#!/usr/bin/python # -*- coding: UTF-8 no BOM -*- import threading,time,os,subprocess,shlex,string import numpy as np from scipy.optimize import curve_fit from scipy.linalg import svd from optparse import OptionParser import damask from damask.util import curve_fit_bound 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 stressInvariants(lambdas): ''' computes stress invariants (i.e. eigenvalues) for a set of principal Cauchy stresses. ''' Is=np.zeros(0,'d') for i in xrange(np.shape(lambdas)[1]): I = np.array([lambdas[0,i]+lambdas[1,i]+lambdas[2,i],\ lambdas[0,i]*lambdas[1,i]+lambdas[1,i]*lambdas[2,i]+lambdas[2,i]*lambdas[0,i],\ lambdas[0,i]*lambdas[1,i]*lambdas[2,i]]) Is = np.append(Is,I) Is = Is.reshape(3,np.shape(lambdas)[1]) return Is def formatOutput(n, type='%-14.6f'): return ''.join([type for i in xrange(n)]) 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 # --------------------------------------------------------------------------------------------- def Tresca(sigmas, sigma0): ''' residuum of Tresca yield criterion (eq. 2.26) ''' 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 vonMises(sigmas, sigma0): ''' residuum of Huber-Mises-Hencky yield criterion (eq. 2.37) ''' return Hosford(sigmas, sigma0, 2.0) def Drucker(sigmas, sigma0, C_D): ''' residuum of Drucker yield criterion (eq. 2.41, F = sigma0) ''' return generalDrucker(sigmas, sigma0, C_D, 1.0) def generalDrucker(sigmas, sigma0, C_D, p): ''' residuum of general Drucker yield criterion (eq. 2.42, F = sigma0) ''' Is = stressInvariants(principalStresses(sigmas)) r = (Is[1,:]**(3.0*p)-C_D*Is[2,:]**(2.0*p)) - sigma0 return r.ravel() def Hosford(sigmas, sigma0, a): ''' residuum of Hershey yield criterion (eq. 2.43, Y = sigma0) ''' lambdas = principalStresses(sigmas) r = ((abs(lambdas[2,:]-lambdas[1,:]))**a\ + (abs(lambdas[1,:]-lambdas[0,:]))**a\ + (abs(lambdas[0,:]-lambdas[2,:]))**a) **(1.0/a)\ -2.0**(1.0/a)*sigma0 return r.ravel() #more to do # KarafillisAndBoyce # --------------------------------------------------------------------------------------------- # isotropic yield surfaces # --------------------------------------------------------------------------------------------- def Hill1948(sigmas, F,G,H,L,M,N): ''' residuum of Hill 1948 quadratic yield criterion (eq. 2.48) ''' r = F*(sigmas[1]-sigmas[2])**2.0\ + G*(sigmas[2]-sigmas[0])**2.0\ + H*(sigmas[0]-sigmas[1])**2.0\ + 2.0*L* sigmas[4]**2.0\ + 2.0*M* sigmas[5]**2.0\ + 2.0*N* sigmas[3]**2.0\ - 1.0 return r.ravel()/2.0 #more to do # Hill 1979 # Hill 1990,1993 need special stresses to fit def generalHosford(sigmas, sigma0, a): ''' residuum of Hershey yield criterion (eq. 2.104, sigma = sigma0) ''' lambdas = principalStresses(sigmas) r = np.amax(np.array([F*(abs(lambdas[:,1]-lambdas[:,2]))**a,\ G*(abs(lambdas[:,2]-lambdas[:,0]))**a,\ H*(abs(lambdas[:,0]-lambdas[:,1]))**a]),1) - sigma0**a return r.ravel() def Barlat1991(sigmas, sigma0, order, a, b, c, f, g, h): ''' residuum of Barlat 1997 yield criterion ''' cos = np.cos; pi = np.pi; abs = np.abs A = a*(sigmas[1] - sigmas[2]) B = b*(sigmas[2] - sigmas[0]) C = c*(sigmas[0] - sigmas[1]) F = f*sigmas[4] G = g*sigmas[5] H = h*sigmas[3] I2 = (F*F + G*G + H*H)/3.0 + ((A-C)**2+(C-B)**2+(B-A)**2)/54.0 I3 = (C-B)*(A-C) * (B-A)/54.0 + F*G*H - \ ( (C-B)*F*F + (A-C)*G*G + (B-A)*H*H )/6.0 theta = np.arccos(I3/I2**1.5) Phi = np.sqrt(3.0*I2)* ( (abs(2.0*cos((2.0*theta + pi)/6.0)))**order + (abs(2.0*cos((2.0*theta + pi*3.0)/6.0)))**order + (abs(2.0*cos(( 2.0*theta + pi*5.0)/6.0)))**order )**(1.0/order) r = Phi/2.0**(1.0/order) - sigma0 return r.ravel() def Barlat1991iso(sigmas, sigma0, m): ''' residuum of isotropic Barlat 1991 yield criterion (eq. 2.37) ''' return Barlat1991(sigmas, sigma0, m, 1.0,1.0,1.0,1.0,1.0,1.0) def Barlat1991aniso(sigmas, sigma0, a,b,c,f,g,h, m): ''' residuum of anisotropic Barlat 1991 yield criterion (eq. 2.37) ''' return Barlat1991(sigmas, sigma0, m, a,b,c,f,g,h) def Barlat1994(sigmas, sigma0, a): ''' residuum of Hershey yield criterion (eq. 2.104, sigma_e = sigma0) ''' return None def Cazacu_Barlat3D(sigmas, sigma0, a1,a2,a3,a4,a5,a6, b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11, c): ''' residuum of the Cazacu–Barlat (CZ) yield criterion ''' s11 = sigmas[0]; s22 = sigmas[1]; s33 = sigmas[2] s12 = sigmas[3]; s23 = sigmas[4]; s31 = sigmas[5] J20 = ( a1*(s22-s33)**2 + a2*(s33-s11)**2 + a3*(s11-s22)**2 )/6.0 + \ a4* s23**2 + a5* s31**2 + a6* s12**2 J30 = ( (b1 +b2 )*s11**3 + (b3 +b4 )*s22**3 + ( b1+b4-b2 + b1+b4-b3 )*s33**3)/27.0- \ ( (b1*s22+b2*s33)*s11**2 + (b3*s33+b4*s11)*s22**2 + ((b1+b4-b2)*s11 + (b1+b4-b3)*s22)*s33**2)/9.0 + \ ( (b1+b4)*s11*s22*s33/9.0 + b11*s12*s23*s31 )*2.0 - \ ( ( 2.0*b9 *s22 - b8*s33 - (2*b9 -b8)*s11 )*s31**2 + ( 2.0*b10*s33 - b5*s22 - (2*b10-b5)*s11 )*s12**2 + ( (b6+b7)*s11 - b6*s22 - b7*s33 )*s23**2 )/3.0 f0 = (J20**3 - c*J30**2)**(1.0/6.0) k2 = (sigma0/3.0) *18.0 **(1.0/6.0) r = f0/k2 - 1.0 return r.ravel() def Cazacu_Barlat2D(sigmas, sigma0, a1,a2,a3,a6, b1,b2,b3,b4,b5,b10, c): ''' residuum of the Cazacu–Barlat (CZ) yield criterion for plain stress ''' s11 = sigmas[0]; s22 = sigmas[1]; s12 = sigmas[3] J20 = ( (a2+a3)*s11**2 + (a1+a3)*s22**2 - 2.0*a3*s11*s22 )/6.0 + a6*s12**2 J30 = ( (b1 + b2 )*s11**3 + (b3 +b4 )*s22**3 )/27.0- \ ( (b1*s11 + b4*s22)*s11*s22 )/9.0 + \ ( b5*s22 + (2*b10-b5)*s11 )*s12**2/3.0 f0 = (J20**3 - c*J30**2)**(1.0/6.0) k2 = (sigma0/3.0) *18.0 **(1.0/6.0) r = f0/k2 - 1.0 return r.ravel() def BBC2003(sigmas, sigma0, a,b,c, d,e,f,g, k): ''' residuum of the BBC2003 yield criterion for plain stress ''' s11 = sigmas[0]; s22 = sigmas[1]; s12 = sigmas[3] k2 = 2.0*k Gamma = s11*(d+e) + s22*(e+f) Psi = ( ( s11*(d-e)/2.0 + s22*(e-f)/2.0 )**2 + (g*s12)**2 )**0.5 sBar = ( a*(b*Gamma + c*Psi)**k2 + a*(b*Gamma - c*Psi)**k2 + (1-a)*(2.0*c*Psi)**k2 )**(1.0/k2) r = sBar/sigma0 - 1.0 return r.ravel() fittingCriteria = { 'tresca' :{'func' : Tresca, 'num' : 1,'err':np.inf, 'name' : 'Tresca', 'paras': 'Initial yield stress:', 'text' : '\nCoefficient of Tresca criterion:\nsigma0: ', 'error': 'The standard deviation error is: ' }, 'vonmises' :{'func' : vonMises, 'num' : 1,'err':np.inf, 'name' : 'Huber-Mises-Hencky(von Mises)', 'paras': 'Initial yield stress:', 'text' : '\nCoefficient of Huber-Mises-Hencky criterion:\nsigma0: ', 'error': 'The standard deviation error is: ' }, 'hosford' :{'func' : Hosford, 'num' : 2,'err':np.inf, 'name' : 'Gerenal Hosford', 'paras': 'Initial yield stress:', 'text' : '\nCoefficients of Hosford criterion:\nsigma0, a: ', 'error': 'The standard deviation errors are: ' }, 'hill1948' :{'func' : Hill1948, 'num' : 6,'err':np.inf, 'name' : 'Hill1948', 'paras': 'Normalized [F, G, H, L, M, N]', 'text' : '\nCoefficients of Hill1948 criterion:\n[F, G, H, L, M, N]:', 'error': 'The standard deviation errors are: ' }, 'drucker' :{'func' : Drucker, 'num' : 2,'err':np.inf, 'name' : 'Drucker', 'paras': 'Initial yield stress, C_D:', 'text' : '\nCoefficients of Drucker criterion:\nsigma0, C_D: ', 'error': 'The standard deviation errors are: ' }, 'barlat1991iso' :{'func' : Barlat1991iso, 'num' : 2,'err':np.inf, 'name' : 'Barlat1991iso', 'paras': 'Initial yield stress, m:', 'text' : '\nCoefficients of isotropic Barlat 1991 criterion:\nsigma0, m:\n', 'error': 'The standard deviation errors are: ' }, 'barlat1991aniso':{'func' : Barlat1991aniso, 'num' : 8,'err':np.inf, 'name' : 'Barlat1991aniso', 'paras': 'Initial yield stress, m, a, b, c, f, g, h:', 'text' : '\nCoefficients of anisotropic Barlat 1991 criterion:\nsigma0, a, b, c, f, g, h, m:\n', 'error': 'The standard deviation errors are: ' }, 'bbc2003' :{'func' : BBC2003, 'num' : 9,'err':np.inf, 'name' : 'Barlat1991aniso', 'paras': 'Initial yield stress, a, b, c, d, e, f, g, k:', 'text' : '\nCoefficients of anisotropic Barlat 1991 criterion:\nsigma0, a, b, c, d, e, f, g, k:\n', 'error': 'The standard deviation errors are: ' }, 'Cazacu_Barlat2D':{'func' : Cazacu_Barlat2D, 'num' : 12,'err':np.inf, 'name' : 'Barlat1991aniso', 'paras': 'Initial yield stress, a1,a2,a3,a6; b1,b2,b3,b4,b5,b10; c:', 'text' : '\nCoefficients of Cazacu Barlat yield criterion for plane stress: \ \n Y, a1,a2,a3,a6; b1,b2,b3,b4,b5,b10; c:\n', 'error': 'The standard deviation errors are: ' }, 'Cazacu_Barlat3D':{'func' : Cazacu_Barlat3D, 'num' : 19,'err':np.inf, 'name' : 'Barlat1991aniso', 'paras': 'Initial yield stress, 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 Y, 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: ' }, 'worst' :{'err':np.inf}, 'best' :{'err':np.inf} } for key in fittingCriteria.keys(): if 'num' in fittingCriteria[key].keys(): fittingCriteria[key]['bound']=[(None,None)]*fittingCriteria[key]['num'] fittingCriteria[key]['guess']=np.ones(fittingCriteria[key]['num'],'d') thresholdParameter = ['totalshear','equivalentStrain'] #--------------------------------------------------------------------------------------------------- class Loadcase(): #--------------------------------------------------------------------------------------------------- ''' Class for generating load cases for the spectral solver ''' # ------------------------------------------------------------------ def __init__(self,finalStrain,incs,time): print('using the random load case generator') self.finalStrain = finalStrain self.incs = incs self.time = time def getLoadcase(self,N=0): defgrad=['*']*9 stress =[0]*9 values=(np.random.random_sample(9)-.5)*self.finalStrain*2 main=np.array([0,4,8]) np.random.shuffle(main) for i in main[:2]: # fill 2 out of 3 main entries defgrad[i]=1.+values[i] stress[i]='*' for off in [[1,3,0],[2,6,0],[5,7,0]]: # fill 3 off-diagonal pairs of defgrad (1 or 2 entries) off=np.array(off) np.random.shuffle(off) for i in off[0:2]: if i != 0: defgrad[i]=values[i] stress[i]='*' return 'f '+' '.join(str(c) for c in defgrad)+\ ' p '+' '.join(str(c) for c in stress)+\ ' incs %s'%self.incs+\ ' time %s'%self.time #--------------------------------------------------------------------------------------------------- class Criterion(object): #--------------------------------------------------------------------------------------------------- ''' Fitting to certain criterion ''' def __init__(self,name='worst'): self.name = name self.results = fittingCriteria if self.name.lower() not in map(str.lower, self.results.keys()): raise Exception('no suitable fitting criterion selected') else: print('fitting to the %s criterion'%name) def fit(self,stress): global fitResults nameCriterion = self.name.lower() funResidum = 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 if fitResults == [] : initialguess = guess0 else : initialguess = np.array(fitResults[-1]) weight = get_weight(np.shape(stress)[1]) try: popt, pcov = \ curve_fit_bound(funResidum, stress, np.zeros(np.shape(stress)[1]), initialguess, weight, bounds) perr = np.sqrt(np.diag(pcov)) fitResults.append(popt.tolist()) print (textParas%array2tuple(popt)) print (textError%array2tuple(perr)) except Exception as detail: print detail pass #--------------------------------------------------------------------------------------------------- class myThread (threading.Thread): #--------------------------------------------------------------------------------------------------- ''' Runner class ''' def __init__(self, threadID): threading.Thread.__init__(self) self.threadID = threadID def run(self): s.acquire() conv=converged() s.release() while not conv: doSim(4.,self.name) s.acquire() conv=converged() s.release() def doSim(delay,thread): s.acquire() me=getLoadcase() if not os.path.isfile('%s.load'%me): print('generating loadcase for sim %s from %s'%(me,thread)) f=open('%s.load'%me,'w') f.write(myLoad.getLoadcase(me)) f.close() s.release() else: s.release() s.acquire() if not os.path.isfile('%s_%i.spectralOut'%(options.geometry,me)): print('starting simulation %s from %s'%(me,thread)) s.release() execute('DAMASK_spectral -g %s -l %i'%(options.geometry,me)) else: s.release() s.acquire() if not os.path.isfile('./postProc/%s_%i.txt'%(options.geometry,me)): print('starting post processing for sim %i from %s'%(me,thread)) s.release() try: execute('postResults --cr f,p --co totalshear %s_%i.spectralOut'%(options.geometry,me)) except: execute('postResults --cr f,p %s_%i.spectralOut'%(options.geometry,me)) execute('addCauchy ./postProc/%s_%i.txt'%(options.geometry,me)) execute('addStrainTensors -l -v ./postProc/%s_%i.txt'%(options.geometry,me)) execute('addMises -s Cauchy -e ln(V) ./postProc/%s_%i.txt'%(options.geometry,me)) else: s.release() s.acquire() print('-'*10) print('reading values for sim %i from %s'%(me,thread)) s.release() refFile = open('./postProc/%s_%i.txt'%(options.geometry,me)) table = damask.ASCIItable(refFile) table.head_read() if options.fitting =='equivalentStrain': thresholdKey = 'Mises(ln(V))' elif options.fitting =='totalshear': thresholdKey = 'totalshear' s.acquire() for l in [thresholdKey,'1_Cauchy']: if l not in table.labels: print '%s not found'%l s.release() table.data_readArray(['%i_Cauchy'%(i+1) for i in xrange(9)]+[thresholdKey]) line = 0 lines = np.shape(table.data)[0] yieldStress = 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 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 break else: line+=1 s.acquire() global stressAll 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(yieldStress[i]/unitGPa,stressAll[i]) myFit.fit(stressAll[i].reshape(len(stressAll[i])//6,6).transpose()) except Exception as detail: print('could not fit for sim %i from %s'%(me,thread)) print detail s.release() return s.release() def getLoadcase(): global N_simulations N_simulations+=1 return N_simulations def converged(): global N_simulations if N_simulations < options.max: return False else: return True # -------------------------------------------------------------------- # MAIN # -------------------------------------------------------------------- parser = OptionParser(option_class=damask.extendableOption, usage='%prog options [file[s]]', description = """ Performs calculations with various loads on given geometry file and fits yield surface. """, version=string.replace(scriptID,'\n','\\n') ) parser.add_option('-l','--load' , dest='load', type='float', nargs=3, help='load: final strain; increments; time %default', metavar='float int float') parser.add_option('-g','--geometry', dest='geometry', type='string', help='name of the geometry file [%default]', metavar='string') parser.add_option('-c','--criterion', dest='criterion', choices=fittingCriteria.keys(), help='criterion for stopping simulations [%default]', metavar='string') parser.add_option('-f','--fitting', dest='fitting', choices=thresholdParameter, help='yield criterion [%default]', metavar='string') parser.add_option('-y','--yieldvalue', dest='yieldValue', type='float', nargs=3, help='yield points: start; end; count %default', metavar='float float int') parser.add_option('--min', dest='min', type='int', help='minimum number of simulations [%default]', metavar='int') parser.add_option('--max', dest='max', type='int', help='maximum number of iterations [%default]', metavar='int') parser.add_option('-t','--threads', dest='threads', type='int', help='number of parallel executions [%default]', metavar='int') parser.set_defaults(min = 12) parser.set_defaults(max = 30) parser.set_defaults(threads = 4) parser.set_defaults(yieldValue = (0.002,0.004,2)) parser.set_defaults(load = (0.010,100,100.0)) parser.set_defaults(criterion = 'worst') parser.set_defaults(fitting = 'totalshear') parser.set_defaults(geometry = '20grains16x16x16') options = parser.parse_args()[0] if not os.path.isfile(options.geometry+'.geom'): parser.error('geometry file %s.geom not found'%options.geometry) if not os.path.isfile('material.config'): parser.error('material.config file not found') if options.threads<1: parser.error('invalid number of threads %i'%options.threads) if options.min<0: parser.error('invalid minimum number of simulations %i'%options.min) if options.maxoptions.yieldValue[1]: parser.error('invalid yield start (below yield end)') if options.yieldValue[2] != int(options.yieldValue[2]): parser.error('count must be an integer') if not os.path.isfile('numerics.config'): print('numerics.config file not found') if not os.path.isfile('material.config'): print('material.config file not found') unitGPa = 10.e8 N_simulations=0 fitResults = [] s=threading.Semaphore(1) stressAll=[np.zeros(0,'d').reshape(0,0) for i in xrange(int(options.yieldValue[2]))] myLoad = Loadcase(options.load[0],options.load[1],options.load[2]) myFit = Criterion(options.criterion) threads=[] for i in range(options.threads): threads.append(myThread(i)) threads[i].start() for i in range(options.threads): threads[i].join() print 'finished fitting to yield criteria'