DAMASK_EICMD/processing/misc/yieldSurface.py

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#!/usr/bin/python
# -*- coding: UTF-8 no BOM -*-
import threading,time,os,subprocess,shlex,string
import numpy as np
from scipy.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]
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def execute(cmd,streamIn=None,wd='./'):
'''
executes a command in given directory and returns stdout and stderr for optional stdin
'''
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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()
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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<EFBFBD>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<EFBFBD>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
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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()
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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')
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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)
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for i in main[:2]: # fill 2 out of 3 main entries
defgrad[i]=1.+values[i]
stress[i]='*'
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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)
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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
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self.results = fittingCriteria
if self.name.lower() not in map(str.lower, self.results.keys()):
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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))
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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()
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me=getLoadcase()
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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))
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f.close()
s.release()
else: s.release()
s.acquire()
if not os.path.isfile('%s_%i.spectralOut'%(options.geometry,me)):
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print('starting simulation %s from %s'%(me,thread))
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s.release()
execute('DAMASK_spectral -g %s -l %i'%(options.geometry,me))
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else: s.release()
s.acquire()
if not os.path.isfile('./postProc/%s_%i.txt'%(options.geometry,me)):
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print('starting post processing for sim %i from %s'%(me,thread))
s.release()
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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))
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else: s.release()
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s.acquire()
print('-'*10)
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print('reading values for sim %i from %s'%(me,thread))
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s.release()
refFile = open('./postProc/%s_%i.txt'%(options.geometry,me))
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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
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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
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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,
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help='load: final strain; increments; time %default', metavar='float int float')
parser.add_option('-g','--geometry', dest='geometry', type='string',
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help='name of the geometry file [%default]', metavar='string')
parser.add_option('-c','--criterion', dest='criterion', choices=fittingCriteria.keys(),
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help='criterion for stopping simulations [%default]', metavar='string')
parser.add_option('-f','--fitting', dest='fitting', choices=thresholdParameter,
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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',
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help='minimum number of simulations [%default]', metavar='int')
parser.add_option('--max', dest='max', type='int',
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help='maximum number of iterations [%default]', metavar='int')
parser.add_option('-t','--threads', dest='threads', type='int',
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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))
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parser.set_defaults(criterion = 'worst')
parser.set_defaults(fitting = 'totalshear')
parser.set_defaults(geometry = '20grains16x16x16')
options = parser.parse_args()[0]
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if not os.path.isfile(options.geometry+'.geom'):
parser.error('geometry file %s.geom not found'%options.geometry)
if not os.path.isfile('material.config'):
parser.error('material.config file not found')
if options.threads<1:
parser.error('invalid number of threads %i'%options.threads)
if options.min<0:
parser.error('invalid minimum number of simulations %i'%options.min)
if options.max<options.min:
parser.error('invalid maximum number of simulations (below minimum)')
if options.yieldValue[0]>options.yieldValue[1]:
parser.error('invalid yield start (below yield end)')
if options.yieldValue[2] != int(options.yieldValue[2]):
parser.error('count must be an integer')
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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])
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myFit = Criterion(options.criterion)
threads=[]
for i in range(options.threads):
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threads.append(myThread(i))
threads[i].start()
for i in range(options.threads):
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threads[i].join()
print 'finished fitting to yield criteria'