Real
FiniteStrainPlasticMaterial::dyieldFunction_dinternal(const Real equivalent_plastic_strain)
{
return -getdYieldStressdPlasticStrain(equivalent_plastic_strain);
}
/*
*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 gradient.
*/
void
FiniteStrainPlasticMaterial::solveStressResid(RankTwoTensor sig_old,RankTwoTensor delta_d,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 /*sig_eqv,*/flow_incr,f,dflow_incr;
Real err1,err2,err3;
unsigned int plastic_flag;
unsigned int iter,maxiter=100;
Real eqvpstrain,eqvpstrain_old,deqvpstrain,fq,rep;
Real yield_stress;
sig_new=sig_old+E_ijkl*delta_d;
eqvpstrain_old=eqvpstrain=_eqv_plastic_strain_old[_qp];
yield_stress=getYieldStress(eqvpstrain);
plastic_flag=isPlastic(sig_new,yield_stress);//Check of plasticity for elastic predictor
if (plastic_flag==1)
{
iter=0;
dflow_incr=0.0;
flow_incr=0.0;
delta_dp.zero();
deqvpstrain=0.0;
sig_new=sig_old+E_ijkl*delta_d;
getFlowTensor(sig_new,&flow_tensor);
flow_dirn=flow_tensor;
resid=flow_dirn*flow_incr-delta_dp;//Residual 1 - refer Hughes Simo
f=getSigEqv(sig_new)-yield_stress;//Residual 2 - f=0
rep=-eqvpstrain+eqvpstrain_old+flow_incr;//Residual 3 rep=0
err1=resid.L2norm();
err2=fabs(f);
err3=fabs(rep);
while ((err1 > _rtol || err2 > _ftol || err3 > _eptol) && iter < maxiter )//Stress update iteration (hardness fixed)
{
iter++;
getJac(sig_new,E_ijkl,flow_incr,&dr_dsig);//Jacobian
dr_dsig_inv=dr_dsig.invSymm();
fq=getdYieldStressdPlasticStrain(eqvpstrain);
dflow_incr=(f-flow_tensor.doubleContraction(dr_dsig_inv*resid)+fq*rep)/(flow_tensor.doubleContraction(dr_dsig_inv*flow_dirn)-fq);
ddsig=dr_dsig_inv*(-resid-flow_dirn*dflow_incr);
flow_incr+=dflow_incr;
delta_dp-=E_ijkl.invSymm()*ddsig;
sig_new+=ddsig;
deqvpstrain=rep+dflow_incr;
eqvpstrain+=deqvpstrain;
getFlowTensor(sig_new,&flow_tensor);
flow_dirn=flow_tensor;
resid=flow_dirn*flow_incr-delta_dp;
f=getSigEqv(sig_new)-yield_stress;
rep=-eqvpstrain+eqvpstrain_old+flow_incr;
err1=resid.L2norm();
err2=fabs(f);
err3=fabs(rep);
}
if (iter>=maxiter)
{
_stress[_qp](2,2)=1e6;
printf("Constitutive Error: Too many iterations %f %f %f \n",err1,err2, err3);//Convergence failure
return;
}
dpn=*dp+delta_dp;
}
*dp=dpn;//Plastic strain in unrotated configuration
*sig=sig_new;
_eqv_plastic_strain[_qp]=eqvpstrain;
}
