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re-write Karafillis-Boyce yield criterion, the old version is actually the generalized Karafillis-Boyce yield criterion, i.e., Born-Besson yield criterion, which has three exponents, it seems unstable. Now retreat to the original Karafillis-Boyce yield criterion (Karafillis, Boyce 1993), which has only one exponents.

This commit is contained in:
Haiming Zhang 2015-05-04 15:00:02 +00:00
parent 1e6c4fa988
commit f5ccc37125
1 changed files with 36 additions and 41 deletions
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77
processing/misc/yieldSurface.py
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@ -815,60 +815,55 @@ def Yld200418p(eqStress, paras, sigmas, mFix, criteria, dim, Jac=False):
def KarafillisBoyce(eqStress, paras, sigmas, mFix, criteria, dim, Jac=False): def KarafillisBoyce(eqStress, paras, sigmas, mFix, criteria, dim, Jac=False):
''' '''
Karafillis-Boyce yield criterion Karafillis-Boyce
the fitted parameters are the fitted parameters are
c11,c12,c13,c14,c15,c16,c21,c22,c23,c24,c25,c26,alpha,b1,b2,a for 3D c11,c12,c13,c14,c15,c16,c,m for 3D
c11,c12,c13,c14,c21,c22,c23,c24,alpha,b1,b2,a for plane stress c11,c12,c13,c14,c,m for plane stress
0<alpha<1, b1,b2,a are optional 0<c<1, m are optional
criteria are invalid input criteria are invalid input
''' '''
ks = lambda (s1,s2,s3,s4,s5,s6),(c1,c2,c3,c4,c5,c6): np.array( [ ks = lambda (s1,s2,s3,s4,s5,s6),(c1,c2,c3,c4,c5,c6): np.array( [
((c2+c3)*s1-c3*s2-c2*s3)/3.0, ((c3+c1)*s2-c3*s1-c1*s3)/3.0, ((c2+c3)*s1-c3*s2-c2*s3)/3.0, ((c3+c1)*s2-c3*s1-c1*s3)/3.0,
((c1+c2)*s3-c2*s1-c1*s2)/3.0, c4*s4, c5*s5, c6*s6 ]) ((c1+c2)*s3-c2*s1-c1*s2)/3.0, c4*s4, c5*s5, c6*s6 ])
if dim == 2: C1,C2,alpha = np.append(paras[0:4],[0.0,0.0]), np.append(paras[4:8],[0.0,0.0]), paras[8] if dim == 2: C1,c = np.append(paras[0:4],[0.0,0.0]), paras[4]
else: C1,C2,alpha = paras[0:6], paras[6:12], paras[12] else: C1,c = paras[0:6], paras[6]
if mFix[0]: b1=b2=a = mFix[1] if mFix[0]: m = mFix[1]
else: b1,b2,a = paras[len(paras)-3:len(paras)] else: m = paras[-1] # Karafillis-Boyce
p,q = ks(sigmas, C1), ks(sigmas, C2) p= ks(sigmas, C1)
plambdas,qlambdas = principalStress(p), principalStress(q) plambdas = principalStress(p)
b1i,b2i,ai,rb2 = 1.0/b1, 1.0/b2, 1.0/a, 3.0**b2/(2.0**b2+2.0) reci_m, m2, rm2, m1 = 1.0/m, m/2.0, 3.0**m/(2.0**(m-1.0)+1.0), m-1.0
difP = np.array([plambdas[1]-plambdas[2], plambdas[2]-plambdas[0], plambdas[0]-plambdas[1]]) difP = np.array([ plambdas[0]-plambdas[1], plambdas[1]-plambdas[2], plambdas[2]-plambdas[0] ])
difPs = difP**2; difPb1 = difPs**(b1/2.0-1.0) difPs = difP**2; difPm1 = difPs**(m2-1.0)
Qs = qlambdas**2 Ps = plambdas**2
phi10, phi20 = np.sum(difPs**(b1/2.0),axis = 0), np.sum(Qs**(b2/2.0),axis = 0) phi1, phi2 = np.sum(difPs**m2, axis = 0), np.sum(Ps**m2, axis = 0)
phi1, phi2 = (0.5*phi10)**b1i, (rb2*phi20)**b2i left = (1.0-c)*phi1+ c*rm2*phi2
Stress = alpha*phi1**a + (1.0-alpha)*phi2**a r = (0.5*left)**reci_m/eqStress
r = Stress**ai/eqStress
if not Jac: if not Jac:
return (r-1.0).ravel() return (r-1.0).ravel()
else: else:
drds = r*ai/Stress drdl, drdm = r*reci_m/left, -r*math_ln(0.5*left)*reci_m*reci_m
dsda = alpha*phi1**a*math_ln(phi1) + (1.0-alpha)*phi2**a*math_ln(phi2) dldm = (1.0-c)*np.sum(difPs**m2*math_ln(difPs), axis=0)*0.5 + \
rm2*c *np.sum( Ps**m2*math_ln(Ps), axis=0)*0.5 + \
rm2*c *phi2* ( np.log(3.0) - 2.0**m1/(2.0**m1 + 1.0)*np.log(2.0) )
dphi1dP = m*np.array([ difPm1[0]*difP[0] - difPm1[2]*difP[2],
difPm1[1]*difP[1] - difPm1[0]*difP[0],
difPm1[2]*difP[2] - difPm1[1]*difP[1] ])
dphi2dP = m*plambdas*Ps**(m2-1.0)
dphi1dP = phi1/phi10*np.array([ -difPb1[1]*difP[1]+difPb1[2]*difP[2],
difPb1[0]*difP[0]-difPb1[2]*difP[2], difPb1[1]*difP[1]-difPb1[0]*difP[0]])
dphi2dQ = phi2/phi20*Qs*qlambdas*(b2/2.0-1.0)
dPdc = principalStrs_Der(p, sigmas, dim, Karafillis=True) dPdc = principalStrs_Der(p, sigmas, dim, Karafillis=True)
dQdc = principalStrs_Der(q, sigmas, dim, Karafillis=True) dldP = (1.0-c)*dphi1dP + c*dphi2dP*rm2
dphi10db1 = np.sum(difPs**(b1/2.0)*math_ln(difPs), axis=0)*0.5
dphi20db2 = np.sum( Qs**(b2/2.0)*math_ln( Qs), axis=0)*0.5
drb2db2 = rb2*math_ln(3.0) - rb2*math_ln(2.0)/(1.0+2.0**(1.0-b2)) jm = drdl * dldm + drdm #drda*(-1.0/m/m)
dphi1db1 = phi1*math_ln(phi10)*(-b1i*b1i) + b1i*phi1/(0.5*phi10)* 0.5*dphi10db1 jc1 = drdl * np.sum([dldP[i]*dPdc[i] for i in xrange(3)],axis=0)
dphi2db2 = phi2*math_ln(phi20)*(-b2i*b2i) + b2i*phi2/(rb2*phi20)*(rb2*dphi20db2 + drb2db2*phi20) jc = drdl * (-phi1 + rm2*phi2)
ja = drds*dsda + r*math_ln(Stress)*(-1.0/a/a) #drda
jb1 = dphi1db1*(drds*a*phi1**(a-1)*alpha ) if mFix[0]: return np.vstack((jc1,jc)).T
jb2 = dphi2db2*(drds*a*phi2**(a-1)*(1.0-alpha)) else: return np.vstack((jc1,jc,jm)).T
jc1 = np.sum([dphi1dP[i]*dPdc[i] for i in xrange(3)],axis=0)*drds*a*phi1**(a-1.0)*alpha
jc2 = np.sum([dphi2dQ[i]*dQdc[i] for i in xrange(3)],axis=0)*drds*a*phi2**(a-1.0)*(1.0-alpha)
jalpha = drds * (phi1**a - phi2**a)
if mFix[0]: return np.vstack((jc1,jc2,jalpha)).T
else: return np.vstack((jc1,jc2,jalpha,jb1,jb2,ja)).T
fitCriteria = { fitCriteria = {
@ -1002,11 +997,11 @@ fitCriteria = {
'error': 'The standard deviation errors are: ' 'error': 'The standard deviation errors are: '
}, },
'karafillis' :{'func' : KarafillisBoyce, 'karafillis' :{'func' : KarafillisBoyce,
'nExpo': 3,'err':np.inf, 'nExpo': 1,'err':np.inf,
'dimen': 3, 'dimen': 3,
'bound': [ [(None,None)]*12+[(0.0,1.0)]+[(1.0,8.0)]*3, [(None,None)]*8+[(0.0,1.0)]+[(1.0,8.0)]*3], 'bound': [ [(None,None)]*6+[(0.0,1.0)]+[(1.0,8.0)], [(None,None)]*4+[(0.0,1.0)]+[(1.0,8.0)]],
'paras': [ 'c11,c12,c13,c14,c15,c16,c21,c22,c23,c24,c25,c26,alpha,b1,b2,a', \ 'paras': [ 'c11,c12,c13,c14,c15,c16,c,m', \
'c11,c12,c13,c14,c21,c22,c23,c24,alpha,b1,b2,a' ], 'c11,c12,c13,c14,c15,c16,c,m' ],
'text' : '\nCoefficients of Karafillis-Boyce yield criterion: ', 'text' : '\nCoefficients of Karafillis-Boyce yield criterion: ',
'error': 'The standard deviation errors are: ' 'error': 'The standard deviation errors are: '
}, },