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DAMASK_EICMD
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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
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(np.array(sigmas[:,i]).reshape(3,3))
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 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 = (lambdas[2,:]-lambdas[1,:])**a\
+ (lambdas[1,:]-lambdas[0,:])**a\
+ (lambdas[0,:]-lambdas[2,:])**a\
-2.0*sigma0**a
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[4]-sigmas[8])**2.0\
+ G*(sigmas[8]-sigmas[0])**2.0\
+ H*(sigmas[0]-sigmas[4])**2.0\
+ 2.0*L* sigmas[5]**2.0\
+ 2.0*M* sigmas[2]**2.0\
+ 2.0*N* sigmas[1]**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=1.0, b=1.0, c=1.0, f=1.0, g=1.0, h=1.0):
'''
residuum of Barlat 1997 yield criterion
'''
cos = np.cos; pi = np.pi; abs = np.abs
A = a*(sigmas[4] - sigmas[8])
B = b*(sigmas[8] - sigmas[0])
C = c*(sigmas[0] - sigmas[4])
F = f*sigmas[5]
G = g*sigmas[2]
H = h*sigmas[1]
I2 = (F*F + G*G + H*H)/3.0 + ((A-C)*(A-C)+(C-B)*(C-B)+(B-A)*(B-A))/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
theta = np.arccos(I3/pow(I2,1.5))
Phi = pow(3.0*I2, order/2.0)* (
pow(abs(2.0*cos((2.0*theta + pi)/6.0)), order) +
pow(abs(2.0*cos((2.0*theta + pi*3.0)/6.0)), order) +
pow(abs(2.0*cos((2.0*theta + pi*5.0)/6.0)), order)
)
r = Phi - 2.0*pow(sigma0, order)
return r.ravel()
def Barlat1991iso(sigmas, sigma0, m):
'''
residuum of isotropic Barlat 1991 yield criterion (eq. 2.37)
'''
return Barlat1991(sigmas, sigma0, m)
def Barlat1991aniso(sigmas, sigma0, m, a,b,c,f,g,h):
'''
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
fittingCriteria = {
'Tresca' :{'fit' :np.ones(1,'d'),'err':np.inf,
'name' :'Tresca',
'paras':'Initial yield stress:'},
'vonMises' :{'fit' :np.ones(1,'d'),'err':np.inf,
'name' :'Huber-Mises-Hencky(von Mises)',
'paras':'Initial yield stress:'},
'Hill1948' :{'fit' :np.ones(6,'d'),'err':np.inf,
'name' :'Hill1948',
'paras':'Normalized [F, G, H, L, M, N]'},
'Drucker' :{'fit' :np.ones(2,'d'),'err':np.inf,
'name' :'Drucker',
'paras':'Initial yield stress, C_D:'},
'Barlat1991iso' :{'fit' :np.ones(2,'d'),'err':np.inf,
'name' :'Barlat1991iso',
'paras':'Initial yield stress, m:'},
'Barlat1991aniso':{'fit' :np.ones(8,'d'),'err':np.inf,
'name' :'Barlat1991aniso',
'paras':'Initial yield stress, m, a, b, c, f, g, h:'},
'worst' :{'err':np.inf},
'best' :{'err':np.inf}
}
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
if self.name.lower() == 'tresca':
funResidum = Tresca
text = '\nCoefficient of Tresca criterion:\nsigma0: '+formatOutput(1)
error='The standard deviation error is: '+formatOutput(1,'%-14.8f')+'\n'
elif self.name.lower() == 'vonmises':
funResidum = vonMises
text = '\nCoefficient of Huber-Mises-Hencky criterion:\nsigma0: '+formatOutput(1)
error='The standard deviation error is: '+formatOutput(1,'%-14.8f')+'\n'
elif self.name.lower() == 'drucker':
funResidum = Drucker
text = '\nCoefficient of Drucker criterion:\nsigma0, C_D: '+formatOutput(2)
error='The standard deviation errors are: '+formatOutput(2,'%-14.8f')+'\n'
elif self.name.lower() == 'hill1948':
funResidum = Hill1948
text = '\nCoefficient of Hill1948 criterion:\n[F, G, H, L, M, N]:'+' '*16+formatOutput(6)
error='The standard deviation errors are: '+formatOutput(6,'%-14.8f')+'\n'
elif self.name.lower() == 'barlat91iso':
funResidum = Barlat1991iso
text = '\nCoefficient of isotropic Barlat 1991 criterion:\nsigma0, m:\n'+formatOutput(2)
error='The standard deviation errors are: '+formatOutput(2,'%-14.8f')+'\n'
elif self.name.lower() == 'barlat91aniso':
funResidum = Barlat1991aniso
text = '\nCoefficient of anisotropic Barlat 1991 criterion:\nsigma0, \m, a, b, c, f, g, h:\n' \
+formatOutput(8)
error='The standard deviation errors are: '+formatOutput(8,'%-14.8f')
if fitResults == []:
initialguess = fittingCriteria[funResidum.__name__]['fit']
else:
initialguess = np.array(fitResults[-1])
weight = get_weight(np.shape(stress)[1])
try:
popt, pcov = \
curve_fit(funResidum, stress, np.zeros(np.shape(stress)[1]),
initialguess, weight)
perr = np.sqrt(np.diag(pcov))
fitResults.append(popt.tolist())
print (text%array2tuple(popt))
print (error%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=[None for i in xrange(int(options.yieldValue[2]))]
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
yieldStress[i] = table.data[line-1,0:9] * (upper-threshold)/(upper-lower) \
+ table.data[line ,0:9] * (threshold-lower)/(upper-lower) # linear interpolation of stress values
yieldStress[i][1] = (yieldStress[i][1] + yieldStress[i][3])/2.0
yieldStress[i][2] = (yieldStress[i][2] + yieldStress[i][6])/2.0
yieldStress[i][5] = (yieldStress[i][5] + yieldStress[i][7])/2.0
yieldStress[i][3] = yieldStress[i][1]
yieldStress[i][6] = yieldStress[i][2]
yieldStress[i][7] = yieldStress[i][5]
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])//9,9).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.max<options.min:
parser.error('invalid maximum number of simulations (below minimum)')
if options.yieldValue[0]>options.yieldValue[1]:
parser.error('invalid yield start (below yield end)')
if options.yieldValue[2] != int(options.yieldValue[2]):
parser.error('count must be an integer')
if not os.path.isfile('numerics.config'):
print('numerics.config file not found')
if not os.path.isfile('material.config'):
print('material.config file not found')
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'
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