//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
}
//Jacobian for stress update algorithm
void
FiniteStrainRatePlasticMaterial::getJac(const RankTwoTensor & sig, const RankFourTensor & E_ijkl, Real flow_incr, Real yield_stress, RankFourTensor & dresid_dsig)
{
RankTwoTensor sig_dev, flow_tensor, flow_dirn,fij;
RankTwoTensor dfi_dft;
RankFourTensor 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;
dfi_dsig = flow_dirn.outerProduct(flow_dirn) * 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));
}
dfd_dsig = f1 * _deltaMixed - f2 * _deltaOuter - f3 * sig_dev.outerProduct(sig_dev); //d_flow_dirn/d_sig - 2nd part
//Jacobian
dresid_dsig = E_ijkl.invSymm() + dfd_dsig * flow_incr + dfi_dsig;
}
/*
*Solves for incremental plastic rate of deformation tensor and stress in unrotated frame.
*Input: Strain incrment, 4th order elasticity tensor, stress tensor in previous incrmenent and
*plastic rate of deformation tensor.
*/
void
FiniteStrainRatePlasticMaterial::returnMap(const RankTwoTensor & sig_old, const RankTwoTensor & delta_d, const RankFourTensor & E_ijkl, RankTwoTensor & dp, RankTwoTensor & sig)
{
RankTwoTensor sig_new, delta_dp, dpn;
RankTwoTensor flow_tensor, flow_dirn;
RankTwoTensor resid,ddsig;
RankFourTensor dr_dsig, dr_dsig_inv;
Real flow_incr, flow_incr_tmp;
Real err1, err3, tol1, tol3;
unsigned int iterisohard, iter, maxiterisohard = 20, maxiter = 50;
Real eqvpstrain;
Real yield_stress, yield_stress_prev;
tol1 = 1e-10;
tol3 = 1e-6;
iterisohard = 0;
eqvpstrain = std::pow(2.0/3.0,0.5) * dp.L2norm();
yield_stress = getYieldStress(eqvpstrain);
err3 = 1.1 * tol3;
while (err3 > tol3 && iterisohard < maxiterisohard) //Hardness update iteration
{
iterisohard++;
iter = 0;
delta_dp.zero();
sig_new = sig_old + E_ijkl * delta_d;
flow_incr=_ref_pe_rate*_dt * std::pow(macaulayBracket(getSigEqv(sig_new) / yield_stress - 1.0), _exponent);
getFlowTensor(sig_new, yield_stress, flow_tensor);
flow_dirn = flow_tensor;
resid = flow_dirn * flow_incr - delta_dp;
err1 = resid.L2norm();
while (err1 > tol1 && iter < maxiter) //Stress update iteration (hardness fixed)
{
iter++;
getJac(sig_new, E_ijkl, flow_incr, yield_stress, dr_dsig); //Jacobian
dr_dsig_inv = dr_dsig.invSymm();
ddsig = -dr_dsig_inv * resid;
sig_new += ddsig; //Update stress
delta_dp -= E_ijkl.invSymm() * ddsig; //Update plastic rate of deformation tensor
flow_incr_tmp = _ref_pe_rate * _dt * std::pow(macaulayBracket(getSigEqv(sig_new) / yield_stress - 1.0), _exponent);
if (flow_incr_tmp < 0.0) //negative flow increment not allowed
mooseError("Constitutive Error-Negative flow increment: Reduce time increment.");
flow_incr = flow_incr_tmp;
getFlowTensor(sig_new, yield_stress, flow_tensor);
flow_dirn = flow_tensor;
resid = flow_dirn * flow_incr - delta_dp; //Residual
err1=resid.L2norm();
}
if (iter>=maxiter)//Convergence failure
mooseError("Constitutive Error-Too many iterations: Reduce time increment.\n"); //Convergence failure
dpn = dp + delta_dp;
eqvpstrain = std::pow(2.0/3.0, 0.5) * dpn.L2norm();
yield_stress_prev = yield_stress;
yield_stress = getYieldStress(eqvpstrain);
err3 = std::abs(yield_stress-yield_stress_prev);
}
if (iterisohard>=maxiterisohard)
mooseError("Constitutive Error-Too many iterations in Hardness Update:Reduce time increment.\n"); //Convergence failure
dp = dpn; //Plastic rate of deformation tensor in unrotated configuration
sig = sig_new;
}
