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fix bugs of barlat1989, barlat1991

This commit is contained in:
Haiming Zhang 2015-05-04 14:52:33 +00:00
parent ce0675f359
commit e0e7bb7a24
1 changed files with 26 additions and 21 deletions
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47
processing/misc/yieldSurface.py
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@ -124,11 +124,11 @@ def principalStrs_Der(p, (s1, s2, s3, s4, s5, s6), dim, Karafillis=False):
[p[1]*p[2]-p[4]**2, p[2]*p[0]-p[5]**2, p[0]*p[1]-p[3]**2, [p[1]*p[2]-p[4]**2, p[2]*p[0]-p[5]**2, p[0]*p[1]-p[3]**2,
-2.0*p[3]*p[2]+2.0*p[4]*p[5], -2.0*p[4]*p[0]+2.0*p[5]*p[3], -2.0*p[5]*p[1]+2.0*p[3]*p[4]] ]) -2.0*p[3]*p[2]+2.0*p[4]*p[5], -2.0*p[4]*p[0]+2.0*p[5]*p[3], -2.0*p[5]*p[1]+2.0*p[3]*p[4]] ])
if Karafillis: if Karafillis:
dpdc = np.array([[zero,s2-s3,s3-s2], [s1-s3,zero,s3-s1], [s1-s2,s2-s1,zero]]) dpdc = np.array([[zero,s1-s3,s1-s2], [s2-s3,zero,s2-s1], [s3-s2,s3-s1,zero]])/3.0
dSdp = np.array([np.dot(dSdI[:,:,i],dIdp[:,:,i]).T for i in xrange(num)]).T dSdp = np.array([np.dot(dSdI[:,:,i],dIdp[:,:,i]).T for i in xrange(num)]).T
if dim == 2: temp = np.vstack([dSdp[:,3]*s4]).T.reshape(num,1,3).T if dim == 2: temp = np.vstack([dSdp[:,3]*s4]).T.reshape(num,1,3).T
else: temp = np.vstack([dSdp[:,3]*s4,dSdp[:,4]*s5,dSdp[:,5]*s6]).T.reshape(num,3,3).T else: temp = np.vstack([dSdp[:,3]*s4,dSdp[:,4]*s5,dSdp[:,5]*s6]).T.reshape(num,3,3).T
return np.concatenate((np.array([np.dot(dSdp[:,0:3,i], dpdc[:,:,i].T).T/3.0 for i in xrange(num)]).T, return np.concatenate((np.array([np.dot(dSdp[:,0:3,i], dpdc[:,:,i]).T for i in xrange(num)]).T,
temp), axis=1) temp), axis=1)
else: else:
if dim == 2: if dim == 2:
@ -482,12 +482,13 @@ def Barlat1989(eqStress, paras, sigmas, mFix, criteria, dim, Jac=False):
''' '''
Barlat-Lian 1989 yield criteria Barlat-Lian 1989 yield criteria
the fitted parameters are: the fitted parameters are:
Anisotropic: a, c, h, p, m; m is optional Anisotropic: a, h, p, m; m is optional
''' '''
a, c, h, p = paras[0:4] a, h, p = paras[0:3]
if mFix[0]: m = mFix[1] if mFix[0]: m = mFix[1]
else: m = paras[-1] else: m = paras[-1]
c = 2.0-a
s11,s22,s12 = sigmas[0], sigmas[1], sigmas[3] s11,s22,s12 = sigmas[0], sigmas[1], sigmas[3]
k1,k2 = 0.5*(s11 + h*s22), (0.25*(s11 - h*s22)**2 + (p*s12)**2)**0.5 k1,k2 = 0.5*(s11 + h*s22), (0.25*(s11 - h*s22)**2 + (p*s12)**2)**0.5
fs = np.array([ (k1+k2)**2, (k1-k2)**2, 4.0*k2**2 ]); fm = fs**(m/2.0) fs = np.array([ (k1+k2)**2, (k1-k2)**2, 4.0*k2**2 ]); fm = fs**(m/2.0)
@ -505,7 +506,7 @@ def Barlat1989(eqStress, paras, sigmas, mFix, criteria, dim, Jac=False):
drdl, drdm = r/m/left, r*math_ln(0.5*left)*(-1.0/m/m) drdl, drdm = r/m/left, r*math_ln(0.5*left)*(-1.0/m/m)
dldm = np.dot(np.array([a,a,c]),fm*math_ln(fs))*0.5 dldm = np.dot(np.array([a,a,c]),fm*math_ln(fs))*0.5
ja,jc = drdl*dlda, drdl*dldc ja = drdl*dlda
jh,jp = drdl*(dldk1*dk1dh + dldk2*dk2dh), drdl*dldk2*dk2dp jh,jp = drdl*(dldk1*dk1dh + dldk2*dk2dh), drdl*dldk2*dk2dp
jm = drdl*dldm + drdm jm = drdl*dldm + drdm
@ -516,12 +517,10 @@ def Barlat1991(eqStress, paras, sigmas, mFix, criteria, dim, Jac=False):
''' '''
Barlat 1991 criteria Barlat 1991 criteria
the fitted parameters are: the fitted parameters are:
Isotropic: sigma0, m
Anisotropic: a, b, c, f, g, h, m for 3D Anisotropic: a, b, c, f, g, h, m for 3D
a, b, c, h, m for plane stress a, b, c, h, m for plane stress
m is optional m is optional
''' '''
sigma0 = eqStress
if dim == 2: coeff = paras[0:4] # plane stress if dim == 2: coeff = paras[0:4] # plane stress
else: coeff = paras[0:6] # general case else: coeff = paras[0:6] # general case
if mFix[0]: m = mFix[1] if mFix[0]: m = mFix[1]
@ -530,7 +529,7 @@ def Barlat1991(eqStress, paras, sigmas, mFix, criteria, dim, Jac=False):
cos = np.cos; sin = np.sin; pi = np.pi; abs = np.abs cos = np.cos; sin = np.sin; pi = np.pi; abs = np.abs
s11,s22,s33,s12,s23,s31 = sigmas s11,s22,s33,s12,s23,s31 = sigmas
if dim == 2: if dim == 2:
dXdx = np.array([s22,s33-s11,s11-s22,s12]) dXdx = np.array([s22,-s11,s11-s22,s12])
A,B,C,H = np.array(coeff)[:,None]*dXdx; F=G=0.0 A,B,C,H = np.array(coeff)[:,None]*dXdx; F=G=0.0
else: else:
dXdx = np.array([s22-s33,s33-s11,s11-s22,s23,s31,s12]) dXdx = np.array([s22-s33,s33-s11,s11-s22,s23,s31,s12])
@ -541,31 +540,37 @@ def Barlat1991(eqStress, paras, sigmas, mFix, criteria, dim, Jac=False):
phi1 = np.arccos(I3/I2**1.5)/3.0 + pi/6.0; absc1 = 2.0*abs(cos(phi1)) phi1 = np.arccos(I3/I2**1.5)/3.0 + pi/6.0; absc1 = 2.0*abs(cos(phi1))
phi2 = phi1 + pi/3.0; absc2 = 2.0*abs(cos(phi2)) phi2 = phi1 + pi/3.0; absc2 = 2.0*abs(cos(phi2))
phi3 = phi2 + pi/3.0; absc3 = 2.0*abs(cos(phi3)) phi3 = phi2 + pi/3.0; absc3 = 2.0*abs(cos(phi3))
left = ( absc1**m + absc2**m + absc3**m )/2.0 left = ( absc1**m + absc2**m + absc3**m )
r = left**(1.0/m)*np.sqrt(3.0*I2)/sigma0 r = (0.5*left)**(1.0/m)*np.sqrt(3.0*I2)/eqStress
if not Jac: if not Jac:
return (r - 1.0).ravel() return (r - 1.0).ravel()
else: else:
dfdl = r/left/m dfdl = r/left/m
jm = r*math_ln(left)*(-1.0/m/m) + dfdl*0.5*( jm = r*math_ln(0.5*left)*(-1.0/m/m) + dfdl*0.5*(
absc1**m*math_ln(absc1) + absc2**m*math_ln(absc2) + absc3**m*math_ln(absc3) ) absc1**m*math_ln(absc1) + absc2**m*math_ln(absc2) + absc3**m*math_ln(absc3) )
da,db,dc = (2.0*A-B-C)/18.0, (2.0*B-C-A)/18.0, (2.0*C-A-B)/18.0 da,db,dc = (2.0*A-B-C)/18.0, (2.0*B-C-A)/18.0, (2.0*C-A-B)/18.0
if dim == 2: if dim == 2:
dI2dx = np.array([da, db, dc, H])/1.5*dXdx dI2dx = np.array([da, db, dc, H])/1.5*dXdx
dI3dx = np.array([da*(B-C) + (H**2-G**2)/2.0, db*(C-A) + (F**2-H**2)/2.0, dc*(A-B) + (G**2-F**2)/2.0, dI3dx = np.array([ da*(B-C) + (H**2-G**2)/2.0,
(G*F + (A-B))*H])/3.0*dXdx db*(C-A) + (F**2-H**2)/2.0,
dc*(A-B) + (G**2-F**2)/2.0,
(G*F + (A-B))*H ])/3.0*dXdx
else: else:
dI2dx = np.array([da, db, dc, F,G,H])/1.5*dXdx dI2dx = np.array([da, db, dc, F,G,H])/1.5*dXdx
dI3dx = np.array([da*(B-C) + (H**2-G**2)/2.0, db*(C-A) + (F**2-H**2)/2.0, dc*(A-B) + (G**2-F**2)/2.0, dI3dx = np.array([ da*(B-C) + (H**2-G**2)/2.0,
(H*G + (B-C))*F, (F*H + (C-A))*G, (G*F + (A-B))*H])/3.0*dXdx db*(C-A) + (F**2-H**2)/2.0,
darccos = -(1.0 - I3**2/I2**3)**(-0.5) dc*(A-B) + (G**2-F**2)/2.0,
(H*G*3.0 + (B-C))*F,
(F*H*3.0 + (C-A))*G,
(G*F*3.0 + (A-B))*H ])/3.0*dXdx
darccos = -1.0/np.sqrt(1.0 - I3**2/I2**3)
dfdcos = lambda phi : dfdl*m*(2.0*abs(cos(phi)))**(m-1.0)*np.sign(cos(phi))*(-sin(phi)/1.5)
dfdc = dfdl*0.5*m
dfdcos = lambda phi : dfdc*(2.0*abs(cos(phi)))**(1.0/m-1.0)*np.sign(cos(phi))*(-sin(phi)/1.5)
dfdthe= (dfdcos(phi1) + dfdcos(phi2) + dfdcos(phi3)) dfdthe= (dfdcos(phi1) + dfdcos(phi2) + dfdcos(phi3))
dfdI2, dfdI3 = dfdthe*darccos*I3*(-1.5)*I2**(-2.5), dfdthe*darccos*I2**(-1.5) dfdI2, dfdI3 = dfdthe*darccos*I3*(-1.5)*I2**(-2.5)+r/2.0/I2, dfdthe*darccos*I2**(-1.5)
if mFix[0]: return np.vstack((dfdI2*dI2dx + dfdI3*dI3dx)).T if mFix[0]: return np.vstack((dfdI2*dI2dx + dfdI3*dI3dx)).T
else: return np.vstack((dfdI2*dI2dx + dfdI3*dI3dx, jm)).T else: return np.vstack((dfdI2*dI2dx + dfdI3*dI3dx, jm)).T
@ -595,7 +600,7 @@ def BBC2000(eqStress, paras, sigmas, mFix, criteria, dim, Jac=False):
if not Jac: if not Jac:
return (r - 1.0).ravel() return (r - 1.0).ravel()
else: else:
drdl,drdk = r/left/k2, r*math_ln(left)*(-1.0/k2/k)*eqStress ##****eqStress should be cut drdl,drdk = r/left/k2, r*math_ln(left)*(-1.0/k2/k)
dldl1,dldl2,dldl3 = a*k2*(l1s**k1)*l1, a*k2*(l2s**k1)*l2, (1-a)*k2*(l3s**k1)*l3 dldl1,dldl2,dldl3 = a*k2*(l1s**k1)*l1, a*k2*(l2s**k1)*l2, (1-a)*k2*(l3s**k1)*l3
dldGama, dldPsi = (dldl1 + dldl2)*b, (dldl1 - dldl2 + 2.0*dldl3)*c dldGama, dldPsi = (dldl1 + dldl2)*b, (dldl1 - dldl2 + 2.0*dldl3)*c
temp = (P*s11 + Q*s22)/Psi temp = (P*s11 + Q*s22)/Psi
@ -636,7 +641,7 @@ def BBC2003(eqStress, paras, sigmas, mFix, criteria, dim, Jac=False):
if not Jac: if not Jac:
return (r - 1.0).ravel() return (r - 1.0).ravel()
else: else:
drdl,drdk = r/left/k2, r*math_ln(left)*(-1.0/k2/k)*eqStress #*** drdl,drdk = r/left/k2, r*math_ln(left)*(-1.0/k2/k)
dldl1,dldl2,dldl3 = a*k2*(l1s**k1)*l1, a*k2*(l2s**k1)*l2, (1-a)*k2*(l3s**k1)*l3 dldl1,dldl2,dldl3 = a*k2*(l1s**k1)*l1, a*k2*(l2s**k1)*l2, (1-a)*k2*(l3s**k1)*l3
dldGama, dldPsi, dldLambda = dldl1+dldl2, dldl1-dldl2, 2.0*dldl3 dldGama, dldPsi, dldLambda = dldl1+dldl2, dldl1-dldl2, 2.0*dldl3