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1. Implement 2D and 3D Cazacu-Barlat yield criteria(the residum and Jacobian); 

2. Both work
This commit is contained in:
Haiming Zhang 2015-02-20 20:34:47 +00:00
parent 09c357c70f
commit a3e5da0bfd
1 changed files with 102 additions and 34 deletions
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136
processing/misc/yieldSurface.py
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@ -201,45 +201,113 @@ class BBC2003(object):
def jac(self, (sigma0, a,b,c, d,e,f,g, k), ydata, sigmas):
return BBC2003Basis(sigma0, a,b,c, d,e,f,g, k, sigmas, Jac=True)
def Cazacu_Barlat3D(sigma0,a1,a2,a3,a4,a5,a6, b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11, c,
ydata, sigmas):
class Cazacu_Barlat2D(object):
'''
residuum of the Cazacu–Barlat (CZ) yield criterion
'''
def __init__(self, uniaxialStress):
self.stress0 = uniaxialStress
def fun(self, (a1,a2,a3,a4,b1,b2,b3,b4,b5,b10,c), ydata, sigmas):
return Cazacu_Barlat2DBasis(a1,a2,a3,a4,b1,b2,b3,b4,b5,b10,c,
self.stress0, sigmas)
def jac(self, (a1,a2,a3,a4,b1,b2,b3,b4,b5,b10,c), ydata, sigmas):
return Cazacu_Barlat2DBasis(a1,a2,a3,a4,b1,b2,b3,b4,b5,b10,c,
self.stress0, sigmas,Jac=True)
class Cazacu_Barlat3D(object):
'''
'''
def __init__(self, uniaxialStress):
self.stress0 = uniaxialStress
def fun(self, (a1,a2,a3,a4,a5,a6,b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,c),ydata, sigmas):
return Cazacu_Barlat3DBasis(a1,a2,a3,a4,a5,a6,b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,c,
self.stress0, sigmas)
def jac(self, (a1,a2,a3,a4,a5,a6,b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,c),ydata, sigmas):
return Cazacu_Barlat3DBasis(a1,a2,a3,a4,a5,a6,b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,c,
self.stress0, sigmas,Jac=True)
def Cazacu_Barlat3DBasis(a1,a2,a3,a4,a5,a6,b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,c,
sigma0,sigmas, Jac = False):
'''
residuum of the 3D Cazacu–Barlat (CZ) yield criterion
'''
s11 = sigmas[0]; s22 = sigmas[1]; s33 = sigmas[2]
s12 = sigmas[3]; s23 = sigmas[4]; s31 = sigmas[5]
s123, s321 = s11*s22*s33, s12*s23*s31
s1_2, s2_2, s3_2 = s11**2, s22**2, s33**2
s1_3, s2_3, s3_3 = s11*s1_2, s22*s2_2, s33*s3_2
s12_2, s23_2, s31_2 = s12**2, s23**2, s31**2
d12_2, d23_2, d31_2 = (s11-s22)**2, (s22-s33)**2, (s33-s11)**2
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
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)**(1.0/6.0)
k2 = (sigma0/3.0) *18.0 **(1.0/6.0)
r = f0/k2 - 1.0
return r.ravel()
f0 = (J20**3 - c*J30**2)/18.0
r = f0**(1.0/6.0)*(3.0/sigma0)
if not Jac:
return (r - 1.0).ravel()
else:
drdf = r/f0/108.0
dj2 = drdf*3.0*J20**2.0
dj3 = -drdf*2.0*J30*c
jc = -drdf*J30**2
def Cazacu_Barlat2D(sigma0,a1,a2,a3,a6, b1,b2,b3,b4,b5,b10, c,
ydata, sigmas):
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_2/3.0*2.0
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_2/3.0*2.0
jb11 = dj3*s321*2.0
jaco = []
for jac in zip(ja1,ja2,ja3,ja4,ja5,ja6,jb1,jb2,jb3,jb4,jb5,jb6,jb7,jb8,jb9,jb10,jb11,jc):
jaco.append(jac)
return np.array(jaco)
def Cazacu_Barlat2DBasis(a1,a2,a3,a4,b1,b2,b3,b4,b5,b10,c,
sigma0,sigmas, Jac = False):
'''
residuum of the Cazacu–Barlat (CZ) yield criterion for plain stress
residuum of the 2D Cazacu–Barlat (CZ) yield criterion for plain stress
'''
s11 = sigmas[0]; s22 = sigmas[1]; s12 = sigmas[3]
s1_2, s2_2 = s11**2, s22**2
s1_3, s2_3 = s11*s1_2, s22*s2_2
s12_2 = s12**2
J20 = ( (a2+a3)*s11**2 + (a1+a3)*s22**2 - 2.0*a3*s11*s22 )/6.0 + a6*s12**2
J20 = ( a1*(s11-s22)**2 + a2*s2_2 + a3*s1_2 )/6.0 + a4*s12_2
J30 = ( (b1+b2)*s1_3 + (b3+b4)*s2_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)/18.0
r = f0**(1.0/6.0)*(3.0/sigma0)
if not Jac:
return (r - 1.0).ravel()
else:
drdf = r/f0/108.0
dj2 = drdf*3.0*J20**2.0
dj3 = -drdf*2.0*J30*c
jc = -drdf*J30**2
ja1,ja2,ja3,ja4 = dj2*(s11-s22)**2/6.0, dj2*s2_2/6.0, dj2*s1_2/6.0, dj2*s12_2
jb1, jb2 = s1_3/27.0 - s1_2*s22/9.0, s1_3/27.0
jb4, jb3 = s2_3/27.0 - s2_2*s11/9.0, s2_3/27.0
jb5, jb10= -s12_2*(s11 - s22)/3.0, s12_2*s11*2.0/3.0
jaco = []
for jac in zip(ja1,ja2,ja3,ja4,jb1,jb2,jb3,jb4,jb5,jb10,jc):
jaco.append(jac)
return np.array(jaco)
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 DruckerBasis(sigma0, C_D, p, sigmas, Jac=False, nParas=2):
s11 = sigmas[0]; s22 = sigmas[1]; s33 = sigmas[2]
@ -721,19 +789,19 @@ fittingCriteria = {
'error': 'The standard deviation errors are: '
},
'Cazacu_Barlat2D':{'func' : Cazacu_Barlat2D,
'num' : 12,'err':np.inf,
'num' : 11,'err':np.inf,
'name' : 'Cazacu Barlat for plain stress',
'paras': 'Initial yield stress, a1,a2,a3,a6; b1,b2,b3,b4,b5,b10; c:',
'paras': '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',
\n 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,
'num' : 18,'err':np.inf,
'name' : 'Cazacu Barlat',
'paras': 'Initial yield stress, a1,a2,a3,a4,a5,a6; b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11; c:',
'paras': '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',
\n 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: '
},
'yld200418p' :{'func' : Yld200418p,
@ -920,7 +988,7 @@ def doSim(delay,thread):
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
dstrain= np.array(table.data[line,10:] - table.data[line-1,10:])
dstrain= np.array(table.data[line,10:] - table.data[line-1,10:]).reshape(3,3)
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