PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,Userctx *user)
{
PetscErrorCode ierr;
SNES snes;
PetscScalar atmp = (PetscScalar) a;
PetscInt i,row;
PetscFunctionBegin;
user->t = t;
ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
ierr = ResidualJacobian(snes,X,A,B,user);CHKERRQ(ierr);
for (i=0;i < ngen;i++) {
row = 9*i;
ierr = MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);CHKERRQ(ierr);
row = 9*i+1;
ierr = MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);CHKERRQ(ierr);
row = 9*i+2;
ierr = MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);CHKERRQ(ierr);
row = 9*i+3;
ierr = MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);CHKERRQ(ierr);
row = 9*i+6;
ierr = MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);CHKERRQ(ierr);
row = 9*i+7;
ierr = MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);CHKERRQ(ierr);
row = 9*i+8;
ierr = MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode AlgJacobian(SNES snes,Vec X,Mat A,Mat B,void *ctx)
{
PetscErrorCode ierr;
Userctx *user=(Userctx*)ctx;
PetscFunctionBegin;
ierr = ResidualJacobian(snes,X,A,B,ctx);CHKERRQ(ierr);
ierr = MatSetOption(A,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE);CHKERRQ(ierr);
ierr = MatZeroRowsIS(A,user->is_diff,1.0,NULL,NULL);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
void DruckerPragerModel<EvalT, Traits>::
computeState(typename Traits::EvalData workset,
std::map<std::string, Teuchos::RCP<PHX::MDField<ScalarT> > > dep_fields,
std::map<std::string, Teuchos::RCP<PHX::MDField<ScalarT> > > eval_fields)
{
// extract dependent MDFields
PHX::MDField<ScalarT> strain = *dep_fields["Strain"];
PHX::MDField<ScalarT> poissons_ratio = *dep_fields["Poissons Ratio"];
PHX::MDField<ScalarT> elastic_modulus = *dep_fields["Elastic Modulus"];
// retrieve appropriate field name strings
std::string cauchy_string = (*field_name_map_)["Cauchy_Stress"];
std::string strain_string = (*field_name_map_)["Strain"];
std::string eqps_string = (*field_name_map_)["eqps"];
std::string friction_string = (*field_name_map_)["Friction_Parameter"];
// extract evaluated MDFields
PHX::MDField<ScalarT> stress = *eval_fields[cauchy_string];
PHX::MDField<ScalarT> eqps = *eval_fields[eqps_string];
PHX::MDField<ScalarT> friction = *eval_fields[friction_string];
PHX::MDField<ScalarT> tangent = *eval_fields["Material Tangent"];
// get State Variables
Albany::MDArray strainold = (*workset.stateArrayPtr)[strain_string + "_old"];
Albany::MDArray stressold = (*workset.stateArrayPtr)[cauchy_string + "_old"];
Albany::MDArray eqpsold = (*workset.stateArrayPtr)[eqps_string + "_old"];
Albany::MDArray frictionold = (*workset.stateArrayPtr)[friction_string + "_old"];
Intrepid::Tensor<ScalarT> id(Intrepid::eye<ScalarT>(num_dims_));
Intrepid::Tensor4<ScalarT> id1(Intrepid::identity_1<ScalarT>(num_dims_));
Intrepid::Tensor4<ScalarT> id2(Intrepid::identity_2<ScalarT>(num_dims_));
Intrepid::Tensor4<ScalarT> id3(Intrepid::identity_3<ScalarT>(num_dims_));
Intrepid::Tensor4<ScalarT> Celastic (num_dims_);
Intrepid::Tensor<ScalarT> sigma(num_dims_), sigmaN(num_dims_), s(num_dims_);
Intrepid::Tensor<ScalarT> epsilon(num_dims_), epsilonN(num_dims_);
Intrepid::Tensor<ScalarT> depsilon(num_dims_);
Intrepid::Tensor<ScalarT> nhat(num_dims_);
ScalarT lambda, mu, kappa;
ScalarT alpha, alphaN;
ScalarT p, q, ptr, qtr;
ScalarT eq, eqN, deq;
ScalarT snorm;
ScalarT Phi;
//local unknowns and residual vectors
std::vector<ScalarT> X(4);
std::vector<ScalarT> R(4);
std::vector<ScalarT> dRdX(16);
for (std::size_t cell(0); cell < workset.numCells; ++cell) {
for (std::size_t pt(0); pt < num_pts_; ++pt) {
lambda = ( elastic_modulus(cell,pt) * poissons_ratio(cell,pt) )
/ ( ( 1 + poissons_ratio(cell,pt) ) * ( 1 - 2 * poissons_ratio(cell,pt) ) );
mu = elastic_modulus(cell,pt) / ( 2 * ( 1 + poissons_ratio(cell,pt) ) );
kappa = lambda + 2.0 * mu / 3.0;
// 4-th order elasticity tensor
Celastic = lambda * id3 + mu * (id1 + id2);
// previous state (the fill doesn't work for state virable)
//sigmaN.fill( &stressold(cell,pt,0,0) );
//epsilonN.fill( &strainold(cell,pt,0,0) );
for (std::size_t i(0); i < num_dims_; ++i) {
for (std::size_t j(0); j < num_dims_; ++j) {
sigmaN(i, j) = stressold(cell, pt, i, j);
epsilonN(i, j) = strainold(cell, pt, i, j);
//epsilon(i,j) = strain(cell,pt,i,j);
}
}
epsilon.fill( &strain(cell,pt,0,0) );
depsilon = epsilon - epsilonN;
alphaN = frictionold(cell,pt);
eqN = eqpsold(cell,pt);
// trial state
sigma = sigmaN + Intrepid::dotdot(Celastic,depsilon);
ptr = Intrepid::trace(sigma) / 3.0;
s = sigma - ptr * id;
snorm = Intrepid::dotdot(s,s);
if(snorm > 0) snorm = std::sqrt(snorm);
qtr = sqrt(3.0/2.0) * snorm;
// unit deviatoric tensor
if (snorm > 0){
nhat = s / snorm;
} else{
nhat = id;
}
// check yielding
Phi = qtr + alphaN * ptr - Cf_;
alpha = alphaN;
p = ptr;
q = qtr;
deq = 0.0;
if(Phi > 1.0e-12) {// plastic yielding
// initialize local unknown vector
X[0] = ptr;
X[1] = qtr;
X[2] = alpha;
X[3] = deq;
LocalNonlinearSolver<EvalT, Traits> solver;
int iter = 0;
ScalarT norm_residual0(0.0), norm_residual(0.0), relative_residual(0.0);
// local N-R loop
while (true) {
ResidualJacobian(X, R, dRdX, ptr, qtr, eqN, mu, kappa);
norm_residual = 0.0;
for (int i = 0; i < 4; i++)
norm_residual += R[i] * R[i];
norm_residual = std::sqrt(norm_residual);
if (iter == 0)
norm_residual0 = norm_residual;
if (norm_residual0 != 0)
relative_residual = norm_residual / norm_residual0;
else
relative_residual = norm_residual0;
//std::cout << iter << " "
//<< Sacado::ScalarValue<ScalarT>::eval(norm_residual)
//<< " " << Sacado::ScalarValue<ScalarT>::eval(relative_residual)
//<< std::endl;
if (relative_residual < 1.0e-11 || norm_residual < 1.0e-11)
break;
if (iter > 20)
break;
// call local nonlinear solver
solver.solve(dRdX, X, R);
iter++;
} // end of local N-R loop
// compute sensitivity information w.r.t. system parameters
// and pack the sensitivity back to X
solver.computeFadInfo(dRdX, X, R);
// update
p = X[0];
q = X[1];
alpha = X[2];
deq = X[3];
}//end plastic yielding
eq = eqN + deq;
s = sqrt(2.0/3.0) * q * nhat;
sigma = s + p * id;
eqps(cell, pt) = eq;
friction(cell,pt) = alpha;
for (std::size_t i(0); i < num_dims_; ++i) {
for (std::size_t j(0); j < num_dims_; ++j) {
stress(cell,pt,i,j) = sigma(i, j);
}
}
}// end loop over pt
} // end loop over cell
}
