add the calculation of Jacobian of isotropic and anisotropic Barlat1991, shows better performance.
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Haiming Zhang
parent
e4874550dc
commit
69af205721
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@ -172,7 +172,7 @@ class Barlat1991iso(object):
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def fun(self, (sigma0, m), ydata, sigmas):
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return Barlat1991Basis(sigma0, 1.0,1.0,1.0,1.0,1.0,1.0, m, sigmas)
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def jac(self, (sigma0, m), ydata, sigmas):
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pass
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return Barlat1991Basis(sigma0, 1.0,1.0,1.0,1.0,1.0,1.0, m, sigmas, Jac=True, nParas=2)
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class Barlat1991aniso(object):
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'''
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@ -181,7 +181,7 @@ class Barlat1991aniso(object):
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def fun(self, (sigma0, a,b,c,f,g,h, m), ydata, sigmas):
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return Barlat1991Basis(sigma0, a,b,c,f,g,h, m, sigmas)
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def jac(self, (sigma0, a,b,c,f,g,h, m), ydata, sigmas):
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pass
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return Barlat1991Basis(sigma0, a,b,c,f,g,h, m, sigmas, Jac=True, nParas=8)
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def Cazacu_Barlat3D(sigma0,a1,a2,a3,a4,a5,a6, b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11, c,
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ydata, sigmas):
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@ -303,37 +303,71 @@ def HosfordBasis(sigma0, F,G,H, a, sigmas, Jac=False, nParas=1):
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for a,b,c,d,e in zip(j1, j2,j3,j4,j5): jaco.append([a,b,c,d,e])
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return np.array(jaco)
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def Barlat1991Basis(sigma0, a, b, c, f, g, h, order, sigmas):
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def Barlat1991Basis(sigma0, a, b, c, f, g, h, m, sigmas, Jac=False, nParas=2):
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'''
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residuum of Barlat 1997 yield criterion
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'''
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cos = np.cos; pi = np.pi; abs = np.abs
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A = a*(sigmas[1] - sigmas[2])
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B = b*(sigmas[2] - sigmas[0])
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C = c*(sigmas[0] - sigmas[1])
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F = f* sigmas[4]
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G = g* sigmas[5]
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H = h* sigmas[3]
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cos = np.cos; sin = np.sin; pi = np.pi; abs = np.abs
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dAda = sigmas[1] - sigmas[2]; A = a*dAda
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dBdb = sigmas[2] - sigmas[0]; B = b*dBdb
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dCdc = sigmas[0] - sigmas[1]; C = c*dCdc
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dFdf = sigmas[4]; F = f*dFdf
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dGdg = sigmas[5]; G = g*dGdg
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dHdh = sigmas[3]; H = h*dHdh
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I2 = (F*F + G*G + H*H)/3.0 + ((A-C)**2+(C-B)**2+(B-A)**2)/54.0
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I3 = (C-B)*(A-C) * (B-A)/54.0 + F*G*H - \
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( (C-B)*F*F + (A-C)*G*G + (B-A)*H*H )/6.0
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I3 = (C-B)*(A-C)*(B-A)/54.0 + F*G*H - \
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( (C-B)*F*F + (A-C)*G*G + (B-A)*H*H )/6.0
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theta = np.arccos(I3/I2**1.5)
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Phi = np.sqrt(3.0*I2)* (
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(abs(2.0*cos((2.0*theta + pi)/6.0)))**order +
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(abs(2.0*cos((2.0*theta + pi*3.0)/6.0)))**order +
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(abs(2.0*cos(( 2.0*theta + pi*5.0)/6.0)))**order
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)**(1.0/order)
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# r = Phi/2.0**(1.0/order) - sigma0
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r = Phi/2.0**(1.0/order)/sigma0 - 1.0
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# Phi = (3.0*I2)**(order/2.0) * (
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# (abs(2.0*cos((2.0*theta + pi)/6.0))) **order +
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# (abs(2.0*cos((2.0*theta + pi*3.0)/6.0)))**order +
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# (abs(2.0*cos((2.0*theta + pi*5.0)/6.0)))**order
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# )
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# r = (Phi - 2.0*sigma0**order)**(1.0/order)
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phi1 = (2.0*theta + pi)/6.0; cos1 = 2.0*cos(phi1); absc1 = abs(cos1)
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phi2 = (2.0*theta + pi*3.0)/6.0; cos2 = 2.0*cos(phi2); absc2 = abs(cos2)
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phi3 = (2.0*theta + pi*5.0)/6.0; cos3 = 2.0*cos(phi3); absc3 = abs(cos3)
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ratio= np.sqrt(3.0*I2)/sigma0; expo = 1.0/m
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left = ( absc1**m + absc2**m + absc3**m )/2.0
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leftNorm = left**expo
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r = ratio*leftNorm - 1.0
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if not Jac:
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return r.ravel()
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else:
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ln = lambda x : np.log(x + 1.0e-32)
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jaco = []
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dfdl = expo*leftNorm/left
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js = -(r + 1.0)/sigma0
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jm = (r+1.0)*ln(left)*(-expo*expo) + ratio*dfdl*0.5*(
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absc1**m*ln(absc1) + absc2**m*ln(absc2) + absc3**m*ln(absc3) )
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if nParas == 2:
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for j1,j2 in zip(js, jm): jaco.append([j1,j2])
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return np.array(jaco)
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else:
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dI2da = (2.0*A-B-C)*dAda/27.0; dI2df = 2.0*F*dFdf/3.0
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dI2db = (2.0*B-C-A)*dBdb/27.0; dI2dg = 2.0*G*dGdg/3.0
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dI2dc = (2.0*C-A-B)*dCdc/27.0; dI2dh = 2.0*H*dHdh/3.0
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dI3da = dI2da*(B-C)/2.0 + (H**2 - G**2)*dAda/6.0
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dI3db = dI2db*(C-A)/2.0 + (F**2 - H**2)*dBdb/6.0
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dI3dc = dI2dc*(A-B)/2.0 + (G**2 - F**2)*dCdc/6.0
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dI3df = ( (H*G + (B-C)) * F/3.0 )*dFdf
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dI3dg = ( (F*H + (C-A)) * G/3.0 )*dGdg
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dI3dh = ( (G*F + (A-B)) * H/3.0 )*dHdh
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darccos = -(1.0 - I3**2/I2**3)**(-0.5)
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dthedI2 = darccos*I3*(-1.5)*I2**(-2.5)
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dthedI3 = darccos*I2**(-1.5)
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dc1dthe = -sin(phi1)/3.0; dc2dthe = -sin(phi2)/3.0; dc3dthe = -sin(phi3)/3.0
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dfdc = ratio * dfdl * 0.5 * m
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dfdc1 = dfdc* absc1**(expo-1.0)*np.sign(cos1)
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dfdc2 = dfdc* absc2**(expo-1.0)*np.sign(cos2)
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dfdc3 = dfdc* absc3**(expo-1.0)*np.sign(cos3)
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dfdthe= (dfdc1*dc1dthe + dfdc2*dc2dthe + dfdc2*dc2dthe)*2.0
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dfdI2 = dfdthe*dthedI2; dfdI3 = dfdthe*dthedI3
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ja = dfdI2*dI2da + dfdI3*dI3da; jf = dfdI2*dI2df + dfdI3*dI3df
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jb = dfdI2*dI2db + dfdI3*dI3db; jg = dfdI2*dI2dg + dfdI3*dI3dg
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jc = dfdI2*dI2dc + dfdI3*dI3dc; jh = dfdI2*dI2dh + dfdI3*dI3dh
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for j1,j2,j3,j4,j5,j6,j7,j8 in zip(js,ja,jb,jc,jf,jg,jh,jm):
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jaco.append([j1,j2,j3,j4,j5,j6,j7,j8])
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return np.array(jaco)
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return r.ravel()
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fittingCriteria = {
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'tresca' :{'func' : Tresca,
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