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add Yld2000 yield criterion, Yld2000 works

This commit is contained in:
Haiming Zhang 2015-04-03 16:20:03 +00:00
parent 2b9964bba5
commit cd2a744db9
1 changed files with 58 additions and 4 deletions
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62
processing/misc/yieldSurface.py
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@ -421,8 +421,7 @@ def Barlat1989(eqStress, paras, sigmas, mFix, criteria, Jac=False):
'''
Barlat-Lian 1989 yield criteria PASS
the fitted parameters are:
Isotropic: sigma0, m
Anisotropic: a, c, h, p, m
Anisotropic: a, c, h, p, m; m is optional
'''
a, c, h, p = paras[0:4]
if mFix[0]: m = mFix[1]
@ -432,10 +431,10 @@ def Barlat1989(eqStress, paras, sigmas, mFix, criteria, Jac=False):
k1,k2 = (s11 + h*s22)/2.0, ((s11 - h*s22)**2/4.0 + (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)
r = (0.5*left)**(1.0/m)/eqStress
if not Jac:
return (r-eqStress).ravel()
return (r-1.0).ravel()
else:
dk1dh = 0.5*s22
dk2dh, dk2dp = 0.5/k2*(s11-h*s22)*(-s22), 0.5/k2*2.0*p*s12**2
@ -612,6 +611,53 @@ def BBC2005(eqStress, paras, sigmas, mFix, criteria, Jac=False):
if mFix[0]: return np.vstack(J).T
else : return np.vstack(J, dldk+dsBarde*dedk).T
def Yld2000(eqStress, paras, sigmas, mFix, criteria, Jac=False):
'''
C: c11,c22,c66 c12=c21=1.0 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]
sdev = np.array([sigmas[0]*2.0/3.0-sigmas[1]/3.0, sigmas[1]*2.0/3.0-sigmas[0]/3.0, sigmas[3]])
X = np.array([ C[0]*sdev[0], C[1]*sdev[1], C[2]*sdev[2] ])
Y = np.array([ D[0]*sdev[0]+ D[1]*sdev[1], D[2]*sdev[0]+ D[3]*sdev[1], D[4]*sdev[2] ])
def priStrs((sx,sy,sxy)):
temp = np.sqrt( (sx-sy)**2 + 4.0*sxy**2 )
return 0.5*(sx+sy + temp), 0.5*(sx+sy - temp)
(X1,X2), (Y1,Y2) = priStrs(X), priStrs(Y) # Principal values of X, Y
phi1, phi21, phi22 = ((X1-X2)**2)**(m/2.0), ((2.0*Y2+Y1)**2)**(m/2.0), ((2.0*Y1+Y2)**2)**(m/2.0)
left = phi1+phi21+phi22
r = (0.5*left)**(1.0/m)
if not Jac:
return (r/eqStress-1.0).ravel()
else:
def dPrincipalds((X1,X2,X12)):
# the derivative of principla with regards to stress
temp = 0.5/( (X1-X2)**2 + 4.0*X12**2 )**0.5
dP1dsi = 0.5*np.array([ 1.0+temp*2.0*(X1-X2), 1.0-temp*2.0*(X1-X2), temp*8.0*X12])
dP2dsi = 0.5*np.array([ 1.0-temp*2.0*(X1-X2), 1.0+temp*2.0*(X1-X2), -temp*8.0*X12])
return dP1dsi, dP2dsi
(dX1dXi, dX2dXi), (dY1dYi, dY2dYi) = dPrincipalds(X), dPrincipalds(Y)
dX1dCi, dX2dCi = dX1dXi*sdev,dX2dXi*sdev
s1,s2,s12 = sdev
dY1dDi, dY2dDi = np.array([dY1dYi[0]*s1, dY1dYi[0]*s2, dY1dYi[1]*s1, dY1dYi[1]*s2, dY1dYi[2]*s12]), \
np.array([dY2dYi[0]*s1, dY2dYi[0]*s2, dY2dYi[1]*s1, dY2dYi[1]*s2, dY2dYi[2]*s12])
dldX1, dldX2 = phi1* m/(X1-X2), phi1*m/(X2-X1)
dldY1, dldY2 = phi21*m/(2.0*Y2+Y1) + 2.0*phi22*m/(2.0*Y1+Y2), \
phi22*m/(2.0*Y1+Y2) + 2.0*phi21*m/(2.0*Y2+Y1)
drdl, drdm = r/m/left, r*math_ln(0.5*left)/(-m*m)
dldm = ( phi1*math_ln((X1-X2)**2) + phi21*math_ln((2.0*Y2+Y1)**2) + phi22*math_ln((2.0*Y1+Y2)**2) )*0.5
jC,jD= drdl*(dldX1*dX1dCi + dldX2*dX2dCi), drdl*(dldY1*dY1dDi + dldY2*dY2dDi)
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, Jac=False):
'''
Yld2004-18p yield criterion
@ -820,6 +866,14 @@ fitCriteria = {
\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: '
},
'yld2000' :{'func' : Yld2000,
'nExpo': 1,'err':np.inf,
'bound': [(None,None)]*8+[(1,8.0)],
'paras': 'c11,c12,c21,c22,c66,d11,d12,d21,d22,d66,m:',
'text' : '\nCoefficients of Yld2000-2D yield criterion: \
\n c11,c12,c21,c22,c66,d11,d12,d21,d22,d66,m:\n',
'error': 'The standard deviation errors are: '
},
'yld200418p' :{'func' : Yld200418p,
'nExpo': 1,'err':np.inf,
'bound': [(None,None)]*18+[(0.0,12.0)],