#!/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 from scipy.optimize import nnls 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 if options.criterion!='facet': 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],options.flag,options.yieldValue, 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() if options.criterion=='facet': doFacetFit() damask.util.croak('Residuals') damask.util.croak(fitResidual) def doFacetFit(): n = options.order Data = np.zeros((options.numpoints, 10)) for i in range(options.numpoints): fileName = options.geometry + '_' + str(i+1) + '.yield' data_i = np.loadtxt(fileName) sv = (data_i[0,0] + data_i[1,1] + data_i[2,2])/3.0 #convert stress and strain form the 6D to 5D space S1 = np.sqrt(2.0)*(data_i[0,0] - data_i[1,1])/2.0 S2 = np.sqrt(6.0)*(data_i[0,0] + data_i[1,1] - 2.0*sv)/2.0 S3 = np.sqrt(2.0)*data_i[1,2] S4 = np.sqrt(2.0)*data_i[2,0] S5 = np.sqrt(2.0)*data_i[0,1] E1 = np.sqrt(2.0)*(data_i[3,0]-data_i[4,1])/2.0 E2 = np.sqrt(6.0)*(data_i[3,0]+data_i[4,1])/2.0 E3 = np.sqrt(2.0)*data_i[4,2] E4 = np.sqrt(2.0)*data_i[5,0] E5 = np.sqrt(2.0)*data_i[3,1] Data[i,:] = [E1,E2,E3,E4,E5,S1,S2,S3,S4,S5] Data[:,5:] = Data[:,5:] / 100000000.0 path=os.path.join(os.getcwd(),'final.mmm') np.savetxt(path, Data, header='', comments='', fmt='% 15.10f') if options.dimension == 2: reducedIndices = [0,1,4,5,6,9] elif options.dimension == 3: reducedIndices = [i for i in range(10)] numDirections = Data.shape[0] Indices = np.arange(numDirections) sdPairs = Data[:,reducedIndices][Indices,:] numPairs = sdPairs.shape[0] dimensionality = sdPairs.shape[1] / 2 ds = sdPairs[:,0:dimensionality] s = sdPairs[:,dimensionality::] A = np.zeros((numPairs, numPairs)) B = np.ones((numPairs,)) for i in range(numPairs): for j in range(numPairs): lamb = 1.0 s_i = s[i,:] ds_j = ds[j,:] A[i,j] = lamb * (np.dot(s_i.ravel(), ds_j.ravel()) ** n) lambdas, residuals = nnls(A, B) nonZeroTerms = np.logical_not(np.isclose(lambdas, 0.)) numNonZeroTerms = np.sum(nonZeroTerms) dataOut = np.zeros((numNonZeroTerms, 6)) if options.dimension == 2: dataOut[:,0] = lambdas[nonZeroTerms] dataOut[:,1] = ds[nonZeroTerms,:][:,0] dataOut[:,2] = ds[nonZeroTerms,:][:,1] dataOut[:,5] = ds[nonZeroTerms,:][:,2] elif options.dimension == 3: dataOut[:,0] = lambdas[nonZeroTerms] dataOut[:,1] = ds[nonZeroTerms,:][:,0] dataOut[:,2] = ds[nonZeroTerms,:][:,1] dataOut[:,3] = ds[nonZeroTerms,:][:,2] dataOut[:,4] = ds[nonZeroTerms,:][:,3] dataOut[:,5] = ds[nonZeroTerms,:][:,4] headerText = 'facet\n 1 \n F \n {0:<3d} \n {1:<3d} '.format(n, numNonZeroTerms) path=os.path.join(os.getcwd(),'facet_o{0}.fac'.format(n)) np.savetxt(path, dataOut, header=headerText, comments='', fmt='% 15.10f') 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 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: if options.criterion=='facet': doSimForFacet(self.name) else: 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() # reading values from ASCII file semaphore.acquire() damask.util.croak('Reading values from simulation %i (%s)'%(loadNo,thread)) semaphore.release() refFile = '%s_%i.yield'%(options.geometry,loadNo) yieldStress = np.empty((6),'d') if not os.path.isfile(refFile): validity = False else: validity = True yieldData = np.loadtxt(refFile) stress = yieldData[:3] yieldStress = t33toSym6(stress) # do the actual fitting procedure and write results to file semaphore.acquire() global stressAll f=open(options.geometry+'_'+options.criterion+'_'+str(time.time())+'.txt','w') f.write(' '.join([options.fitting]+myFit.report_labels())+'\n') try: if validity: stressAll=np.append(stressAll, yieldStress/stressUnit) f.write(' '.join(map(str,myFit.fit(stressAll.reshape(len(stressAll)//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 doSimForFacet(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() def loadcaseNo(): global N_simulations N_simulations+=1 return N_simulations def converged(): global N_simulations; fitResidual if options.criterion=='facet': if N_simulations == options.numpoints: return True else: return False else: 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', help='yield points %default', metavar='float') 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.add_option('--flag', dest='flag', type='string', help='yield stop flag, totalStrain, plasticStrain or plasticWork', metavar='string') parser.add_option('--numpoints', dest='numpoints', type='int', help='number of yield points to fit facet potential [%default]', metavar='int') parser.add_option('--order', dest='order', type='int', help='order of facet potential [%default]', metavar='int') parser.set_defaults(min = 12, max = 20, threads = 4, yieldValue = 0.002, load = (0.010,100,100.0), criterion = 'vonmises', fitting = 'totalshear', geometry = '20grains16x16x16', bounds = None, dimension = '3', exponent = -1.0, flag = 'totalStrain', numpoints = 100, order = 8 ) 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)') 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) N_simulations=0 Guess = [] threads=[] semaphore=threading.Semaphore(1) dDim = None myLoad = None myFit = None if options.criterion == 'facet': run = runFit(options.exponent, options.eqStress, options.dimension, options.criterion) else: run = runFit(options.exponent, options.eqStress, options.dimension, options.criterion) damask.util.croak('Finished fitting to yield criteria')