5,b10),c,sigmas, nDim = 2)
def jac(self, (a1,a2,a3,a4,b1,b2,b3,b4,b5,b10,c), ydata, sigmas):
return Cazacu_BarlatBasis(self.stress0, (a1,a2,a3,a4),
(b1,b2,b3,b4,b5,b10),c,sigmas,Jac=True, nDim = 2)
class Cazacu_Barlat3D(object):
'''
'''
def __init__(self, uniaxialStress):
self.stress0 = uniaxialStress
def fun(self, (a1,a2,a3,a4,a5,a6,b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,c),ydata, sigmas):
return Cazacu_BarlatBasis(self.stress0, (a1,a2,a3,a4,a5,a6),
(b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11),c,sigmas)
def jac(self, (a1,a2,a3,a4,a5,a6,b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,c),ydata, sigmas):
return Cazacu_BarlatBasis(self.stress0, (a1,a2,a3,a4,a5,a6),
(b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11),c,sigmas,Jac=True)
class Vegter(object):
'''
Vegter yield criterion
'''
def __init__(self, refPts, refNormals,nspace=11):
self.refPts, self.refNormals = self._getRefPointsNormals(refPts, refNormals)
self.hingePts = self._getHingePoints()
self.nspace = nspace
def _getRefPointsNormals(self,refPtsQtr,refNormalsQtr):
if len(refPtsQtr) == 12:
refPts = refPtsQtr
refNormals = refNormalsQtr
else:
refPts = np.empty([13,2])
refNormals = np.empty([13,2])
refPts[12] = refPtsQtr[0]
refNormals[12] = refNormalsQtr[0]
for i in xrange(3):
refPts[i] = refPtsQtr[i]
refPts[i+3] = refPtsQtr[3-i][::-1]
refPts[i+6] =-refPtsQtr[i]
refPts[i+9] =-refPtsQtr[3-i][::-1]
refNormals[i] = refNormalsQtr[i]
refNormals[i+3] = refNormalsQtr[3-i][::-1]
refNormals[i+6] =-refNormalsQtr[i]
refNormals[i+9] =-refNormalsQtr[3-i][::-1]
return refPts,refNormals
def _getHingePoints(self):
'''
calculate the hinge point B according to the reference points A,C and the normals n,m
refPoints = np.array([[p1_x, p1_y], [p2_x, p2_y]]);
refNormals = np.array([[n1_x, n1_y], [n2_x, n2_y]])
'''
def hingPoint(points, normals):
A1 = points[0][0]; A2 = points[0][1]
C1 = points[1][0]; C2 = points[1][1]
n1 = normals[0][0]; n2 = normals[0][1]
m1 = normals[1][0]; m2 = normals[1][1]
B1 = (m2*(n1*A1 + n2*A2) - n2*(m1*C1 + m2*C2))/(n1*m2-m1*n2)
B2 = (n1*(m1*C1 + m2*C2) - m1*(n1*A1 + n2*A2))/(n1*m2-m1*n2)
return np.array([B1,B2])
return np.array([hingPoint(self.refPts[i:i+2],self.refNormals[i:i+2]) for i in xrange(len(self.refPts)-1)])
def getBezier(self):
def bezier(R,H):
b = []
for mu in np.linspace(0.0,1.0,self.nspace):
b.append(np.array(R[0]*np.ones_like(mu) + 2.0*mu*(H - R[0]) + mu**2*(R[0]+R[1] - 2.0*H)))
return b
return np.array([bezier(self.refPts[i:i+2],self.hingePts[i]) for i in xrange(len(self.refPts)-1)])
def VetgerCriterion(stress,lankford, rhoBi0, theta=0.0):
'''
0-pure shear; 1-uniaxial; 2-plane strain; 3-equi-biaxial
'''
def getFourierParas(r):
# get the value after Fourier transformation
nset = len(r)
lmatrix = np.empty([nset,nset])
theta = np.linspace(0.0,np.pi/2,nset)
for i,th in enumerate(theta):
lmatrix[i] = np.array([np.cos(2*j*th) for j in xrange(nset)])
return np.linalg.solve(lmatrix, r)
nps = len(stress)
if nps%4 != 0:
print ('Warning: the number of stress points is uncorrect, stress points of %s are missing in set %i'%(
['eq-biaxial, plane strain & uniaxial', 'eq-biaxial & plane strain','eq-biaxial'][nps%4-1],nps/4+1))
else:
nset = nps/4
strsSet = stress.reshape(nset,4,2)
refPts = np.empty([4,2])
fouriercoeffs = np.array([np.cos(2.0*i*theta) for i in xrange(nset)])
for i in xrange(2):
refPts[3,i] = sum(strsSet[:,3,i])/nset
for j in xrange(3):
refPts[j,i] = np.dot(getFourierParas(strsSet[:,j,i]), fouriercoeffs)
rhoUn = np.dot(getFourierParas(-lankford/(lankford+1)), fouriercoeffs)
rhoBi = (rhoBi0+1 + (rhoBi0-1)*np.cos(2.0*theta))/(rhoBi0+1 - (rhoBi0-1)*np.cos(2.0*theta))
nVec = lambda rho : np.array([1.0,rho]/np.sqrt(1.0+rho**2))
refNormals = np.array([nVec(-1.0),nVec(rhoUn),nVec(0.0),nVec(rhoBi)])
vegter = Vegter(refPts, refNormals)
def Cazacu_BarlatBasis(sigma0,coeffa,coeffb,c,sigmas, Jac = False, nDim = 3):
'''
residuum of the 3D Cazacu<63>Barlat (CB) yield criterion
'''
s11,s22,s33,s12,s23,s31 = sigmas
if nDim == 2: s33=s23=s31 = np.zeros_like(s11)
s1_2, s2_2, s3_2, s12_2, s23_2, s31_2 = np.array([s11,s22,s33,s12,s23,s31])**2
s1_3, s2_3, s3_3, s123, s321 = s11*s1_2, s22*s2_2, s33*s3_2,s11*s22*s33, s12*s23*s31
d12,d23,d31 = s11-s22, s22-s33, s33-s11
jb1 = (s1_3 + 2.0*s3_3)/27.0 - s22*s1_2/9.0 - (s11+s22)*s3_2/9.0 + s123/4.5
jb2 = (s1_3 - s3_3)/27.0 - s33*s1_2/9.0 + s11 *s3_2/9.0
jb3 = (s2_3 - s3_3)/27.0 - s33*s2_2/9.0 + s22 *s3_2/9.0
jb4 = (s2_3 + 2.0*s3_3)/27.0 - s11*s2_2/9.0 - (s11+s22)*s3_2/9.0 + s123/4.5
jb5, jb10 = -d12*s12_2/3.0, -d31*s12_2/1.5
jb6, jb7 = -d12*s23_2/3.0, d31*s23_2/3.0
jb8, jb9 = d31*s31_2/3.0, d12*s31_2/1.5
jb11 = s321*2.0
if nDim == 3:
dJ2da = np.array([d12**2/6.0, d23**2/6.0, d31**2/6.0, s12_2,s23_2,s31_2])
dJ3db = np.array([jb1,jb2,jb3,jb4,jb5,jb6,jb7,jb8,jb9,jb10,jb11])
else: # plane stress
dJ2da = np.array([d12**2/6.0, s2_2/6.0, s1_2/6.0, s12_2])
dJ3db = np.array([jb1,jb2,jb3,jb4,jb5,jb10])
J20 = np.dot(coeffa,dJ2da)
J30 = np.dot(coeffb,dJ3db)
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:
df = r/f0/108.0
return np.vstack((df*3.0*J20**2.0*dJ2da, -df*2.0*J30*c*dJ3db, -df*J30**2)).T
def DruckerBasis(sigma0, C_D, p, sigmas, Jac=False, nParas=2):
I1,I2,I3 = invariant(sigmas)
J2 = I1**2/3.0 - I2
J3 = I1**3/13.5 - I1*I2/3.0 + I3
J2_3p = J2**(3.0*p); J3_2p = J3**(2.0*p)
left = J2_3p - C_D*J3_2p
r = left**(1.0/(6.0*p))*3.0**0.5/sigma0
if not Jac:
return (r - 1.0).ravel()
else:
drdl = r/left/(6.0*p)
if nParas == 2:
return np.vstack((-r/sigma0, -drdl*J3_2p)).T
else:
dldp = 3.0*J2_3p*math_ln(J2) - 2.0*C_D*J3_2p*math_ln(J3)
jp = drdl*dldp + r*math_ln(left)/(-6.0*p*p)
return np.vstack((-r/sigma0, -drdl*J3_2p, jp)).T
def Hill1948Basis(coeff, sigmas, Jac=False):
s11,s22,s33,s12,s23,s31 = sigmas
jac = np.array([(s22-s33)**2,(s33-s11)**2,(s11-s22)**2, 2.0*s23**2,2.0*s31**2,2.0*s12**2])
if not Jac:
return (np.dot(coeff,jac)/2.0-0.5).ravel()
else:
return jac.T
def Hill1979Basis(sigma0, coeff,m, sigmas, Jac=False):
s1,s2,s3 = principalStresses(sigmas)
diffs = np.array([s2-s3, s3-s1, s1-s2, 2.0*s1-s2-s3, 2.0*s2-s3-s1, 2.0*s3-s1-s2])**2
diffsm = diffs**(m/2.0)
base = np.dot(coeff,diffsm)
r = base**(1.0/m)/sigma0 #left = base**mi
if not Jac:
return (r-1.0).ravel()
else:
drdb = r/base/m
dbdm = np.dot(coeff,diffsm*math_ln(diffs)) #****0.5
jm = drdb*dbdm + r*math_ln(base)/(-m**2)
return np.vstack((drdb*diffsm, jm)).T
def HosfordBasis(sigma0, coeff, a, sigmas, Jac=False, nParas=1):
'''
residuum of Hershey yield criterion (eq. 2.43, Y = sigma0)
'''
s1,s2,s3 = principalStresses(sigmas)
diffs = np.abs(np.array([s2-s3, s3-s1, s1-s2]))
diffsm = diffs**a
base = np.dot(coeff,diffsm)
r = base**(1.0/a)/sigma0
if not Jac:
return (r - 1.0).ravel()
else:
if nParas == 1: # von Mises
return -r/sigma0
else:
dbda = np.dot(coeff,diffsm*math_ln(diffs))
dldb = r/base/a
ja = dldb*dbda + r*math_ln(base)/(-a**a)
if nParas == 2: # isotropic Hosford
return np.vstack((-r/sigma0, ja)).T
else: # anisotropic Hosford
return np.vstack((dldb*diffsm, ja)).T
def Barlat1991Basis(sigma0, coeff, m, sigmas, Jac=False, nParas=2):
'''
residuum of Barlat 1997 yield criterion
'''
cos = np.cos; sin = np.sin; pi = np.pi; abs = np.abs
s1,s2,s3,s4,s5,s6 = sigmas
dXdx = np.array([s2-s3,s3-s1,s1-s2,s5,s6,s4])
A,B,C,F,G,H = np.array(coeff)[:,None]*dXdx
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
phi1 = np.arccos(I3/I2**1.5)/3.0 + pi/6.0; absc1 = 2.0*abs(cos(phi1))
phi2 = phi1 + pi/3.0; absc2 = 2.0*abs(cos(phi2))
phi3 = phi2 + pi/3.0; absc3 = 2.0*abs(cos(phi3))
left = ( absc1**m + absc2**m + absc3**m )/2.0
r = left**(1.0/m)*np.sqrt(3.0*I2)/sigma0
if not Jac:
return (r - 1.0).ravel()
else:
dfdl = r/left/m
jm = r*math_ln(left)/(-m**2) + dfdl*0.5*(
absc1**m*math_ln(absc1) + absc2**m*math_ln(absc2) + absc3**m*math_ln(absc3) )
if nParas == 2:
js = -(r + 1.0)/sigma0
return np.vstack((js,jm)).T
else:
da,db,dc = (2.0*A-B-C)/18.0, (2.0*B-C-A)/18.0, (2.0*C-A-B)/18.0
dI2dx = np.array([da, db, dc, F,G,H])/1.5*dXdx
dI3dx = np.array([da*(B-C) + (H**2-G**2)/2.0, db*(C-A) + (F**2-H**2)/2.0, dc*(A-B) + (G**2-F**2)/2.0,
(H*G + (B-C))*F, (F*H + (C-A))*G, (G*F + (A-B))*H])/3.0*dXdx
darccos = -(1.0 - I3**2/I2**3)**(-0.5)
dfdc = dfdl*0.5*m
dfdcos = lambda phi : dfdc*(2.0*abs(cos(phi)))**(1.0/m-1.0)*np.sign(cos(phi))*(-sin(phi)/1.5)
dfdthe= (dfdcos(phi1) + dfdcos(phi2) + dfdcos(phi3))
dfdI2 = dfdthe*darccos*I3*(-1.5)*I2**(-2.5); dfdI3 = dfdthe*darccos*I2**(-1.5)
return np.vstack((dfdI2*dI2dx + dfdI3*dI3dx, jm)).T
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; l1s = l1**2
l2 = b*Gamma - c*Psi; l2s = l2**2
l3 = 2.0*c*Psi; 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)
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
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
return np.vstack((ja,jb,jc,jd, je, jf,jg,jk)).T
def BBC2005Basis(sigma0, a,b,L, M, N, P, Q, R, k, sigmas, Jac=False):
'''
residuum of the BBC2005 yield criterion for plain stress
'''
s11 = sigmas[0]; s22 = sigmas[1]; s12 = sigmas[3]
k2 = 2.0*k
Gamma = L*s11 + M*s22
Lambda = ( (N*s11 - P*s22)**2 + s12**2 )**0.5
Psi = ( (Q*s11 - R*s22)**2 + s12**2 )**0.5
l1 = Lambda + Gamma; l2 = Lambda - Gamma; l3 = Lambda + Psi; l4 = Lambda - Psi
l1s = l1**2; l2s = l2**2; l3s = l3**2; l4s = l4**2
left = a*l1s**k + a*l2s**k + b*l3s**k + b*l4s**k
sBar = left**(1.0/k2); r = sBar/sigma0 - 1.0
if not Jac:
return r.ravel()
else:
ln = lambda x : np.log(x + 1.0e-32)
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 = b*k*(l3s**k1)*(2.0*l3)
dldl4 = b*k*(l4s**k1)*(2.0*l4)
dldLambda = dldl1 + dldl2 + dldl3 + dldl4
dldGama = dldl1 - dldl2
dldPsi = dldl3 - dldl4
temp = (N*s11 - P*s22)/Lambda
dLambdadN = s11*temp; dLambdadP = -s22*temp
temp = (Q*s11 - R*s22)/Psi
dPsidQ = s11*temp; dPsidR = -s22*temp
dldk = a*ln(l1s)*l1s**k + a*ln(l2s)*l2s**k + b*ln(l3s)*l3s**k + b*ln(l4s)*l4s**k
J = dsBardl * np.array( [
l1s**k+l2s**k, l3s**k+l4s**k,dldGama*s11,dldGama*s22,dldLambda*dLambdadN,
dldLambda*dLambdadP, dldPsi*dPsidQ, dldPsi*dPsidR, dldk+dsBarde*dedk ])
return np.vstack(J).T
def principalStress(p):
sin = np.sin; cos = np.cos
I1,I2,I3 = invariant(p)
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
return np.array( [t1 + t2*cos(phi), t1+t2*cos(phi+np.pi*2.0/3.0), t1+t2*cos(phi+np.pi*4.0/3.0)])
def principalStrs_Der(p, (s1, s2, s3, s4, s5, s6), Karafillis=False):
sin = np.sin; cos = np.cos
I1,I2,I3 = invariant(p)
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, dphidI2, dphidI3 = dphidcs*dcsdI1, dphidcs*dcsdI2, dphidcs*dcsdI3
dI1s3I2dI1= I1/I1s3I2; dI1s3I2dI2 = -1.5/I1s3I2
third2 = 2.0*third; tcoeff = third2*I1s3I2
dSidIj = lambda theta : ( tcoeff*(-sin(theta))*dphidI1 + third2*dI1s3I2dI1*cos(theta) + third,
tcoeff*(-sin(theta))*dphidI2 + third2*dI1s3I2dI2*cos(theta),
tcoeff*(-sin(theta))*dphidI3)
dSdI = np.array([dSidIj(phi),dSidIj(phi+np.pi*2.0/3.0),dSidIj(phi+np.pi*4.0/3.0)]) # i=1,2,3; j=1,2,3
# calculate the derivation of principal stress with regards to the anisotropic coefficients
one = np.ones_like(s1); zero = np.zeros_like(s1); dim = len(s1)
dIdp = np.array([[one, one, one, zero, zero, zero],
[p[1]+p[2], p[2]+p[0], p[0]+p[1], -2.0*p[3], -2.0*p[4], -2.0*p[5]],
[p[1]*p[2]-p[4]**2, p[2]*p[0]-p[5]**2, p[0]*p[1]-p[3]**2,
-2.0*p[3]*p[2]+2.0*p[4]*p[5], -2.0*p[4]*p[0]+2.0*p[5]*p[3], -2.0*p[5]*p[1]+2.0*p[3]*p[4]] ])
if Karafillis:
dpdc = np.array([[zero,s2-s3,s3-s2], [s1-s3,zero,s3-s1], [s1-s2,s2-s1,zero]])
dSdp = np.array([np.dot(dSdI[:,:,i],dIdp[:,:,i]).T for i in xrange(dim)]).T
return np.concatenate((np.array([np.dot(dSdp[:,0:3,i], dpdc[:,:,i].T).T/3.0 for i in xrange(dim)]).T,
np.vstack([dSdp[:,3]*s4,dSdp[:,4]*s5,dSdp[:,5]*s6]).T.reshape(dim,3,3).T), axis=1)
else:
dIdc=np.array([[-dIdp[i,0]*s2, -dIdp[i,1]*s1, -dIdp[i,1]*s3,
-dIdp[i,2]*s2, -dIdp[i,2]*s1, -dIdp[i,0]*s3,
dIdp[i,3]*s4, dIdp[i,4]*s5, dIdp[i,5]*s6 ] for i in xrange(3)])
return np.array([np.dot(dSdI[:,:,i],dIdc[:,:,i]).T for i in xrange(dim)]).T
def Yld200418pBasis(sigma0, C, D, m, sigmas, Jac=False):
'''
C: c12,c21,c23,c32,c13,c31,c44,c55,c66
D: d12,d21,d23,d32,d31,d13,d44,d55,d66
'''
sv = (sigmas[0] + sigmas[1] + sigmas[2])/3.0
sdev = np.vstack((sigmas[0:3]-sv,sigmas[3:6]))
ys = lambda sdev, C: np.array([-C[0]*sdev[1]-C[5]*sdev[2], -C[1]*sdev[0]-C[2]*sdev[2],
-C[4]*sdev[0]-C[3]*sdev[1], C[6]*sdev[3],C[7]*sdev[4], C[8]*sdev[5]])
p,q = ys(sdev, C), ys(sdev, D)
pLambdas, qLambdas = principalStress(p), principalStress(q) # no sort
m2 = m/2.0; m1 = 1.0/m; m21 = m2-1.0; x3 = xrange(3); dim = len(sv)
PiQj = np.array([(pLambdas[i,:]-qLambdas[j,:]) for i in x3 for j in x3])
QiPj = np.array([(qLambdas[i,:]-pLambdas[j,:]) for i in x3 for j in x3]).reshape(3,3,dim)
PiQjs = PiQj**2
phi = np.sum(PiQjs**m2,axis=0)
r = (0.25*phi)**m1/sigma0 - 1.0
if not Jac:
return r.ravel()
else:
drdphi = (r+1.0)*m1/phi
dphidm = np.sum(PiQjs**m2*math_ln(PiQjs),axis=0)*0.5
dPdc, dQdd = principalStrs_Der(p, sdev), principalStrs_Der(q, sdev)
PiQjs3d = (PiQjs**m21).reshape(3,3,dim)
dphidP = -m*np.array([np.diag(np.dot(PiQjs3d[:,:,i], QiPj [:,:,i])) for i in xrange(dim)]).T
dphidQ = m*np.array([np.diag(np.dot(QiPj [:,:,i], PiQjs3d[:,:,i])) for i in xrange(dim)]).T
jm = drdphi*dphidm + (r+1.0)*math_ln(0.25*phi)*(-m1*m1)
jc = drdphi*np.sum([dphidP[i]*dPdc[i] for i in x3],axis=0)
jd = drdphi*np.sum([dphidQ[i]*dQdd[i] for i in x3],axis=0)
return np.vstack((jc,jd, jm)).T
def KarafillisBoyceBasis(sigma0, C1,C2, b1, b2, a, alpha , sigmas, Jac=False):
ks = lambda (s1,s2,s3,s4,s5,s6),(c1,c2,c3,c4,c5,c6): np.array( [
((c2+c3)*s1-c3*s2-c2*s3)/3.0, ((c3+c1)*s2-c3*s1-c1*s3)/3.0,
((c1+c2)*s3-c2*s1-c1*s2)/3.0, c4*s4, c5*s5, c6*s6 ])
p,q = ks(sigmas, C1), ks(sigmas, C2)
plambdas,qlambdas = principalStress(p), principalStress(q)
b1i,b2i,ai,rb2 = 1.0/b1, 1.0/b2, 1.0/a, 3.0**b2/(2.0**b2+2.0)
difP = np.array([plambdas[1]-plambdas[2], plambdas[2]-plambdas[0], plambdas[0]-plambdas[1]])
difPs = difP**2; difPb1 = difPs**(b1/2.0-1.0)
Qs = qlambdas**2
phi10, phi20 = np.sum(difPs**(b1/2.0),axis = 0), np.sum(Qs**(b2/2.0),axis = 0)
phi1, phi2 = (0.5*phi10)**b1i, (rb2*phi20)**b2i
Stress = alpha*phi1**a + (1.0-alpha)*phi2**a
r = Stress**ai/sigma0
if not Jac:
return (r-1.0).ravel()
else:
drds = r*ai/Stress
dsda = alpha*phi1**a*math_ln(phi1) + (1.0-alpha)*phi2**a*math_ln(phi2)
dphi1dP = phi1/phi10*np.array([ -difPb1[1]*difP[1]+difPb1[2]*difP[2],
difPb1[0]*difP[0]-difPb1[2]*difP[2], difPb1[1]*difP[1]-difPb1[0]*difP[0]])
dphi2dQ = phi2/phi20*Qs*qlambdas*(b2/2.0-1.0)
dPdc = principalStrs_Der(p, sigmas, Karafillis=True)
dQdc = principalStrs_Der(q, sigmas, Karafillis=True)
dphi10db1 = np.sum(difPs**(b1/2.0)*math_ln(difPs), axis=0)*0.5
dphi20db2 = np.sum( Qs**(b2/2.0)*math_ln( Qs), axis=0)*0.5
drb2db2 = rb2*math_ln(3.0) - rb2*math_ln(2.0)/(1.0+2.0**(1.0-b2))
dphi1db1 = phi1*math_ln(phi10)*(-b1i*b1i) + b1i*phi1/(0.5*phi10)* 0.5*dphi10db1
dphi2db2 = phi2*math_ln(phi20)*(-b2i*b2i) + b2i*phi2/(rb2*phi20)*(rb2*dphi20db2 + drb2db2*phi20)
ja = drds*dsda - r*math_ln(Stress)/a/a #drda
jb1 = dphi1db1*(drds*a*phi1**(a-1)*alpha )
jb2 = dphi2db2*(drds*a*phi2**(a-1)*(1.0-alpha))
jc1 = np.sum([dphi1dP[i]*dPdc[i] for i in xrange(3)],axis=0)*drds*a*phi1**(a-1.0)*alpha
jc2 = np.sum([dphi2dQ[i]*dQdc[i] for i in xrange(3)],axis=0)*drds*a*phi2**(a-1.0)*(1.0-alpha)
jalpha = drds * (phi1**a - phi2**a)
return np.vstack((jc1,jc2,jb1,jb2,ja,jalpha)).T
fittingCriteria = {
'tresca' :{'func' : Tresca,
'num' : 1,
'name' : 'Tresca',
'paras': 'Initial yield stress:',
'text' : '\nCoefficient of Tresca criterion:\nsigma0: ',
'error': 'The standard deviation error is: '
},
'vonmises' :{'func' : vonMises,
'num' : 1,
'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,
'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,
'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,
'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,
'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,
'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,
'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,
'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,
'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,
'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: '
},
'bbc2005' :{'func' : BBC2005,
'num' : 9,'err':np.inf,
'name' : 'Banabic-Balan-Comsa 2003',
'paras': 'a, b, L ,M, N, P, Q, R, k:',
'text' : '\nCoefficients of Banabic-Balan-Comsa 2005 criterion: a, b, L ,M, N, P, Q, R, k:\n',
'error': 'The standard deviation errors are: '
},
'Cazacu_Barlat2D':{'func' : Cazacu_Barlat2D,
'num' : 11,
'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,
'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,
'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,
'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: '
}
}
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,ND=3,RD=1,nSet=1,dimension=3,vegter=False):
print('using the random load case generator')
self.finalStrain = finalStrain
self.incs = incs
self.time = time
self.ND = ND
self.RD = RD
self.nSet = nSet
self.dimension = dimension
self.vegter = vegter
self.NgeneratedLoadCases = 0
if self.vegter:
self.vegterLoadcase = self._vegterLoadcase()
def getLoadcase(self,number):
if self.dimension == 3:
print 'generate random 3D load case'
return self._getLoadcase3D()
else:
if self.vegter is True:
print 'generate load case for Vegter'
return self._getLoadcase2dVegter(number)
else:
print 'generate random 2D load case'
return self._getLoadcase2dRandom()
def getLoadcase3D(self):
self.NgeneratedLoadCases+=1
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
def _getLoadcase2dVegter(self,number): #for a 2D simulation, I would use this generator before switching to a random 2D generator
NDzero=[[1,2,3,6],[1,3,5,7],[2,5,6,7]] # no deformation / * for stress
# biaxial f1 = f2
# shear f1 = -f2
# unixaial f1 , f2 =0
# plane strain f1 , s2 =0
# modulo to get one out of 4
stress =['*', '*', '0']*3
defgrad = self.vegterLoadcase[number-1]
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
def _vegterLoadcase(self):
'''
generate the stress points for Vegter criteria
'''
theta = np.linspace(0.0,np.pi/2.0,self.nSet)
f = [0.0, 0.0, '*']*3; loadcase = []
for i in xrange(self.nSet*4): loadcase.append(f)
# more to do for F
F = np.array([ [[1.1, 0.1], [0.1, 1.1]], # uniaxial tension
[[1.1, 0.1], [0.1, 1.1]], # shear
[[1.1, 0.1], [0.1, 1.1]], # eq-biaxial
[[1.1, 0.1], [0.1, 1.1]], # eq-biaxial
])
for i,t in enumerate(theta):
R = np.array([np.cos(t), np.sin(t), -np.sin(t), np.cos(t)]).reshape(2,2)
for j in xrange(4):
loadcase[i*4+j][0],loadcase[i*4+j][1],loadcase[i*4+j][3],loadcase[i*4+j][4] = np.dot(R.T,np.dot(F[j],R)).reshape(4)
return loadcase
def _getLoadcase2dRandom(self):
'''
generate random stress points for 2D tests
'''
self.NgeneratedLoadCases+=1
defgrad=['0', '0', '*']*3
stress =['*', '*', '0']*3
defgrad[0],defgrad[1],defgrad[3],defgrad[4] = (np.random.random_sample(4)-.5)*self.finalStrain*2.0 + np.eye(2).reshape(4)
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
def _defgradScale(self, defgrad, finalStrain):
'''
'''
defgrad0 = (np.array([ 0.0 if i is '*' else i for i in defgrad ]))
det0 = 1.0 - numpy.linalg.det(defgrad0.reshape(3,3))
if defgrad0[0] == 0.0: defgrad0[0] = det0/(defgrad0[4]*defgrad0[8]-defgrad0[5]*defgrad0[7])
if defgrad0[4] == 0.0: defgrad0[4] = det0/(defgrad0[0]*defgrad0[8]-defgrad0[2]*defgrad0[6])
if defgrad0[8] == 0.0: defgrad0[8] = det0/(defgrad0[0]*defgrad0[4]-defgrad0[1]*defgrad0[3])
strain = np.dot(defgrad0.reshape(3,3).T,defgrad0.reshape(3,3)) - np.eye(3)
eqstrain = 2.0/3.0*np.sqrt( 1.5*(strain[0][0]**2+strain[1][1]**2+strain[2][2]**2) +
3.0*(strain[0][1]**2+strain[1][2]**2+strain[2][0]**2) )
r = finalStrain*1.25/eqstrain
# if r>1.0: defgrad =( np.array([i*r if i is not '*' else i for i in defgrad]))
#---------------------------------------------------------------------------------------------------
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=loadcaseNo()
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 loadcaseNo():
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')
)
# maybe make an option to specifiy if 2D/3D fitting should be done?
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.add_option('-d','--dimension', dest='dimension', type='int',
help='dimension of the virtual test [%default]', metavar='int')
parser.add_option('-v', '--vegter', dest='vegter', action='store_true',
help='Vegter criteria [%default]')
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')
parser.set_defaults(dimension = 3)
parser.set_defaults(vegter = 'False')
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')
if options.vegter is True:
options.dimension = 2
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],
nSet = 10, dimension = options.dimension, vegter = options.vegter)
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'