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