1432 lines
56 KiB
Python
Executable File
1432 lines
56 KiB
Python
Executable File
#!/usr/bin/env python2.7
|
|
# -*- coding: UTF-8 no BOM -*-
|
|
|
|
import threading,time,os
|
|
import numpy as np
|
|
from optparse import OptionParser
|
|
import damask
|
|
from damask.util import leastsqBound
|
|
|
|
scriptName = os.path.splitext(os.path.basename(__file__))[0]
|
|
scriptID = ' '.join([scriptName,damask.version])
|
|
|
|
def runFit(exponent, eqStress, dimension, criterion):
|
|
global threads, myFit, myLoad
|
|
global fitResidual
|
|
global Guess, dDim
|
|
|
|
dDim = dimension - 3
|
|
nParas = len(fitCriteria[criterion]['bound'][dDim])
|
|
nExpo = fitCriteria[criterion]['nExpo']
|
|
|
|
if exponent > 0.0: # User defined exponents
|
|
nParas = nParas-nExpo
|
|
fitCriteria[criterion]['bound'][dDim] = fitCriteria[criterion]['bound'][dDim][:nParas]
|
|
|
|
for i in range(nParas):
|
|
temp = fitCriteria[criterion]['bound'][dDim][i]
|
|
if fitCriteria[criterion]['bound'][dDim][i] == (None,None):
|
|
Guess.append(1.0)
|
|
else:
|
|
g = (temp[0]+temp[1])/2.0
|
|
if g == 0: g = temp[1]*0.5
|
|
Guess.append(g)
|
|
|
|
myLoad = Loadcase(options.load[0],options.load[1],options.load[2],
|
|
nSet = 10, dimension = dimension, vegter = options.criterion=='vegter')
|
|
|
|
|
|
myFit = Criterion(exponent,eqStress, dimension, criterion)
|
|
for t in range(options.threads):
|
|
threads.append(myThread(t))
|
|
threads[t].start()
|
|
|
|
for t in range(options.threads):
|
|
threads[t].join()
|
|
damask.util.croak('Residuals')
|
|
damask.util.croak(fitResidual)
|
|
|
|
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 range(np.shape(sigmas)[1]):
|
|
eigenvalues = np.linalg.eigvalsh(sym6toT33(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 principalStress(p):
|
|
I = invariant(p)
|
|
|
|
I1s3I2= (I[0]**2 - 3.0*I[1])**0.5
|
|
numer = 2.0*I[0]**3 - 9.0*I[0]*I[1] + 27.0*I[2]
|
|
denom = 2.0*I1s3I2**3
|
|
cs = numer/denom
|
|
|
|
phi = np.arccos(cs)/3.0
|
|
t1 = I[0]/3.0; t2 = 2.0/3.0*I1s3I2
|
|
return np.array( [t1 + t2*np.cos(phi),
|
|
t1 + t2*np.cos(phi+np.pi*2.0/3.0),
|
|
t1 + t2*np.cos(phi+np.pi*4.0/3.0)])
|
|
|
|
def principalStrs_Der(p, s, dim, Karafillis=False):
|
|
"""Derivative of principal stress with respect to stress"""
|
|
third = 1.0/3.0
|
|
third2 = 2.0*third
|
|
|
|
I = invariant(p)
|
|
I1s3I2= np.sqrt(I[0]**2 - 3.0*I[1])
|
|
numer = 2.0*I[0]**3 - 9.0*I[0]*I[1] + 27.0*I[2]
|
|
denom = 2.0*I1s3I2**3
|
|
cs = numer/denom
|
|
phi = np.arccos(cs)/3.0
|
|
|
|
dphidcs = -third/np.sqrt(1.0 - cs**2)
|
|
dcsddenom = 0.5*numer*(-1.5)*I1s3I2**(-5.0)
|
|
dcsdI1 = (6.0*I[0]**2 - 9.0*I[1])*denom + dcsddenom*(2.0*I[0])
|
|
dcsdI2 = ( - 9.0*I[0])*denom + dcsddenom*(-3.0)
|
|
dcsdI3 = 27.0*denom
|
|
dphidI1, dphidI2, dphidI3 = dphidcs*dcsdI1, dphidcs*dcsdI2, dphidcs*dcsdI3
|
|
|
|
dI1s3I2dI1 = I[0]/I1s3I2
|
|
dI1s3I2dI2 = -1.5/I1s3I2
|
|
tcoeff = third2*I1s3I2
|
|
|
|
dSidIj = lambda theta : ( tcoeff*(-np.sin(theta))*dphidI1 + third2*dI1s3I2dI1*np.cos(theta) + third,
|
|
tcoeff*(-np.sin(theta))*dphidI2 + third2*dI1s3I2dI2*np.cos(theta),
|
|
tcoeff*(-np.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(s); zero = np.zeros_like(s); num = len(s)
|
|
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,s[0]-s[2],s[0]-s[1]], [s[1]-s[2],zero,s[1]-s[0]], [s[2]-s[1],s[2]-s[0],zero]])/3.0
|
|
dSdp = np.array([np.dot(dSdI[:,:,i],dIdp[:,:,i]).T for i in range(num)]).T
|
|
if dim == 2:
|
|
temp = np.vstack([dSdp[:,3]*s[3]]).T.reshape(num,1,3).T
|
|
else:
|
|
temp = np.vstack([dSdp[:,3]*s[3],dSdp[:,4]*s[4],dSdp[:,5]*s[5]]).T.reshape(num,3,3).T
|
|
|
|
return np.concatenate((np.array([np.dot(dSdp[:,0:3,i], dpdc[:,:,i]).T for i in range(num)]).T,
|
|
temp), axis=1)
|
|
else:
|
|
if dim == 2:
|
|
dIdc=np.array([[-dIdp[i,0]*s[1], -dIdp[i,1]*s[0], -dIdp[i,1]*s[2],
|
|
-dIdp[i,2]*s[1], -dIdp[i,2]*s[0], -dIdp[i,0]*s[2],
|
|
dIdp[i,3]*s[3] ] for i in range(3)])
|
|
else:
|
|
dIdc=np.array([[-dIdp[i,0]*s[1], -dIdp[i,1]*s[0], -dIdp[i,1]*s[2],
|
|
-dIdp[i,2]*s[1], -dIdp[i,2]*s[0], -dIdp[i,0]*s[2],
|
|
dIdp[i,3]*s[3], dIdp[i,4]*s[4], dIdp[i,5]*s[5] ] for i in range(3)])
|
|
return np.array([np.dot(dSdI[:,:,i],dIdc[:,:,i]).T for i in range(num)]).T
|
|
|
|
def invariant(sigmas):
|
|
I = np.zeros(3)
|
|
s11,s22,s33,s12,s23,s31 = sigmas
|
|
I[0] = s11 + s22 + s33
|
|
I[1] = s11*s22 + s22*s33 + s33*s11 - s12**2 - s23**2 - s31**2
|
|
I[2] = s11*s22*s33 + 2.0*s12*s23*s31 - s12**2*s33 - s23**2*s11 - s31**2*s22
|
|
return I
|
|
|
|
def math_ln(x):
|
|
return np.log(x + 1.0e-32)
|
|
|
|
def sym6toT33(sym6):
|
|
"""Shape the symmetric stress tensor(6) into (3,3)"""
|
|
return np.array([[sym6[0],sym6[3],sym6[5]],
|
|
[sym6[3],sym6[1],sym6[4]],
|
|
[sym6[5],sym6[4],sym6[2]]])
|
|
|
|
def t33toSym6(t33):
|
|
"""Shape the stress tensor(3,3) into symmetric (6)"""
|
|
return np.array([ t33[0,0],
|
|
t33[1,1],
|
|
t33[2,2],
|
|
(t33[0,1] + t33[1,0])/2.0, # 0 3 5
|
|
(t33[1,2] + t33[2,1])/2.0, # * 1 4
|
|
(t33[2,0] + t33[0,2])/2.0,]) # * * 2
|
|
|
|
class Criteria(object):
|
|
def __init__(self, criterion, uniaxialStress,exponent, dimension):
|
|
self.stress0 = uniaxialStress
|
|
if exponent < 0.0: # Fitting exponent m
|
|
self.mFix = [False, exponent]
|
|
else: # fixed exponent m
|
|
self.mFix = [True, exponent]
|
|
self.func = fitCriteria[criterion]['func']
|
|
self.criteria = criterion
|
|
self.dim = dimension
|
|
def fun(self, paras, ydata, sigmas):
|
|
return self.func(self.stress0, paras, sigmas,self.mFix,self.criteria,self.dim)
|
|
def jac(self, paras, ydata, sigmas):
|
|
return self.func(self.stress0, paras, sigmas,self.mFix,self.criteria,self.dim,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 range(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 range(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 range(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 range(nset)])
|
|
return np.linalg.solve(lmatrix, r)
|
|
|
|
nps = len(stress)
|
|
if nps%4 != 0:
|
|
damask.util.croak('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 range(nset)])
|
|
for i in range(2):
|
|
refPts[3,i] = sum(strsSet[:,3,i])/nset
|
|
for j in range(3):
|
|
refPts[j,i] = np.dot(getFourierParas(strsSet[:,j,i]), fouriercoeffs)
|
|
|
|
|
|
def Tresca(eqStress=None, #not needed/supported
|
|
paras=None,
|
|
sigmas=None,
|
|
mFix=None, #not needed/supported
|
|
criteria=None, #not needed/supported
|
|
dim=3,
|
|
Jac=False):
|
|
"""
|
|
Tresca yield criterion
|
|
|
|
the fitted parameter is paras(sigma0)
|
|
"""
|
|
if not Jac:
|
|
lambdas = principalStresses(sigmas)
|
|
r = np.amax(np.array([abs(lambdas[2,:]-lambdas[1,:]),\
|
|
abs(lambdas[1,:]-lambdas[0,:]),\
|
|
abs(lambdas[0,:]-lambdas[2,:])]),0) - paras
|
|
return r.ravel()
|
|
else:
|
|
return -np.ones(len(sigmas))
|
|
|
|
def Cazacu_Barlat(eqStress=None,
|
|
paras=None,
|
|
sigmas=None,
|
|
mFix=None,#not needed/supported
|
|
criteria=None,
|
|
dim=3, #2D also possible
|
|
Jac=False):
|
|
"""
|
|
Cazacu-Barlat (CB) yield criterion
|
|
|
|
the fitted parameters are:
|
|
a1,a2,a3,a6; b1,b2,b3,b4,b5,b10; c for plane stress
|
|
a1,a2,a3,a4,a5,a6; b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11; c: for general case
|
|
mFix is ignored
|
|
"""
|
|
s11,s22,s33,s12,s23,s31 = sigmas
|
|
if dim == 2:
|
|
(a1,a2,a3,a4), (b1,b2,b3,b4,b5,b10), c = paras[0:4],paras[4:10],paras[10]
|
|
a5 = a6 = b6 = b7 = b8 = b9 = b11 = 0.0
|
|
s33 = s23 = s31 = np.zeros_like(s11)
|
|
else:
|
|
(a1,a2,a3,a4,a5,a6), (b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11), c = paras[0:6],paras[6:17],paras[17]
|
|
|
|
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_2,d23_2,d31_2 = (s11-s22)**2, (s22-s33)**2, (s33-s11)**2
|
|
|
|
J20 = ( a1*d12_2 + a2*d23_2 + a3*d31_2 )/6.0 + a4*s12_2 + a5*s23_2 + a6*s31_2
|
|
J30 = ( (b1 +b2 )*s1_3 + (b3 +b4 )*s2_3 + ( b1+b4-b2 + b1+b4-b3 )*s3_3 )/27.0- \
|
|
( (b1*s22+b2*s33)*s1_2 + (b3*s33+b4*s11)*s2_2 + ((b1+b4-b2)*s11 + (b1+b4-b3)*s22)*s3_2 )/9.0 + \
|
|
( (b1+b4)*s123/9.0 + b11*s321 )*2.0 - \
|
|
( ( 2.0*b9 *s22 - b8*s33 - (2.0*b9 -b8)*s11 )*s31_2 +
|
|
( 2.0*b10*s33 - b5*s22 - (2.0*b10-b5)*s11 )*s12_2 +
|
|
( (b6+b7)*s11 - b6*s22 - b7*s33 )*s23_2
|
|
)/3.0
|
|
f0 = J20**3 - c*J30**2
|
|
r = f0**(1.0/6.0)*np.sqrt(3.0)/eqStress
|
|
|
|
if not Jac:
|
|
return (r - 1.0).ravel()
|
|
else:
|
|
drdf = r/f0/6.0
|
|
dj2, dj3 = drdf*3.0*J20**2, -drdf*2.0*J30*c
|
|
jc = -drdf*J30**2
|
|
|
|
ja1,ja2,ja3 = dj2*d12_2/6.0, dj2*d23_2/6.0, dj2*d31_2/6.0
|
|
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 )
|
|
jb4 = dj3*( (s2_3 + 2.0*s3_3)/27.0 - s11*s2_2/9.0 - (s11+s22)*s3_2/9.0 + s123/4.5 )
|
|
|
|
jb5, jb10 = dj3*(s22 - s11)*s12_2/3.0, dj3*(s11 - s33)*s12_2/1.5
|
|
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_2/1.5
|
|
jb11 = dj3*s321*2.0
|
|
if dim == 2:
|
|
return np.vstack((ja1,ja2,ja3,ja4,jb1,jb2,jb3,jb4,jb5,jb10,jc)).T
|
|
else:
|
|
return np.vstack((ja1,ja2,ja3,ja4,ja5,ja6,jb1,jb2,jb3,jb4,jb5,jb6,jb7,jb8,jb9,jb10,jb11,jc)).T
|
|
|
|
def Drucker(eqStress=None,#not needed/supported
|
|
paras=None,
|
|
sigmas=None,
|
|
mFix=None, #not needed/supported
|
|
criteria=None,
|
|
dim=3,
|
|
Jac=False):
|
|
"""
|
|
Drucker yield criterion
|
|
|
|
the fitted parameters are
|
|
sigma0, C_D for Drucker(p=1);
|
|
sigma0, C_D, p for general Drucker
|
|
eqStress, mFix are invalid inputs
|
|
"""
|
|
if criteria == 'drucker':
|
|
sigma0, C_D= paras
|
|
p = 1.0
|
|
else:
|
|
sigma0, C_D = paras[0:2]
|
|
if mFix[0]: p = mFix[1]
|
|
else: p = paras[-1]
|
|
I = invariant(sigmas)
|
|
J = np.zeros([3])
|
|
J[1] = I[0]**2/3.0 - I[1]
|
|
J[2] = I[0]**3/13.5 - I[0]*I[1]/3.0 + I[2]
|
|
J2_3p = J[1]**(3.0*p)
|
|
J3_2p = J[2]**(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 criteria == 'drucker':
|
|
return np.vstack((-r/sigma0, -drdl*J3_2p)).T
|
|
else:
|
|
dldp = 3.0*J2_3p*math_ln(J[1]) - 2.0*C_D*J3_2p*math_ln(J[2])
|
|
jp = drdl*dldp + r*math_ln(left)/(-6.0*p*p)
|
|
|
|
if mFix[0]: return np.vstack((-r/sigma0, -drdl*J3_2p)).T
|
|
else: return np.vstack((-r/sigma0, -drdl*J3_2p, jp)).T
|
|
|
|
def Hill1948(eqStress=None,#not needed/supported
|
|
paras=None,
|
|
sigmas=None,
|
|
mFix=None, #not needed/supported
|
|
criteria=None,#not needed/supported
|
|
dim=3,
|
|
Jac=False):
|
|
"""
|
|
Hill 1948 yield criterion
|
|
|
|
the fitted parameters are:
|
|
F, G, H, L, M, N for 3D
|
|
F, G, H, N for 2D
|
|
"""
|
|
s11,s22,s33,s12,s23,s31 = sigmas
|
|
if dim == 2: # plane stress
|
|
jac = np.array([ s22**2, s11**2, (s11-s22)**2, 2.0*s12**2])
|
|
else: # general case
|
|
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(paras,jac)/2.0-0.5).ravel()
|
|
else:
|
|
return jac.T
|
|
|
|
def Hill1979(eqStress=None,#not needed/supported
|
|
paras=None,
|
|
sigmas=None,
|
|
mFix=None,
|
|
criteria=None,#not needed/supported
|
|
dim=3,
|
|
Jac=False):
|
|
"""
|
|
Hill 1979 yield criterion
|
|
|
|
the fitted parameters are: f,g,h,a,b,c,m
|
|
"""
|
|
if mFix[0]:
|
|
m = mFix[1]
|
|
else:
|
|
m = paras[-1]
|
|
|
|
coeff = paras[0:6]
|
|
s = principalStresses(sigmas)
|
|
diffs = np.array([s[1]-s[2], s[2]-s[0], s[0]-s[1],\
|
|
2.0*s[0]-s[1]-s[2], 2.0*s[1]-s[2]-s[0], 2.0*s[2]-s[0]-s[1]])**2
|
|
|
|
diffsm = diffs**(m/2.0)
|
|
left = np.dot(coeff,diffsm)
|
|
r = (0.5*left)**(1.0/m)/eqStress #left = base**mi
|
|
|
|
if not Jac:
|
|
return (r-1.0).ravel()
|
|
else:
|
|
drdl, dldm = r/left/m, np.dot(coeff,diffsm*math_ln(diffs))*0.5
|
|
jm = drdl*dldm + r*math_ln(0.5*left)*(-1.0/m/m) #/(-m**2)
|
|
|
|
if mFix[0]: return np.vstack((drdl*diffsm)).T
|
|
else: return np.vstack((drdl*diffsm, jm)).T
|
|
|
|
def Hosford(eqStress=None,
|
|
paras=None,
|
|
sigmas=None,
|
|
mFix=None,
|
|
criteria=None,
|
|
dim=3,
|
|
Jac=False):
|
|
"""
|
|
Hosford family criteria
|
|
|
|
the fitted parameters are:
|
|
von Mises: sigma0
|
|
Hershey: (1) sigma0, a, when a is not fixed; (2) sigma0, when a is fixed
|
|
general Hosford: (1) F,G,H, a, when a is not fixed; (2) F,G,H, when a is fixed
|
|
"""
|
|
if criteria == 'vonmises':
|
|
sigma0 = paras
|
|
coeff = np.ones(3)
|
|
a = 2.0
|
|
elif criteria == 'hershey':
|
|
sigma0 = paras[0]
|
|
coeff = np.ones(3)
|
|
if mFix[0]: a = mFix[1]
|
|
else: a = paras[1]
|
|
else:
|
|
sigma0 = eqStress
|
|
coeff = paras[0:3]
|
|
if mFix[0]: a = mFix[1]
|
|
else: a = paras[3]
|
|
|
|
s = principalStresses(sigmas)
|
|
diffs = np.array([s[1]-s[2], s[2]-s[0], s[0]-s[1]])**2
|
|
diffsm = diffs**(a/2.0)
|
|
left = np.dot(coeff,diffsm)
|
|
r = (0.5*left)**(1.0/a)/sigma0
|
|
|
|
if not Jac:
|
|
return (r-1.0).ravel()
|
|
else:
|
|
if criteria == 'vonmises': # von Mises
|
|
return -r/sigma0
|
|
else:
|
|
drdl, dlda = r/left/a, np.dot(coeff,diffsm*math_ln(diffs))*0.5
|
|
ja = drdl*dlda + r*math_ln(0.5*left)*(-1.0/a/a)
|
|
if criteria == 'hershey': # Hershey
|
|
if mFix[0]: return -r/sigma0
|
|
else: return np.vstack((-r/sigma0, ja)).T
|
|
else: # Anisotropic Hosford
|
|
if mFix[0]: return np.vstack((drdl*diffsm)).T
|
|
else: return np.vstack((drdl*diffsm, ja)).T
|
|
|
|
def Barlat1989(eqStress=None,
|
|
paras=None,
|
|
sigmas=None,
|
|
mFix=None,
|
|
criteria=None,
|
|
dim=3,
|
|
Jac=False):
|
|
"""
|
|
Barlat-Lian 1989 yield criteria
|
|
|
|
the fitted parameters are:
|
|
Anisotropic: a, h, p, m; m is optional
|
|
"""
|
|
a, h, p = paras[0:3]
|
|
if mFix[0]: m = mFix[1]
|
|
else: m = paras[-1]
|
|
|
|
c = 2.0-a
|
|
s11,s22,s12 = sigmas[0], sigmas[1], sigmas[3]
|
|
k1,k2 = 0.5*(s11 + h*s22), (0.25*(s11 - h*s22)**2 + (p*s12)**2)**0.5
|
|
fs = np.array([ (k1+k2)**2, (k1-k2)**2, 4.0*k2**2 ]); fm = fs**(m/2.0)
|
|
left = np.dot(np.array([a,a,c]),fm)
|
|
r = (0.5*left)**(1.0/m)/eqStress
|
|
|
|
if not Jac:
|
|
return (r-1.0).ravel()
|
|
else:
|
|
dk1dh = 0.5*s22
|
|
dk2dh, dk2dp = 0.25*(s11-h*s22)*(-s22)/k2, p*s12**2/k2
|
|
dlda, dldc = fm[0]+fm[1], fm[2]
|
|
fm1 = fs**(m/2.0-1.0)*m
|
|
dldk1, dldk2 = a*fm1[0]*(k1+k2)+a*fm1[1]*(k1-k2), a*fm1[0]*(k1+k2)-a*fm1[1]*(k1-k2)+c*fm1[2]*k2*4.0
|
|
drdl, drdm = r/m/left, r*math_ln(0.5*left)*(-1.0/m/m)
|
|
dldm = np.dot(np.array([a,a,c]),fm*math_ln(fs))*0.5
|
|
|
|
ja,jc = drdl*dlda, drdl*dldc
|
|
jh,jp = drdl*(dldk1*dk1dh + dldk2*dk2dh), drdl*dldk2*dk2dp
|
|
jm = drdl*dldm + drdm
|
|
|
|
if mFix[0]: return np.vstack((ja,jc,jh,jp)).T
|
|
else: return np.vstack((ja,jc,jh,jp,jm)).T
|
|
|
|
def Barlat1991(eqStress, paras, sigmas, mFix, criteria, dim, Jac=False):
|
|
"""
|
|
Barlat 1991 criteria
|
|
|
|
the fitted parameters are:
|
|
Anisotropic: a, b, c, f, g, h, m for 3D
|
|
a, b, c, h, m for plane stress
|
|
m is optional
|
|
"""
|
|
if dim == 2: coeff = paras[0:4] # plane stress
|
|
else: coeff = paras[0:6] # general case
|
|
if mFix[0]: m = mFix[1]
|
|
else: m = paras[-1]
|
|
|
|
s11,s22,s33,s12,s23,s31 = sigmas
|
|
if dim == 2:
|
|
dXdx = np.array([s22,-s11,s11-s22,s12])
|
|
A,B,C,H = np.array(coeff)[:,None]*dXdx; F=G=0.0
|
|
else:
|
|
dXdx = np.array([s22-s33,s33-s11,s11-s22,s23,s31,s12])
|
|
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 + np.pi/6.0; absc1 = 2.0*np.abs(np.cos(phi1))
|
|
phi2 = phi1 + np.pi/3.0; absc2 = 2.0*np.abs(np.cos(phi2))
|
|
phi3 = phi2 + np.pi/3.0; absc3 = 2.0*np.abs(np.cos(phi3))
|
|
left = ( absc1**m + absc2**m + absc3**m )
|
|
r = (0.5*left)**(1.0/m)*np.sqrt(3.0*I2)/eqStress
|
|
|
|
if not Jac:
|
|
return (r - 1.0).ravel()
|
|
else:
|
|
dfdl = r/left/m
|
|
jm = r*math_ln(0.5*left)*(-1.0/m/m) + dfdl*0.5*(
|
|
absc1**m*math_ln(absc1) + absc2**m*math_ln(absc2) + absc3**m*math_ln(absc3) )
|
|
|
|
da,db,dc = (2.0*A-B-C)/18.0, (2.0*B-C-A)/18.0, (2.0*C-A-B)/18.0
|
|
if dim == 2:
|
|
dI2dx = np.array([da, db, dc, 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,
|
|
(G*F + (A-B))*H ])/3.0*dXdx
|
|
else:
|
|
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*3.0 + (B-C))*F,
|
|
(F*H*3.0 + (C-A))*G,
|
|
(G*F*3.0 + (A-B))*H ])/3.0*dXdx
|
|
darccos = -1.0/np.sqrt(1.0 - I3**2/I2**3)
|
|
|
|
dfdcos = lambda phi : dfdl*m*(2.0*abs(np.cos(phi)))**(m-1.0)*np.sign(np.cos(phi))*(-np.sin(phi)/1.5)
|
|
|
|
dfdthe= (dfdcos(phi1) + dfdcos(phi2) + dfdcos(phi3))
|
|
dfdI2, dfdI3 = dfdthe*darccos*I3*(-1.5)*I2**(-2.5)+r/2.0/I2, dfdthe*darccos*I2**(-1.5)
|
|
|
|
if mFix[0]: return np.vstack((dfdI2*dI2dx + dfdI3*dI3dx)).T
|
|
else: return np.vstack((dfdI2*dI2dx + dfdI3*dI3dx, jm)).T
|
|
|
|
def BBC2000(eqStress, paras, sigmas, mFix, criteria, dim, Jac=False):
|
|
"""
|
|
BBC2000 yield criterion
|
|
|
|
the fitted parameters are
|
|
d,e,f,g, b,c,a, k; k is optional
|
|
criteria are invalid input
|
|
"""
|
|
d,e,f,g, b,c,a= paras[0:7]
|
|
if mFix[0]: k = mFix[1]
|
|
else: k = paras[-1]
|
|
|
|
s11,s22,s12 = sigmas[0], sigmas[1], sigmas[3]
|
|
k2 = 2.0*k; k1 = k - 1.0
|
|
M,N,P,Q,R = d+e, e+f, (d-e)/2.0, (e-f)/2.0, g**2
|
|
Gamma = M*s11 + N*s22
|
|
Psi = ( (P*s11 + Q*s22)**2 + s12**2*R )**0.5
|
|
|
|
l1, l2, l3 = b*Gamma + c*Psi, b*Gamma - c*Psi, 2.0*c*Psi
|
|
l1s,l2s,l3s = l1**2, l2**2, l3**2
|
|
|
|
left = a*l1s**k + a*l2s**k + (1-a)*l3s**k
|
|
r = left**(1.0/k2)/eqStress
|
|
if not Jac:
|
|
return (r - 1.0).ravel()
|
|
else:
|
|
drdl,drdk = r/left/k2, r*math_ln(left)*(-1.0/k2/k)
|
|
dldl1,dldl2,dldl3 = a*k2*(l1s**k1)*l1, a*k2*(l2s**k1)*l2, (1-a)*k2*(l3s**k1)*l3
|
|
dldGama, dldPsi = (dldl1 + dldl2)*b, (dldl1 - dldl2 + 2.0*dldl3)*c
|
|
temp = (P*s11 + Q*s22)/Psi
|
|
dPsidP, dPsidQ, dPsidR = temp*s11, temp*s22, 0.5*s12**2/Psi
|
|
dlda = l1s**k + l2s**k - l3s**k
|
|
dldb = dldl1*Gamma + dldl2*Gamma
|
|
dldc = dldl1*Psi - dldl2*Psi + dldl3*2.0*Psi
|
|
dldk = a*math_ln(l1s)*l1s**k + a*math_ln(l2s)*l2s**k + (1-a)*math_ln(l3s)*l3s**k
|
|
|
|
J = drdl*np.array([dldGama*s11+dldPsi*dPsidP*0.5, dldGama*(s11+s22)+dldPsi*(-dPsidP+dPsidQ)*0.5, #jd,je
|
|
dldGama*s22-dldPsi*dPsidQ*0.5, dldPsi*dPsidR*2.0*g, #jf,jg
|
|
dldb, dldc, dlda]) #jb,jc,ja
|
|
if mFix[0]: return np.vstack(J).T
|
|
else: return np.vstack((J, drdl*dldk + drdk)).T
|
|
|
|
|
|
def BBC2003(eqStress, paras, sigmas, mFix, criteria, dim, Jac=False):
|
|
"""
|
|
BBC2003 yield criterion
|
|
|
|
the fitted parameters are
|
|
M,N,P,Q,R,S,T,a, k; k is optional
|
|
criteria are invalid input
|
|
"""
|
|
M,N,P,Q,R,S,T,a = paras[0:8]
|
|
if mFix[0]: k = mFix[1]
|
|
else: k = paras[-1]
|
|
|
|
s11,s22,s12 = sigmas[0], sigmas[1], sigmas[3]
|
|
k2 = 2.0*k; k1 = k - 1.0
|
|
Gamma = 0.5 * (s11 + M*s22)
|
|
Psi = ( 0.25*(N*s11 - P*s22)**2 + Q*Q*s12**2 )**0.5
|
|
Lambda = ( 0.25*(R*s11 - S*s22)**2 + T*T*s12**2 )**0.5
|
|
|
|
l1, l2, l3 = Gamma + Psi, Gamma - Psi, 2.0*Lambda
|
|
l1s,l2s,l3s = l1**2, l2**2, l3**2
|
|
left = a*l1s**k + a*l2s**k + (1-a)*l3s**k
|
|
r = left**(1.0/k2)/eqStress
|
|
if not Jac:
|
|
return (r - 1.0).ravel()
|
|
else:
|
|
drdl,drdk = r/left/k2, r*math_ln(left)*(-1.0/k2/k)
|
|
dldl1,dldl2,dldl3 = a*k2*(l1s**k1)*l1, a*k2*(l2s**k1)*l2, (1-a)*k2*(l3s**k1)*l3
|
|
|
|
dldGamma, dldPsi, dldLambda = dldl1+dldl2, dldl1-dldl2, 2.0*dldl3
|
|
temp = 0.25/Psi*(N*s11 - P*s22)
|
|
dPsidN, dPsidP, dPsidQ = s11*temp, -s22*temp, Q*s12**2/Psi
|
|
temp = 0.25/Lambda*(R*s11 - S*s22)
|
|
dLambdadR, dLambdadS, dLambdadT = s11*temp, -s22*temp, T*s12**2/Psi
|
|
dldk = a*math_ln(l1s)*l1s**k + a*math_ln(l2s)*l2s**k + (1-a)*math_ln(l3s)*l3s**k
|
|
|
|
J = drdl * np.array([dldGamma*s22*0.5, #jM
|
|
dldPsi*dPsidN, dldPsi*dPsidP, dldPsi*dPsidQ, #jN, jP, jQ
|
|
dldLambda*dLambdadR, dldLambda*dLambdadS, dldLambda*dLambdadT, #jR, jS, jT
|
|
l1s**k + l2s**k - l3s**k ]) #ja
|
|
|
|
if mFix[0]: return np.vstack(J).T
|
|
else : return np.vstack((J, drdl*dldk+drdk)).T
|
|
|
|
def BBC2005(eqStress, paras, sigmas, mFix, criteria, dim, Jac=False):
|
|
"""
|
|
BBC2005 yield criterion
|
|
|
|
the fitted parameters are
|
|
a, b, L ,M, N, P, Q, R, k k are optional
|
|
criteria is invalid input
|
|
"""
|
|
a,b,L, M, N, P, Q, R = paras[0:8]
|
|
if mFix[0]: k = mFix[1]
|
|
else: k = paras[-1]
|
|
|
|
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/eqStress - 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/eqStress
|
|
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])
|
|
|
|
if mFix[0]: return np.vstack(J).T
|
|
else : return np.vstack(J, dldk+dsBarde*dedk).T
|
|
|
|
def Yld2000(eqStress, paras, sigmas, mFix, criteria, dim, Jac=False):
|
|
"""
|
|
Yld2000 yield criterion
|
|
|
|
C: c11,c22,c66 c12=c21=1.0 JAC NOT PASS
|
|
D: d11,d12,d21,d22,d66
|
|
"""
|
|
C,D = paras[0:3], paras[3:8]
|
|
if mFix[0]: m = mFix[1]
|
|
else: m = paras[-1]
|
|
|
|
s11, s22, s12 = sigmas[0],sigmas[1],sigmas[3]
|
|
X = np.array([ 2.0*C[0]*s11-C[0]*s22, 2.0*C[1]*s22-C[1]*s11, 3.0*C[2]*s12 ])/3.0 # a1,a2,a7
|
|
Y = np.array([ (8.0*D[2]-2.0*D[0]-2.0*D[3]+2.0*D[1])*s11 + (4.0*D[3]-4.0*D[1]-4.0*D[2]+ D[0])*s22,
|
|
(4.0*D[0]-4.0*D[2]-4.0*D[1]+ D[3])*s11 + (8.0*D[1]-2.0*D[3]-2.0*D[0]+2.0*D[2])*s22,
|
|
9.0*D[4]*s12 ])/9.0
|
|
|
|
def priStrs(s):
|
|
temp = np.sqrt( (s[0]-s[1])**2 + 4.0*s[2]**2 )
|
|
return 0.5*(s[0]+s[1] + temp), 0.5*(s[0]+s[1] - temp)
|
|
m2 = m/2.0; m21 = m2 - 1.0
|
|
(X1,X2), (Y1,Y2) = priStrs(X), priStrs(Y) # Principal values of X, Y
|
|
phi1s, phi21s, phi22s = (X1-X2)**2, (2.0*Y2+Y1)**2, (2.0*Y1+Y2)**2
|
|
phi1, phi21, phi22 = phi1s**m2, phi21s**m2, phi22s**m2
|
|
left = phi1 + phi21 + phi22
|
|
r = (0.5*left)**(1.0/m)/eqStress
|
|
|
|
if not Jac:
|
|
return (r-1.0).ravel()
|
|
else:
|
|
drdl, drdm = r/m/left, r*math_ln(0.5*left)*(-1.0/m/m) #/(-m*m)
|
|
dldm = ( phi1*math_ln(phi1s) + phi21*math_ln(phi21s) + phi22*math_ln(phi22s) )*0.5
|
|
zero = np.zeros_like(s11); num = len(s11)
|
|
def dPrincipalds(X):
|
|
"""Derivative of principla with respect to stress"""
|
|
temp = 1.0/np.sqrt( (X[0]-X[1])**2 + 4.0*X[2]**2 )
|
|
dP1dsi = 0.5*np.array([ 1.0+temp*(X[0]-X[1]), 1.0-temp*(X[0]-X[1]), temp*4.0*X[2]])
|
|
dP2dsi = 0.5*np.array([ 1.0-temp*(X[0]-X[1]), 1.0+temp*(X[0]-X[1]), -temp*4.0*X[2]])
|
|
return np.array([dP1dsi, dP2dsi])
|
|
|
|
dXdXi, dYdYi = dPrincipalds(X), dPrincipalds(Y)
|
|
dXidC = np.array([ [ 2.0*s11-s22, zero, zero ], #dX11dC
|
|
[ zero, 2.0*s22-s11, zero ], #dX22dC
|
|
[ zero, zero, 3.0*s12 ] ])/3.0 #dX12dC
|
|
dYidD = np.array([ [ -2.0*s11+ s22, 2.0*s11-4.0*s22, 8.0*s11-4.0*s22, -2.0*s11+4.0*s22, zero ], #dY11dD
|
|
[ 4.0*s11-2.0*s22, -4.0*s11+8.0*s22, -4.0*s11+2.0*s22, s11-2.0*s22, zero ], #dY22dD
|
|
[ zero, zero, zero, zero, 9.0*s12 ] ])/9.0 #dY12dD
|
|
|
|
dXdC=np.array([np.dot(dXdXi[:,:,i], dXidC[:,:,i]).T for i in range(num)]).T
|
|
dYdD=np.array([np.dot(dYdYi[:,:,i], dYidD[:,:,i]).T for i in range(num)]).T
|
|
|
|
dldX = m*np.array([ phi1s**m21*(X1-X2), phi1s**m21*(X2-X1)])
|
|
dldY = m*np.array([phi21s**m21*(2.0*Y2+Y1) + 2.0*phi22s**m21*(2.0*Y1+Y2), \
|
|
phi22s**m21*(2.0*Y1+Y2) + 2.0*phi21s**m21*(2.0*Y2+Y1) ])
|
|
jC = drdl*np.array([np.dot(dldX[:,i], dXdC[:,:,i]) for i in range(num)]).T
|
|
jD = drdl*np.array([np.dot(dldY[:,i], dYdD[:,:,i]) for i in range(num)]).T
|
|
|
|
jm = drdl*dldm + drdm
|
|
if mFix[0]: return np.vstack((jC,jD)).T
|
|
else: return np.vstack((jC,jD,jm)).T
|
|
|
|
def Yld200418p(eqStress, paras, sigmas, mFix, criteria, dim, Jac=False):
|
|
"""
|
|
Yld2004-18p yield criterion
|
|
|
|
the fitted parameters are
|
|
C: c12,c21,c23,c32,c31,c13,c44,c55,c66; D: d12,d21,d23,d32,d31,d13,d44,d55,d66 for 3D
|
|
C: c12,c21,c23,c32,c31,c13,c44; D: d12,d21,d23,d32,d31,d13,d44 for 2D
|
|
and m, m are optional
|
|
criteria is ignored
|
|
"""
|
|
if dim == 2: C,D = np.append(paras[0:7],[0.0,0.0]), np.append(paras[7:14],[0.0,0.0])
|
|
else: C,D = paras[0:9], paras[9:18]
|
|
if mFix[0]: m = mFix[1]
|
|
else: m = paras[-1]
|
|
|
|
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; x3 = range(3); num = 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,num)
|
|
PiQjs = PiQj**2
|
|
left = np.sum(PiQjs**m2,axis=0)
|
|
r = (0.25*left)**(1.0/m)/eqStress
|
|
|
|
if not Jac:
|
|
return (r - 1.0).ravel()
|
|
else:
|
|
drdl, drdm = r/m/left, r*math_ln(0.25*left)*(-1.0/m/m)
|
|
dldm = np.sum(PiQjs**m2*math_ln(PiQjs),axis=0)*0.5
|
|
dPdc, dQdd = principalStrs_Der(p, sdev, dim), principalStrs_Der(q, sdev, dim)
|
|
PiQjs3d = ( PiQjs**(m2-1.0) ).reshape(3,3,num)
|
|
dldP = -m*np.array([np.diag(np.dot(PiQjs3d[:,:,i], QiPj [:,:,i])) for i in range(num)]).T
|
|
dldQ = m*np.array([np.diag(np.dot(QiPj [:,:,i], PiQjs3d[:,:,i])) for i in range(num)]).T
|
|
|
|
jm = drdl*dldm + drdm
|
|
jc = drdl*np.sum([dldP[i]*dPdc[i] for i in x3],axis=0)
|
|
jd = drdl*np.sum([dldQ[i]*dQdd[i] for i in x3],axis=0)
|
|
|
|
if mFix[0]: return np.vstack((jc,jd)).T
|
|
else: return np.vstack((jc,jd,jm)).T
|
|
|
|
def KarafillisBoyce(eqStress, paras, sigmas, mFix, criteria, dim, Jac=False):
|
|
"""
|
|
Karafillis-Boyce
|
|
|
|
the fitted parameters are
|
|
c11,c12,c13,c14,c15,c16,c,m for 3D
|
|
c11,c12,c13,c14,c,m for plane stress
|
|
0<c<1, m are optional
|
|
criteria are invalid input
|
|
"""
|
|
ks = lambda s,c: np.array( [
|
|
((c[1]+c[2])*s[0]-c[2]*s[1]-c[1]*s[2])/3.0, ((c[2]+c[0])*s[1]-c[2]*s[0]-c[0]*s[2])/3.0,
|
|
((c[0]+c[1])*s[2]-c[1]*s[0]-c[0]*s[1])/3.0, c[3]*s[3], c[4]*s[4], c[5]*s[5] ])
|
|
if dim == 2: C1,c = np.append(paras[0:4],[0.0,0.0]), paras[4]
|
|
else: C1,c = paras[0:6], paras[6]
|
|
if mFix[0]: m = mFix[1]
|
|
else: m = paras[-1] # Karafillis-Boyce
|
|
|
|
p= ks(sigmas, C1)
|
|
plambdas = principalStress(p)
|
|
reci_m, m2, rm2, m1 = 1.0/m, m/2.0, 3.0**m/(2.0**(m-1.0)+1.0), m-1.0
|
|
|
|
difP = np.array([ plambdas[0]-plambdas[1], plambdas[1]-plambdas[2], plambdas[2]-plambdas[0] ])
|
|
difPs = difP**2; difPm1 = difPs**(m2-1.0)
|
|
Ps = plambdas**2
|
|
|
|
phi1, phi2 = np.sum(difPs**m2, axis = 0), np.sum(Ps**m2, axis = 0)
|
|
left = (1.0-c)*phi1+ c*rm2*phi2
|
|
r = (0.5*left)**reci_m/eqStress
|
|
|
|
if not Jac:
|
|
return (r-1.0).ravel()
|
|
else:
|
|
drdl, drdm = r*reci_m/left, -r*math_ln(0.5*left)*reci_m*reci_m
|
|
dldm = (1.0-c)*np.sum(difPs**m2*math_ln(difPs), axis=0)*0.5 + \
|
|
rm2*c *np.sum( Ps**m2*math_ln(Ps), axis=0)*0.5 + \
|
|
rm2*c *phi2* ( np.log(3.0) - 2.0**m1/(2.0**m1 + 1.0)*np.log(2.0) )
|
|
dphi1dP = m*np.array([ difPm1[0]*difP[0] - difPm1[2]*difP[2],
|
|
difPm1[1]*difP[1] - difPm1[0]*difP[0],
|
|
difPm1[2]*difP[2] - difPm1[1]*difP[1] ])
|
|
dphi2dP = m*plambdas*Ps**(m2-1.0)
|
|
|
|
dPdc = principalStrs_Der(p, sigmas, dim, Karafillis=True)
|
|
dldP = (1.0-c)*dphi1dP + c*dphi2dP*rm2
|
|
|
|
jm = drdl * dldm + drdm #drda*(-1.0/m/m)
|
|
jc1 = drdl * np.sum([dldP[i]*dPdc[i] for i in range(3)],axis=0)
|
|
jc = drdl * (-phi1 + rm2*phi2)
|
|
|
|
if mFix[0]: return np.vstack((jc1,jc)).T
|
|
else: return np.vstack((jc1,jc,jm)).T
|
|
|
|
|
|
|
|
fitCriteria = {
|
|
'tresca' :{'name': 'Tresca',
|
|
'func': Tresca,
|
|
'nExpo': 0,'err':np.inf,
|
|
'dimen': [3],
|
|
'bound': [[(None,None)]],
|
|
'labels': [['sigma0']],
|
|
},
|
|
'vonmises' :{'name': 'Huber-Mises-Hencky',
|
|
'func' : Hosford,
|
|
'nExpo': 0,'err':np.inf,
|
|
'dimen': [3],
|
|
'bound': [[(None,None)]],
|
|
'labels': [['sigma0']],
|
|
},
|
|
'hershey' :{'name': 'Hershey',
|
|
'func': Hosford,
|
|
'nExpo': 1,'err':np.inf,
|
|
'dimen': [3],
|
|
'bound': [[(None,None)]+[(1.0,8.0)]],
|
|
'labels': [['sigma0','a']],
|
|
},
|
|
'hosford' :{'name': 'General Hosford',
|
|
'func': Hosford,
|
|
'nExpo': 1,'err':np.inf,
|
|
'dimen': [3],
|
|
'bound': [[(0.0,2.0)]*3+[(1.0,8.0)] ],
|
|
'labels': [['F','G','H','a']],
|
|
},
|
|
'hill1948' :{'name': 'Hill 1948',
|
|
'func': Hill1948,
|
|
'nExpo': 0,'err':np.inf,
|
|
'dimen': [2,3],
|
|
'bound': [[(None,None)]*6, [(None,None)]*4 ],
|
|
'labels': [['F','G','H','L','M','N'],['F','G','H','N']],
|
|
},
|
|
'hill1979' :{'name': 'Hill 1979',
|
|
'func': Hill1979,
|
|
'nExpo': 1,'err':np.inf,
|
|
'dimen': [3],
|
|
'bound': [[(-2.0,2.0)]*6+[(1.0,8.0)] ],
|
|
'labels': [['f','g','h','a','b','c','m']],
|
|
},
|
|
'drucker' :{'name': 'Drucker',
|
|
'func': Drucker,
|
|
'nExpo': 0,'err':np.inf,
|
|
'dimen': [3],
|
|
'bound': [[(None,None)]+[(-3.375, 2.25)]],
|
|
'labels': [['sigma0','C_D']],
|
|
},
|
|
'gdrucker' :{'name': 'General Drucker',
|
|
'func': Drucker,
|
|
'nExpo': 1,'err':np.inf,
|
|
'dimen': [3],
|
|
'bound': [[(None,None)]+[(-3.375, 2.25)]+[(1.0,8.0)] ],
|
|
'labels': [['sigma0','C_D', 'p']],
|
|
},
|
|
'barlat1989' :{'name': 'Barlat 1989',
|
|
'func': Barlat1989,
|
|
'nExpo': 1,'err':np.inf,
|
|
'dimen': [2],
|
|
'bound': [[(-3.0,3.0)]*4+[(1.0,8.0)] ],
|
|
'labels': [['a','c','h','f', 'm']],
|
|
},
|
|
'barlat1991' :{'name': 'Barlat 1991',
|
|
'func': Barlat1991,
|
|
'nExpo': 1,'err':np.inf,
|
|
'dimen': [2,3],
|
|
'bound': [[(-2,2)]*6+[(1.0,8.0)], [(-2,2)]*4+[(1.0,8.0)]],
|
|
'labels': [['a','b','c','f','g','h','m'],['a','b','c','f','m']],
|
|
},
|
|
'bbc2000' :{'name': 'Banabic-Balan-Comsa 2000',
|
|
'func': BBC2000,
|
|
'nExpo': 1,'err':np.inf,
|
|
'dimen': [2],
|
|
'bound': [[(None,None)]*7+[(1.0,8.0)]],
|
|
'labels': [['d','e','f','g','b','c','a','k']],
|
|
},
|
|
'bbc2003' :{'name': 'Banabic-Balan-Comsa 2003',
|
|
'func' : BBC2003,
|
|
'nExpo': 1,'err':np.inf,
|
|
'dimen': [2],
|
|
'bound': [[(None,None)]*8+[(1.0,8.0)]],
|
|
'labels': [['M','N','P','Q','R','S','T','a','k']],
|
|
},
|
|
'bbc2005' :{'name': 'Banabic-Balan-Comsa 2005',
|
|
'func' : BBC2005,
|
|
'nExpo': 1,'err':np.inf,
|
|
'dimen': [2],
|
|
'bound': [[(None,None)]*8+[(1.0,8.0)] ],
|
|
'labels': [['L','M','N','P','Q','R','a','b','k']],
|
|
},
|
|
'cazacu' :{'name': 'Cazacu Barlat',
|
|
'func': Cazacu_Barlat,
|
|
'nExpo': 0,'err':np.inf,
|
|
'dimen': [2,3],
|
|
'bound': [[(None,None)]*16+[(-2.5,2.5)]+[(None,None)]],
|
|
'labels': [['a1','a2','a3','a4','a5','a6', 'b1','b2','b3','b4','b5','b6','b7','b8','b9','b10','b11', 'c'],
|
|
['a1','a2','a3','a6', 'b1','b2','b3','b4','b5','b10', 'c']],
|
|
},
|
|
'yld2000' :{'name': 'Yld2000-2D',
|
|
'func': Yld2000,
|
|
'nExpo': 1,'err':np.inf,
|
|
'dimen': [2],
|
|
'bound': [[(None,None)]*8+[(1.0,8.0)]],
|
|
'labels': [['a1','a2','a7','a3','a4','a5','a6','a8','m']],
|
|
},
|
|
'yld200418p' :{'name': 'Yld2004-18p',
|
|
'func' : Yld200418p,
|
|
'nExpo': 1,'err':np.inf,
|
|
'dimen': [3],
|
|
'bound': [[(None,None)]*18+[(1.0,8.0)], [(None,None)]*14+[(1.0,8.0)]],
|
|
'labels': [['c12','c21','c23','c32','c31','c13','c44','c55','c66',
|
|
'd12','d21','d23','d32','d31','d13','d44','d55','d66','m'],
|
|
['c12','c21','c23','c32','c31','c13','c44','d12','d21','d23','d32','d31','d13','d44','m']],
|
|
},
|
|
'karafillis' :{'name': 'Karafillis-Boyce',
|
|
'func' : KarafillisBoyce,
|
|
'nExpo': 1,'err':np.inf,
|
|
'dimen': [2,3],
|
|
'bound': [[(None,None)]*6+[(0.0,1.0)]+[(1.0,8.0)], [(None,None)]*4+[(0.0,1.0)]+[(1.0,8.0)]],
|
|
'labels': [['c11','c12','c13','c14','c15','c16','c','m'],
|
|
['c11','c12','c13','c14','c','m']],
|
|
},
|
|
'vegter' :{'name': 'Vegter',
|
|
'labels': 'a,b,c,d,e,f,g,h',
|
|
'dimen': [2],
|
|
},
|
|
}
|
|
|
|
thresholdParameter = ['totalshear','equivalentStrain']
|
|
|
|
#---------------------------------------------------------------------------------------------------
|
|
class Loadcase():
|
|
"""Generating load cases for the spectral solver"""
|
|
|
|
def __init__(self,finalStrain,incs,time,nSet=1,dimension=3,vegter=False):
|
|
self.finalStrain = finalStrain
|
|
self.incs = incs
|
|
self.time = time
|
|
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:
|
|
damask.util.croak('Generate random 3D load case')
|
|
return self._getLoadcase3D()
|
|
else:
|
|
if self.vegter is True:
|
|
damask.util.croak('Generate load case for Vegter')
|
|
return self._getLoadcase2dVegter(number)
|
|
else:
|
|
damask.util.croak('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]='*'
|
|
ratio = self._defgradScale(defgrad)
|
|
for i in [0,4,8]:
|
|
if defgrad[i] != '*': defgrad[i] = (defgrad[i]-1.0)*ratio + 1.0
|
|
for i in [1,2,3,5,6,7]:
|
|
if defgrad[i] != '*': defgrad[i] = defgrad[i]*ratio
|
|
|
|
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
|
|
# 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 (incomplete/untested)"""
|
|
theta = np.linspace(0.0,np.pi/2.0,self.nSet)
|
|
f = [0.0, 0.0, '*']*3; loadcase = []
|
|
for i in range(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 range(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):
|
|
def fill_star(a,b):
|
|
if a != '*' and b != '*': return a,b
|
|
elif a == '*' and b != '*': return b,b
|
|
elif a != '*' and b == '*': return a,a
|
|
else : return 0.0,0.0
|
|
defgrad0 = defgrad[:]
|
|
defgrad0[1],defgrad0[3] = fill_star(defgrad[1], defgrad[3])
|
|
defgrad0[2],defgrad0[6] = fill_star(defgrad[2], defgrad[6])
|
|
defgrad0[5],defgrad0[7] = fill_star(defgrad[5], defgrad[7])
|
|
for i in [0,4,8]:
|
|
if defgrad0[i] == '*': defgrad0[i] = 0.0
|
|
det0 = 1.0 - np.linalg.det(np.array(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 = 0.5*(np.dot(np.array(defgrad0).reshape(3,3).T,np.array(defgrad0).reshape(3,3)) - np.eye(3)) #Green Strain
|
|
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) )
|
|
ratio = self.finalStrain*1.05/eqstrain
|
|
return max(ratio,1.0)
|
|
|
|
#---------------------------------------------------------------------------------------------------
|
|
class Criterion(object):
|
|
"""Fitting to certain criterion"""
|
|
|
|
def __init__(self, exponent, uniaxial, dimension, label='vonmises'):
|
|
self.name = label
|
|
self.expo = exponent
|
|
self.uniaxial= uniaxial
|
|
self.dimen = dimension
|
|
self.results = fitCriteria
|
|
|
|
if self.name.lower() not in map(str.lower, self.results.keys()):
|
|
raise Exception('No suitable fitting criterion selected')
|
|
else:
|
|
damask.util.croak('Fitting to the %s criterion'%fitCriteria[self.name]['name'])
|
|
|
|
def report_labels(self):
|
|
if len(fitCriteria[self.name]['labels']) > 1 and self.dimen == 2:
|
|
return fitCriteria[self.name]['labels'][1]
|
|
else:
|
|
return fitCriteria[self.name]['labels'][0]
|
|
|
|
def report_name(self):
|
|
return fitCriteria[self.name]['name']
|
|
|
|
def fit(self,stress):
|
|
global fitResults; fitErrors; fitResidual
|
|
if options.exponent > 0.0: nExponent = options.exponent
|
|
else: nExponent = 0
|
|
nameCriterion = self.name.lower()
|
|
criteria = Criteria(nameCriterion,self.uniaxial,self.expo, self.dimen)
|
|
bounds = fitCriteria[nameCriterion]['bound'][dDim] # Default bounds, no bound
|
|
guess0 = Guess # Default initial guess, depends on bounds
|
|
|
|
if fitResults == []:
|
|
initialguess = guess0
|
|
else:
|
|
initialguess = np.array(fitResults[-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)
|
|
else:
|
|
residual = criteria.fun(popt, ydata, stress)
|
|
fitResidual.append(np.linalg.norm(residual)/np.sqrt(len(residual)))
|
|
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())
|
|
fitErrors .append(perr.tolist())
|
|
|
|
popt = np.concatenate((np.array(popt), np.repeat(options.exponent,nExponent)))
|
|
perr = np.concatenate((np.array(perr), np.repeat(0.0,nExponent)))
|
|
|
|
damask.util.croak('Needed {} function calls for fitting'.format(infodict['nfev']))
|
|
except Exception as detail:
|
|
damask.util.croak(detail)
|
|
pass
|
|
return popt
|
|
|
|
#---------------------------------------------------------------------------------------------------
|
|
class myThread (threading.Thread):
|
|
"""Runner"""
|
|
|
|
def __init__(self, threadID):
|
|
threading.Thread.__init__(self)
|
|
self.threadID = threadID
|
|
def run(self):
|
|
semaphore.acquire()
|
|
conv=converged()
|
|
semaphore.release()
|
|
while not conv:
|
|
doSim(self.name)
|
|
semaphore.acquire()
|
|
conv=converged()
|
|
semaphore.release()
|
|
|
|
def doSim(thread):
|
|
semaphore.acquire()
|
|
global myLoad
|
|
loadNo=loadcaseNo()
|
|
if not os.path.isfile('%s.load'%loadNo):
|
|
damask.util.croak('Generating load case for simulation %s (%s)'%(loadNo,thread))
|
|
f=open('%s.load'%loadNo,'w')
|
|
f.write(myLoad.getLoadcase(loadNo))
|
|
f.close()
|
|
semaphore.release()
|
|
else: semaphore.release()
|
|
|
|
# if spectralOut does not exist, run simulation
|
|
semaphore.acquire()
|
|
if not os.path.isfile('%s_%i.spectralOut'%(options.geometry,loadNo)):
|
|
damask.util.croak('Starting simulation %i (%s)'%(loadNo,thread))
|
|
semaphore.release()
|
|
damask.util.execute('DAMASK_spectral -g %s -l %i'%(options.geometry,loadNo))
|
|
else: semaphore.release()
|
|
|
|
# if ASCII tables do not exist, run postprocessing
|
|
semaphore.acquire()
|
|
if not os.path.isfile('./postProc/%s_%i.txt'%(options.geometry,loadNo)):
|
|
damask.util.croak('Starting post processing for simulation %i (%s)'%(loadNo,thread))
|
|
semaphore.release()
|
|
try:
|
|
damask.util.execute('postResults --cr f,p --co totalshear %s_%i.spectralOut'%(options.geometry,loadNo))
|
|
except:
|
|
damask.util.execute('postResults --cr f,p %s_%i.spectralOut'%(options.geometry,loadNo))
|
|
damask.util.execute('addCauchy ./postProc/%s_%i.txt'%(options.geometry,loadNo))
|
|
damask.util.execute('addStrainTensors -0 -v ./postProc/%s_%i.txt'%(options.geometry,loadNo))
|
|
damask.util.execute('addMises -s Cauchy -e ln(V) ./postProc/%s_%i.txt'%(options.geometry,loadNo))
|
|
else: semaphore.release()
|
|
|
|
# reading values from ASCII table (including linear interpolation between points)
|
|
semaphore.acquire()
|
|
damask.util.croak('Reading values from simulation %i (%s)'%(loadNo,thread))
|
|
refFile = './postProc/%s_%i.txt'%(options.geometry,loadNo)
|
|
table = damask.ASCIItable(refFile,readonly=True)
|
|
table.head_read()
|
|
|
|
thresholdKey = {'equivalentStrain':'Mises(ln(V))',
|
|
'totalshear': 'totalshear',
|
|
}[options.fitting]
|
|
|
|
for l in [thresholdKey,'1_Cauchy']:
|
|
if l not in table.labels(raw = True): damask.util.croak('%s not found'%l)
|
|
semaphore.release()
|
|
|
|
table.data_readArray(['%i_Cauchy'%(i+1) for i in range(9)]+[thresholdKey]+['%i_ln(V)'%(i+1) for i in range(9)])
|
|
|
|
validity = np.zeros((int(options.yieldValue[2])), dtype=bool) # found data for desired threshold
|
|
yieldStress = np.empty((int(options.yieldValue[2]),6),'d')
|
|
deformationRate = np.empty((int(options.yieldValue[2]),6),'d')
|
|
|
|
line = 0
|
|
for i,threshold in enumerate(np.linspace(options.yieldValue[0],options.yieldValue[1],options.yieldValue[2])):
|
|
while line < np.shape(table.data)[0]:
|
|
if abs(table.data[line,9])>= threshold:
|
|
upper,lower = abs(table.data[line,9]),abs(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
|
|
yieldStress[i,:] = t33toSym6(stress)
|
|
|
|
dstrain= np.array(table.data[line,10:] - table.data[line-1,10:]).reshape(3,3)
|
|
deformationRate[i,:] = t33toSym6(dstrain)
|
|
|
|
validity[i] = True
|
|
break
|
|
else:
|
|
line+=1
|
|
if not validity[i]:
|
|
semaphore.acquire()
|
|
damask.util.croak('The data of result %i at the threshold %f is invalid,'%(loadNo,threshold)\
|
|
+'the fitting at this point is skipped')
|
|
semaphore.release()
|
|
|
|
# do the actual fitting procedure and write results to file
|
|
semaphore.acquire()
|
|
global stressAll, strainAll
|
|
f=open(options.geometry+'_'+options.criterion+'_'+str(time.time())+'.txt','w')
|
|
f.write(' '.join([options.fitting]+myFit.report_labels())+'\n')
|
|
try:
|
|
for i,threshold in enumerate(np.linspace(options.yieldValue[0],options.yieldValue[1],options.yieldValue[2])):
|
|
if validity[i]:
|
|
stressAll[i]=np.append(stressAll[i], yieldStress[i]/stressUnit)
|
|
strainAll[i]=np.append(strainAll[i], deformationRate[i])
|
|
f.write( str(threshold)+' '+
|
|
' '.join(map(str,myFit.fit(stressAll[i].reshape(len(stressAll[i])//6,6).transpose())))+'\n')
|
|
except Exception:
|
|
damask.util.croak('Could not fit results of simulation (%s)'%thread)
|
|
semaphore.release()
|
|
return
|
|
damask.util.croak('\n')
|
|
semaphore.release()
|
|
|
|
def loadcaseNo():
|
|
global N_simulations
|
|
N_simulations+=1
|
|
return N_simulations
|
|
|
|
def converged():
|
|
global N_simulations; fitResidual
|
|
|
|
if N_simulations < options.max:
|
|
if len(fitResidual) > 5 and N_simulations >= options.min:
|
|
residualList = np.array(fitResidual[len(fitResidual)-5:])
|
|
if np.std(residualList)/np.max(residualList) < 0.05:
|
|
return True
|
|
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 = scriptID)
|
|
|
|
# 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=fitCriteria.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('-b','--bound', dest='bounds', type='float', nargs=2,
|
|
help='yield points: start; end; count %default', metavar='float float')
|
|
parser.add_option('-d','--dimension', dest='dimension', type='choice', choices=['2','3'],
|
|
help='dimension of the virtual test [%default]', metavar='int')
|
|
parser.add_option('-e', '--exponent', dest='exponent', type='float',
|
|
help='exponent of non-quadratic criteria', metavar='int')
|
|
parser.add_option('-u', '--uniaxial', dest='eqStress', type='float',
|
|
help='Equivalent stress', metavar='float')
|
|
|
|
parser.set_defaults(min = 12,
|
|
max = 30,
|
|
threads = 4,
|
|
yieldValue = (0.002,0.004,2),
|
|
load = (0.010,100,100.0),
|
|
criterion = 'vonmises',
|
|
fitting = 'totalshear',
|
|
geometry = '20grains16x16x16',
|
|
bounds = None,
|
|
dimension = '3',
|
|
exponent = -1.0,
|
|
)
|
|
|
|
options = parser.parse_args()[0]
|
|
|
|
if options.threads < 1:
|
|
parser.error('invalid number of threads {}'.format(options.threads))
|
|
if options.min < 0:
|
|
parser.error('invalid minimum number of simulations {}'.format(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')
|
|
|
|
for check in [options.geometry+'.geom','numerics.config','material.config']:
|
|
if not os.path.isfile(check):
|
|
damask.util.croak('"{}" file not found'.format(check))
|
|
|
|
options.dimension = int(options.dimension)
|
|
|
|
stressUnit = 1.0e9 if options.criterion == 'hill1948' else 1.0e6
|
|
|
|
|
|
if options.dimension not in fitCriteria[options.criterion]['dimen']:
|
|
parser.error('invalid dimension for selected criterion')
|
|
|
|
if options.criterion not in ['vonmises','tresca','drucker','hill1948'] and options.eqStress is None:
|
|
parser.error('please specify an equivalent stress (e.g. fitting to von Mises)')
|
|
|
|
# global variables
|
|
fitResults = []
|
|
fitErrors = []
|
|
fitResidual = []
|
|
stressAll= [np.zeros(0,'d').reshape(0,0) for i in range(int(options.yieldValue[2]))]
|
|
strainAll= [np.zeros(0,'d').reshape(0,0) for i in range(int(options.yieldValue[2]))]
|
|
N_simulations=0
|
|
Guess = []
|
|
threads=[]
|
|
semaphore=threading.Semaphore(1)
|
|
dDim = None
|
|
myLoad = None
|
|
myFit = None
|
|
|
|
run = runFit(options.exponent, options.eqStress, options.dimension, options.criterion)
|
|
|
|
damask.util.croak('Finished fitting to yield criteria')
|