//Jacobian for stress update algorithm
void
FiniteStrainPlasticMaterial::getJac(RankTwoTensor sig, RankFourTensor E_ijkl, Real flow_incr, RankFourTensor* dresid_dsig)
{
RankTwoTensor sig_dev, flow_tensor, flow_dirn;
RankTwoTensor dfi_dft,dfi_dsig;
RankFourTensor dft_dsig,dfd_dft,dfd_dsig;
Real sig_eqv/*,val*/;
Real f1,f2,f3;
RankFourTensor temp;
sig_dev=getSigDev(sig);
sig_eqv=getSigEqv(sig);
getFlowTensor(sig,&flow_tensor);
flow_dirn=flow_tensor;
f1=3.0/(2.0*sig_eqv);
f2=f1/3.0;
f3=9.0/(4.0*pow(sig_eqv,3.0));
for (int i=0;i<3;i++)
for (int j=0;j<3;j++)
for (int k=0;k<3;k++)
for (int l=0;l<3;l++)
dft_dsig(i,j,k,l)=f1*deltaFunc(i,k)*deltaFunc(j,l)-f2*deltaFunc(i,j)*deltaFunc(k,l)-f3*sig_dev(i,j)*sig_dev(k,l);
dfd_dsig=dft_dsig;
*dresid_dsig=E_ijkl.invSymm()+dfd_dsig*flow_incr;
}
//Jacobian for stress update algorithm
void
FiniteStrainRatePlasticMaterial::getJac(const RankTwoTensor & sig, const RankFourTensor & E_ijkl, Real flow_incr, Real yield_stress, RankFourTensor & dresid_dsig)
{
unsigned i, j, k ,l;
RankTwoTensor sig_dev, flow_tensor, flow_dirn,fij;
RankTwoTensor dfi_dft;
RankFourTensor dft_dsig, dfd_dft, dfd_dsig, dfi_dsig;
Real sig_eqv;
Real f1, f2, f3;
Real dfi_dseqv;
sig_dev = sig.deviatoric();
sig_eqv = getSigEqv(sig);
getFlowTensor(sig, yield_stress, flow_tensor);
flow_dirn = flow_tensor;
dfi_dseqv = _ref_pe_rate * _dt * _exponent * std::pow(macaulayBracket(sig_eqv / yield_stress - 1.0), _exponent - 1.0) / yield_stress;
for (i = 0; i < 3; ++i)
for (j = 0; j < 3; ++j)
for (k = 0; k < 3; ++k)
for (l = 0; l < 3; ++l)
dfi_dsig(i,j,k,l) = flow_dirn(i,j) * flow_dirn(k,l) * dfi_dseqv; //d_flow_increment/d_sig
f1 = 0.0;
f2 = 0.0;
f3 = 0.0;
if (sig_eqv > 1e-8)
{
f1 = 3.0 / (2.0 * sig_eqv);
f2 = f1 / 3.0;
f3 = 9.0 / (4.0 * std::pow(sig_eqv, 3.0));
}
for (i = 0; i < 3; ++i)
for (j = 0; j < 3; ++j)
for (k = 0; k < 3; ++k)
for (l = 0; l < 3; ++l)
dft_dsig(i,j,k,l) = f1 * deltaFunc(i,k) * deltaFunc(j,l) - f2 * deltaFunc(i,j) * deltaFunc(k,l) - f3 * sig_dev(i,j) * sig_dev(k,l); //d_flow_dirn/d_sig - 2nd part
dfd_dsig = dft_dsig; //d_flow_dirn/d_sig
dresid_dsig = E_ijkl.invSymm() + dfd_dsig * flow_incr + dfi_dsig; //Jacobian
}