void PoissonModel::set_lam(double x){Lam()->set(x);}
/* Take increments in strain and calculate new Particle: strains, rotation strain,
stresses, strain energy,
dvij are (gradient rates X time increment) to give deformation gradient change
For Axisymmetry: x->R, y->Z, z->theta, np==AXISYMMEtRIC_MPM, otherwise dvzz=0
This material tracks pressure and stores deviatoric stress only in particle stress tensor
*/
void ClampedNeohookean::MPMConstitutiveLaw(MPMBase *mptr,Matrix3 du,double delTime,int np,void *properties,
ResidualStrains *res,int historyOffset) const
{
// Update total deformation gradient, and calculate trial B
Tensor Btrial;
double detDF = IncrementDeformation(mptr,du,&Btrial,np);
// global J
double J = detDF * mptr->GetHistoryDble(J_History,historyOffset);
mptr->SetHistoryDble(J_History,J,historyOffset);
// convert Btrial to matrix to get eigenvalues and check for clamping
Matrix3 Belas(Btrial.xx,Btrial.xy,Btrial.xz,
Btrial.xy,Btrial.yy,Btrial.yz,
Btrial.xz,Btrial.yz,Btrial.zz);
if(np!=THREED_MPM) Belas.setIs2D(true);
// get Eigenvalues and Eigenvectors
Vector lam2 = Belas.Eigenvalues();
// clamp eigenvalues if needed
bool clamped = false;
if(lam2.x<lamMin2 || lam2.x>lamMax2 || lam2.y<lamMin2 || lam2.y>lamMax2 || lam2.z<lamMin2 || lam2.z>lamMax2)
clamped = true;
// Get Je and Jp, adjusting if clamped
double Je,Jp;
Matrix3 Ucol;
if(clamped)
{ // Find Belas = U.LAM.UT
Ucol = Belas.Eigenvectors(lam2);
// clamp values now
if(lam2.x<lamMin2)
lam2.x = lamMin2;
else if(lam2.x>lamMax2)
lam2.x = lamMax2;
if(lam2.y<lamMin2)
lam2.y = lamMin2;
else if(lam2.y>lamMax2)
lam2.y = lamMax2;
if(lam2.z<lamMin2)
lam2.z = lamMin2;
else if(lam2.z>lamMax2)
lam2.z = lamMax2;
Matrix3 UcolT = Ucol.Transpose();
Matrix3 Lam(lam2.x,0.,0.,lam2.y,lam2.z);
Matrix3 LamUcolT = Lam*UcolT;
Belas = Ucol*LamUcolT;
// get Je and Jp
Je = sqrt(lam2.x*lam2.y*lam2.z);
Jp = J/Je;
mptr->SetHistoryDble(JP_HISTORY,Jp,historyOffset);
}
else
{ Jp = mptr->GetHistoryDble(JP_HISTORY,historyOffset);
Je = J/Jp;
if(elasticModel==ELASTIC_DISNEY)
Ucol = Belas.Eigenvectors(lam2);
}
// store B elastic
Tensor *sp=mptr->GetStressTensor();
Tensor *B = mptr->GetAltStrainTensor();
B->xx = Belas(0,0);
B->yy = Belas(1,1);
B->zz = Belas(2,2);
B->xy = Belas(0,1);
if(np==THREED_MPM)
{ B->xz = Belas(0,2);
B->yz = Belas(1,2);
}
// change mechanical properties by hardening
double arg = exp(hardening*(1.-Jp));
double altGsp = pr.Gsp*arg;
double altLamesp = pr.Lamesp*arg;
// account for residual stresses
double dJres = GetIncrementalResJ(mptr,res);
double Jres = dJres*mptr->GetHistoryDble(J_History+1,historyOffset);
mptr->SetHistoryDble(J_History+1,Jres,historyOffset);
double resStretch = pow(Jres,1./3.);
double Jres23 = resStretch*resStretch;
// account for residual stresses relative to elastic J
double Jeff = Je/Jres;
// for incremental energy, store initial stress and pressure
Tensor *sporig=mptr->GetStressTensor();
Tensor st0 = *sporig;
double Pfinal,p0=mptr->GetPressure();
if(elasticModel==ELASTIC_DISNEY)
{ // Use model from Disney paper
// Get Cauchy stress/rho0
double sig[3][3];
double lam[3];
lam[0]=sqrt(lam2.x)/resStretch;
lam[1]=sqrt(lam2.y)/resStretch;
lam[2]=sqrt(lam2.z)/resStretch;
for(int i=0;i<3;i++)
{ for(int j=i;j<3;j++)
{ sig[i][j] = 0.;
for(int k=0;k<3;k++)
{ sig[i][j] += (2.*altGsp*lam[k]*(lam[k]-1)/Jeff + altLamesp*(Jeff-1))*Ucol(i,k)*Ucol(j,k);
}
}
}
// update pressure (*J to get Kirchoff pressure)
Pfinal = -J*(sig[0][0]+sig[1][1]+sig[2][2])/3.;
mptr->SetPressure(Pfinal);
// get and set deviatoric stress
// find eviatoric (Kirchoff stress)/rho0 = deviatoric (Cauchy stress)J/rho0
sp->xx = J*sig[0][0]+Pfinal;
sp->yy = J*sig[1][1]+Pfinal;
sp->zz = J*sig[2][2]+Pfinal;
sp->xy = J*sig[0][1];
if(np==THREED_MPM)
{ sp->xz = J*sig[0][2];
sp->yz = J*sig[1][2];
}
}
else
{ // Use standard neo-Hookean law
// update pressure (*J to get Kirchoff pressure)
Pfinal = -J*(GetVolumetricTerms(Jeff,altLamesp) + (altGsp/Jeff)*((B->xx+B->yy+B->zz)/(3.*Jres23) - 1.));
mptr->SetPressure(Pfinal);
// Account for density change in specific stress
// i.e.. Get (Kirchoff Stress)/rho0
double GJeff = J*resStretch*altGsp/Je; // = J*(Jres^(1/3) G/Je) to get Kirchoff
// find deviatoric (Kirchoff stress)/rho0 = deviatoric (Cauchy stress)J/rho0
double I1third = (B->xx+B->yy+B->zz)/3.;
sp->xx = GJeff*(B->xx-I1third);
sp->yy = GJeff*(B->yy-I1third);
sp->zz = GJeff*(B->zz-I1third);
sp->xy = GJeff*B->xy;
if(np==THREED_MPM)
{ sp->xz = GJeff*B->xz;
sp->yz = GJeff*B->yz;
}
}
// work and residual energies
double delV = 1. - 1./detDF; // total volume change
double avgP = 0.5*(p0+Pfinal);
double dilEnergy = -avgP*delV;
// incremental residual energy
double delVres = 1. - 1./dJres;
double resEnergy = -avgP*delVres;
// incremental work energy = shear energy
double shearEnergy = 0.5*((sp->xx+st0.xx)*du(0,0) + (sp->yy+st0.yy)*du(1,1) + (sp->zz+st0.zz)*du(2,2)+
(sp->xy+st0.xy)*(du(0,1)+du(1,0)));
if(np==THREED_MPM)
{ shearEnergy += 0.5*((sp->xz+st0.xz)*(du(0,2)+du(2,0)) + (sp->yz+st0.yz)*(du(1,2)+du(2,1)));
}
// strain energy
double dU = dilEnergy + shearEnergy;
mptr->AddWorkEnergyAndResidualEnergy(dU,resEnergy);
// thermodynamics heat and temperature
// Should find energy dissipated by plasticity and add in third term
IncrementHeatEnergy(mptr,res->dT,0.,0.);
}
double PoissonModel::lam()const{return Lam()->value();}
