void StVenantKirchhoffModel<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> def_grad = *dep_fields["F"];
PHX::MDField<ScalarT> J = *dep_fields["J"];
PHX::MDField<ScalarT> poissons_ratio = *dep_fields["Poissons Ratio"];
PHX::MDField<ScalarT> elastic_modulus = *dep_fields["Elastic Modulus"];
// extract evaluated MDFields
std::string cauchy = (*field_name_map_)["Cauchy_Stress"];
PHX::MDField<ScalarT> stress = *eval_fields[cauchy];
ScalarT lambda;
ScalarT mu;
Intrepid::Tensor<ScalarT> F(num_dims_), C(num_dims_), sigma(num_dims_);
Intrepid::Tensor<ScalarT> I(Intrepid::eye<ScalarT>(num_dims_));
Intrepid::Tensor<ScalarT> S(num_dims_), E(num_dims_);
for (int cell(0); cell < workset.numCells; ++cell) {
for (int 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)));
F.fill(def_grad,cell, pt,0,0);
C = F * transpose(F);
E = 0.5 * ( C - I );
S = lambda * Intrepid::trace(E) * I + 2.0 * mu * E;
sigma = (1.0 / Intrepid::det(F) ) * F * S * Intrepid::transpose(F);
for (int i = 0; i < num_dims_; ++i) {
for (int j = 0; j < num_dims_; ++j) {
stress(cell, pt, i, j) = sigma(i, j);
}
}
}
}
}
void HyperelasticDamageModel<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> def_grad = *dep_fields["F"];
PHX::MDField<ScalarT> J = *dep_fields["J"];
PHX::MDField<ScalarT> poissons_ratio = *dep_fields["Poissons Ratio"];
PHX::MDField<ScalarT> elastic_modulus = *dep_fields["Elastic Modulus"];
PHX::MDField<ScalarT> delta_time = *dep_fields["Delta Time"];
// extract evaluated MDFields
std::string cauchy = (*field_name_map_)["Cauchy_Stress"];
PHX::MDField<ScalarT> stress = *eval_fields[cauchy];
PHX::MDField<ScalarT> alpha = *eval_fields["alpha"];
PHX::MDField<ScalarT> damage;
if (!have_damage_) {
damage = *eval_fields["local damage"];
}
PHX::MDField<ScalarT> source = *eval_fields["Damage_Source"];
//get state variables
Albany::MDArray alpha_old = (*workset.stateArrayPtr)["alpha_old"];
ScalarT kappa;
ScalarT mu, mubar;
ScalarT Jm53, Jm23;
ScalarT smag;
ScalarT energy;
ScalarT dt = delta_time(0);
Intrepid::Tensor<ScalarT> F(num_dims_), b(num_dims_), sigma(num_dims_);
Intrepid::Tensor<ScalarT> I(Intrepid::eye<ScalarT>(num_dims_));
Intrepid::Tensor<ScalarT> s(num_dims_), n(num_dims_);
for (int cell(0); cell < workset.numCells; ++cell) {
for (int pt(0); pt < num_pts_; ++pt) {
kappa = elastic_modulus(cell, pt)
/ (3. * (1. - 2. * poissons_ratio(cell, pt)));
mu = elastic_modulus(cell, pt) / (2. * (1. + poissons_ratio(cell, pt)));
Jm53 = std::pow(J(cell, pt), -5. / 3.);
Jm23 = Jm53 * J(cell, pt);
F.fill(def_grad,cell, pt,0,0);
b = F * transpose(F);
mubar = (1.0 / 3.0) * mu * Jm23 * Intrepid::trace(b);
sigma = 0.5 * kappa * (J(cell, pt) - 1. / J(cell, pt)) * I
+ mu * Jm53 * Intrepid::dev(b);
energy = 0.5 * kappa
* (0.5 * (J(cell, pt) * J(cell, pt) - 1.0) - std::log(J(cell, pt)))
+ 0.5 * mu * (Jm23 * Intrepid::trace(b) - 3.0);
if (have_temperature_) {
ScalarT delta_temp = temperature_(cell, pt) - ref_temperature_;
energy += heat_capacity_
* ((delta_temp) - temperature_(cell, pt)
* std::log(temperature_(cell, pt) / ref_temperature_))
- 3.0 * expansion_coeff_ * (J(cell, pt) - 1.0 / J(cell, pt))
* delta_temp;
sigma -= expansion_coeff_ * (1.0 + 1.0 / (J(cell, pt) * J(cell, pt)))
* delta_temp * I;
}
alpha(cell, pt) = std::max((ScalarT) alpha_old(cell, pt), energy);
source(cell, pt) = (max_damage_ / damage_saturation_)
* std::exp(-alpha(cell, pt) / damage_saturation_)
* (alpha(cell, pt) - alpha_old(cell, pt)) / dt;
if (!have_damage_) {
damage(cell, pt) = max_damage_
* (1.0 - std::exp(-alpha(cell, pt) / damage_saturation_));
}
for (int i = 0; i < num_dims_; ++i) {
for (int j = 0; j < num_dims_; ++j) {
stress(cell, pt, i, j) = (1.0 - damage(cell, pt)) * sigma(i, j);
}
}
}
}
}
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
}
void ElasticDamageModel<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)
{
//bool print = false;
//if (typeid(ScalarT) == typeid(RealType)) print = true;
//cout.precision(15);
// 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 energy_string = (*field_name_map_)["Matrix_Energy"];
std::string damage_string = (*field_name_map_)["Matrix_Damage"];
std::string tangent_string = (*field_name_map_)["Material Tangent"];
// extract evaluated MDFields
PHX::MDField<ScalarT> stress = *eval_fields[cauchy_string];
PHX::MDField<ScalarT> energy = *eval_fields[energy_string];
PHX::MDField<ScalarT> damage = *eval_fields[damage_string];
PHX::MDField<ScalarT> tangent;
if(compute_tangent_) {
tangent = *eval_fields[tangent_string];
}
// previous state
Albany::MDArray energy_old =
(*workset.stateArrayPtr)[energy_string + "_old"];
ScalarT mu, lame;
ScalarT alpha, damage_deriv;
// Define some tensors for use
Intrepid::Tensor<ScalarT> I(Intrepid::eye<ScalarT>(num_dims_));
Intrepid::Tensor<ScalarT> epsilon(num_dims_), sigma(num_dims_);
Intrepid::Tensor4<ScalarT> Ce(num_dims_);
Intrepid::Tensor4<ScalarT> id4(num_dims_);
Intrepid::Tensor4<ScalarT> id3(Intrepid::identity_3<ScalarT>(num_dims_));
id4 = 0.5 * (Intrepid::identity_1<ScalarT>(num_dims_)
+ Intrepid::identity_2<ScalarT>(num_dims_));
for (int cell = 0; cell < workset.numCells; ++cell) {
for (int pt = 0; pt < num_pts_; ++pt) {
// local parameters
mu = elastic_modulus(cell, pt)
/ (2.0 * (1.0 + poissons_ratio(cell, pt)));
lame = elastic_modulus(cell, pt) * poissons_ratio(cell, pt)
/ (1.0 + poissons_ratio(cell, pt))
/ (1.0 - 2.0 * poissons_ratio(cell, pt));
// small strain tensor
epsilon.fill(strain,cell, pt,0,0);
// undamaged elasticity tensor
Ce = lame * id3 + 2.0 * mu * id4;
// undamaged energy
energy(cell, pt) =
0.5 * Intrepid::dotdot(Intrepid::dotdot(epsilon, Ce), epsilon);
// undamaged Cauchy stress
sigma = Intrepid::dotdot(Ce, epsilon);
// maximum thermodynamic force
alpha = energy_old(cell, pt);
if (energy(cell, pt) > alpha) alpha = energy(cell, pt);
// damage term
damage(cell, pt) = max_damage_
* (1 - std::exp(-alpha / saturation_));
// derivative of damage w.r.t alpha
damage_deriv =
max_damage_ / saturation_ * std::exp(-alpha / saturation_);
// tangent for matrix considering damage
if(compute_tangent_) {
Ce = (1.0 - damage(cell, pt)) * Ce
- damage_deriv * Intrepid::tensor(sigma, sigma);
}
// total Cauchy stress
for (int i(0); i < num_dims_; ++i) {
for (int j(0); j < num_dims_; ++j) {
stress(cell, pt, i, j) =
(1.0 - damage(cell, pt)) * sigma(i, j);
}
}
// total tangent
if(compute_tangent_) {
for (int i(0); i < num_dims_; ++i) {
for (int j(0); j < num_dims_; ++j) {
for (int k(0); k < num_dims_; ++k) {
for (int l(0); l < num_dims_; ++l) {
tangent(cell, pt, i, j, k, l) = Ce(i, j, k, l);
}
}
}
}
}// compute_tangent_
} // pt
} // cell
}
void AnisotropicHyperelasticDamageModel<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)
{
bool print = false;
//if (typeid(ScalarT) == typeid(RealType)) print = true;
//cout.precision(15);
// retrive appropriate field name strings
std::string F_string = (*field_name_map_)["F"];
std::string J_string = (*field_name_map_)["J"];
std::string cauchy_string = (*field_name_map_)["Cauchy_Stress"];
std::string matrix_energy_string = (*field_name_map_)["Matrix_Energy"];
std::string f1_energy_string = (*field_name_map_)["F1_Energy"];
std::string f2_energy_string = (*field_name_map_)["F2_Energy"];
std::string matrix_damage_string = (*field_name_map_)["Matrix_Damage"];
std::string f1_damage_string = (*field_name_map_)["F1_Damage"];
std::string f2_damage_string = (*field_name_map_)["F2_Damage"];
// extract dependent MDFields
PHX::MDField<ScalarT> def_grad = *dep_fields[F_string];
PHX::MDField<ScalarT> J = *dep_fields[J_string];
PHX::MDField<ScalarT> poissons_ratio = *dep_fields["Poissons Ratio"];
PHX::MDField<ScalarT> elastic_modulus = *dep_fields["Elastic Modulus"];
// extract evaluated MDFields
PHX::MDField<ScalarT> stress = *eval_fields[cauchy_string];
PHX::MDField<ScalarT> energy_m = *eval_fields[matrix_energy_string];
PHX::MDField<ScalarT> energy_f1 = *eval_fields[f1_energy_string];
PHX::MDField<ScalarT> energy_f2 = *eval_fields[f2_energy_string];
PHX::MDField<ScalarT> damage_m = *eval_fields[matrix_damage_string];
PHX::MDField<ScalarT> damage_f1 = *eval_fields[f1_damage_string];
PHX::MDField<ScalarT> damage_f2 = *eval_fields[f2_damage_string];
// previous state
Albany::MDArray energy_m_old =
(*workset.stateArrayPtr)[matrix_energy_string + "_old"];
Albany::MDArray energy_f1_old =
(*workset.stateArrayPtr)[f1_energy_string + "_old"];
Albany::MDArray energy_f2_old =
(*workset.stateArrayPtr)[f2_energy_string + "_old"];
ScalarT kappa, mu, Jm53, Jm23, p, I4_f1, I4_f2;
ScalarT alpha_f1, alpha_f2, alpha_m;
// Define some tensors for use
Intrepid::Tensor<ScalarT> I(Intrepid::eye<ScalarT>(num_dims_));
Intrepid::Tensor<ScalarT> F(num_dims_), s(num_dims_), b(num_dims_), C(
num_dims_);
Intrepid::Tensor<ScalarT> sigma_m(num_dims_), sigma_f1(num_dims_), sigma_f2(
num_dims_);
Intrepid::Tensor<ScalarT> M1dyadM1(num_dims_), M2dyadM2(num_dims_);
Intrepid::Tensor<ScalarT> S0_f1(num_dims_), S0_f2(num_dims_);
Intrepid::Vector<ScalarT> M1(num_dims_), M2(num_dims_);
for (int cell = 0; cell < workset.numCells; ++cell) {
for (int pt = 0; pt < num_pts_; ++pt) {
// local parameters
kappa = elastic_modulus(cell, pt)
/ (3. * (1. - 2. * poissons_ratio(cell, pt)));
mu = elastic_modulus(cell, pt) / (2. * (1. + poissons_ratio(cell, pt)));
Jm53 = std::pow(J(cell, pt), -5. / 3.);
Jm23 = std::pow(J(cell, pt), -2. / 3.);
F.fill(def_grad,cell, pt,0,0);
// compute deviatoric stress
b = F * Intrepid::transpose(F);
s = mu * Jm53 * Intrepid::dev(b);
// compute pressure
p = 0.5 * kappa * (J(cell, pt) - 1. / (J(cell, pt)));
sigma_m = s + p * I;
// compute energy for M
energy_m(cell, pt) = 0.5 * kappa
* (0.5 * (J(cell, pt) * J(cell, pt) - 1.0) - std::log(J(cell, pt)))
+ 0.5 * mu * (Jm23 * Intrepid::trace(b) - 3.0);
// damage term in M
alpha_m = energy_m_old(cell, pt);
if (energy_m(cell, pt) > alpha_m) alpha_m = energy_m(cell, pt);
damage_m(cell, pt) = max_damage_m_
* (1 - std::exp(-alpha_m / saturation_m_));
//-----------compute stress in Fibers
// Right Cauchy-Green Tensor C = F^{T} * F
C = Intrepid::transpose(F) * F;
// Fiber orientation vectors
//
// fiber 1
for (int i = 0; i < num_dims_; ++i) {
M1(i) = direction_f1_[i];
}
M1 = M1 / norm(M1);
// fiber 2
for (int i = 0; i < num_dims_; ++i) {
M2(i) = direction_f2_[i];
}
M2 = M2 / norm(M2);
// Anisotropic invariants I4 = M_{i} * C * M_{i}
I4_f1 = Intrepid::dot(M1, Intrepid::dot(C, M1));
I4_f2 = Intrepid::dot(M2, Intrepid::dot(C, M2));
M1dyadM1 = Intrepid::dyad(M1, M1);
M2dyadM2 = Intrepid::dyad(M2, M2);
// undamaged stress (2nd PK stress)
S0_f1 = (4.0 * k_f1_ * (I4_f1 - 1.0)
* std::exp(q_f1_ * (I4_f1 - 1) * (I4_f1 - 1))) * M1dyadM1;
S0_f2 = (4.0 * k_f2_ * (I4_f2 - 1.0)
* std::exp(q_f2_ * (I4_f2 - 1) * (I4_f2 - 1))) * M2dyadM2;
// compute energy for fibers
energy_f1(cell, pt) = k_f1_
* (std::exp(q_f1_ * (I4_f1 - 1) * (I4_f1 - 1)) - 1) / q_f1_;
energy_f2(cell, pt) = k_f2_
* (std::exp(q_f2_ * (I4_f2 - 1) * (I4_f2 - 1)) - 1) / q_f2_;
// Fiber Cauchy stress
sigma_f1 = (1.0 / J(cell, pt))
* Intrepid::dot(F, Intrepid::dot(S0_f1, Intrepid::transpose(F)));
sigma_f2 = (1.0 / J(cell, pt))
* Intrepid::dot(F, Intrepid::dot(S0_f2, Intrepid::transpose(F)));
// maximum thermodynamic forces
alpha_f1 = energy_f1_old(cell, pt);
alpha_f2 = energy_f2_old(cell, pt);
if (energy_f1(cell, pt) > alpha_f1) alpha_f1 = energy_f1(cell, pt);
if (energy_f2(cell, pt) > alpha_f2) alpha_f2 = energy_f2(cell, pt);
// damage term in fibers
damage_f1(cell, pt) = max_damage_f1_
* (1 - std::exp(-alpha_f1 / saturation_f1_));
damage_f2(cell, pt) = max_damage_f2_
* (1 - std::exp(-alpha_f2 / saturation_f2_));
// total Cauchy stress (M, Fibers)
for (int i(0); i < num_dims_; ++i) {
for (int j(0); j < num_dims_; ++j) {
stress(cell, pt, i, j) =
volume_fraction_m_ * (1 - damage_m(cell, pt)) * sigma_m(i, j)
+ volume_fraction_f1_ * (1 - damage_f1(cell, pt))
* sigma_f1(i, j)
+ volume_fraction_f2_ * (1 - damage_f2(cell, pt))
* sigma_f2(i, j);
}
}
if (print) {
std::cout << " matrix damage: " << damage_m(cell, pt) << std::endl;
std::cout << " matrix energy: " << energy_m(cell, pt) << std::endl;
std::cout << " fiber1 damage: " << damage_f1(cell, pt) << std::endl;
std::cout << " fiber1 energy: " << energy_f1(cell, pt) << std::endl;
std::cout << " fiber2 damage: " << damage_f2(cell, pt) << std::endl;
std::cout << " fiber2 energy: " << energy_f2(cell, pt) << std::endl;
}
} // pt
} // cell
}
void ElastoViscoplasticModel<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)
{
std::string cauchy_string = (*field_name_map_)["Cauchy_Stress"];
std::string Fp_string = (*field_name_map_)["Fp"];
std::string eqps_string = (*field_name_map_)["eqps"];
std::string eps_ss_string = (*field_name_map_)["eps_ss"];
std::string kappa_string = (*field_name_map_)["isotropic_hardening"];
std::string source_string = (*field_name_map_)["Mechanical_Source"];
std::string F_string = (*field_name_map_)["F"];
std::string J_string = (*field_name_map_)["J"];
// extract dependent MDFields
PHX::MDField<ScalarT> def_grad_field = *dep_fields[F_string];
PHX::MDField<ScalarT> J = *dep_fields[J_string];
PHX::MDField<ScalarT> poissons_ratio = *dep_fields["Poissons Ratio"];
PHX::MDField<ScalarT> elastic_modulus = *dep_fields["Elastic Modulus"];
PHX::MDField<ScalarT> yield_strength = *dep_fields["Yield Strength"];
PHX::MDField<ScalarT> hardening_modulus = *dep_fields["Hardening Modulus"];
PHX::MDField<ScalarT> recovery_modulus = *dep_fields["Recovery Modulus"];
PHX::MDField<ScalarT> flow_exp = *dep_fields["Flow Rule Exponent"];
PHX::MDField<ScalarT> flow_coeff = *dep_fields["Flow Rule Coefficient"];
PHX::MDField<ScalarT> delta_time = *dep_fields["Delta Time"];
// extract evaluated MDFields
PHX::MDField<ScalarT> stress_field = *eval_fields[cauchy_string];
PHX::MDField<ScalarT> Fp_field = *eval_fields[Fp_string];
PHX::MDField<ScalarT> eqps_field = *eval_fields[eqps_string];
PHX::MDField<ScalarT> eps_ss_field = *eval_fields[eps_ss_string];
PHX::MDField<ScalarT> kappa_field = *eval_fields[kappa_string];
PHX::MDField<ScalarT> source_field;
if (have_temperature_) {
source_field = *eval_fields[source_string];
}
// get State Variables
Albany::MDArray Fp_field_old = (*workset.stateArrayPtr)[Fp_string + "_old"];
Albany::MDArray eqps_field_old = (*workset.stateArrayPtr)[eqps_string + "_old"];
Albany::MDArray eps_ss_field_old = (*workset.stateArrayPtr)[eps_ss_string + "_old"];
Albany::MDArray kappa_field_old = (*workset.stateArrayPtr)[kappa_string + "_old"];
// define constants
RealType sq23(std::sqrt(2. / 3.));
RealType sq32(std::sqrt(3. / 2.));
// pre-define some tensors that will be re-used below
Intrepid::Tensor<ScalarT> F(num_dims_), be(num_dims_);
Intrepid::Tensor<ScalarT> s(num_dims_), sigma(num_dims_);
Intrepid::Tensor<ScalarT> N(num_dims_), A(num_dims_);
Intrepid::Tensor<ScalarT> expA(num_dims_), Fpnew(num_dims_);
Intrepid::Tensor<ScalarT> I(Intrepid::eye<ScalarT>(num_dims_));
Intrepid::Tensor<ScalarT> Fpn(num_dims_), Cpinv(num_dims_), Fpinv(num_dims_);
for (std::size_t cell(0); cell < workset.numCells; ++cell) {
for (std::size_t pt(0); pt < num_pts_; ++pt) {
ScalarT bulk = elastic_modulus(cell, pt)
/ (3. * (1. - 2. * poissons_ratio(cell, pt)));
ScalarT mu = elastic_modulus(cell, pt) / (2. * (1. + poissons_ratio(cell, pt)));
ScalarT Y = yield_strength(cell, pt);
ScalarT Jm23 = std::pow(J(cell, pt), -2. / 3.);
// assign local state variables
//
//ScalarT kappa = kappa_field(cell,pt);
ScalarT kappa_old = kappa_field_old(cell,pt);
ScalarT eps_ss = eps_ss_field(cell,pt);
ScalarT eps_ss_old = eps_ss_field_old(cell,pt);
ScalarT eqps_old = eqps_field_old(cell,pt);
// fill local tensors
//
F.fill(&def_grad_field(cell, pt, 0, 0));
for (std::size_t i(0); i < num_dims_; ++i) {
for (std::size_t j(0); j < num_dims_; ++j) {
Fpn(i, j) = ScalarT(Fp_field_old(cell, pt, i, j));
}
}
// compute trial state
// compute the Kirchhoff stress in the current configuration
//
Cpinv = Intrepid::inverse(Fpn) * Intrepid::transpose(Intrepid::inverse(Fpn));
be = Jm23 * F * Cpinv * Intrepid::transpose(F);
s = mu * Intrepid::dev(be);
ScalarT smag = Intrepid::norm(s);
ScalarT mubar = Intrepid::trace(be) * mu / (num_dims_);
// check yield condition
//
ScalarT Phi = sq32 * smag - ( Y + kappa_old );
std::cout << "======== Phi: " << Phi << std::endl;
std::cout << "======== eps: " << std::numeric_limits<RealType>::epsilon() << std::endl;
if (Phi > std::numeric_limits<RealType>::epsilon()) {
// return mapping algorithm
//
bool converged = false;
int iter = 0;
RealType max_norm = std::numeric_limits<RealType>::min();
// hardening and recovery parameters
//
ScalarT H = hardening_modulus(cell, pt);
ScalarT Rd = recovery_modulus(cell, pt);
// flow rule temperature dependent parameters
//
ScalarT f = flow_coeff(cell,pt);
ScalarT n = flow_exp(cell,pt);
// This solver deals with Sacado type info
//
LocalNonlinearSolver<EvalT, Traits> solver;
// create some vectors to store solver data
//
std::vector<ScalarT> R(2);
std::vector<ScalarT> dRdX(4);
std::vector<ScalarT> X(2);
// initial guess
X[0] = 0.0;
X[1] = eps_ss_old;
// create a copy of be as a Fad
Intrepid::Tensor<Fad> beF(num_dims_);
for (std::size_t i = 0; i < num_dims_; ++i) {
for (std::size_t j = 0; j < num_dims_; ++j) {
beF(i, j) = be(i, j);
}
}
Fad two_mubarF = 2.0 * Intrepid::trace(beF) * mu / (num_dims_);
//Fad sq32F = std::sqrt(3.0/2.0);
// FIXME this seems to be necessary to get PhiF to compile below
// need to look into this more, it appears to be a conflict
// between the Intrepid::norm and FadType operations
//
Fad smagF = smag;
while (!converged) {
// set up data types
//
std::vector<Fad> XFad(2);
std::vector<Fad> RFad(2);
std::vector<ScalarT> Xval(2);
for (std::size_t i = 0; i < 2; ++i) {
Xval[i] = Sacado::ScalarValue<ScalarT>::eval(X[i]);
XFad[i] = Fad(2, i, Xval[i]);
}
// get solution vars
//
Fad dgamF = XFad[0];
Fad eps_ssF = XFad[1];
// compute yield function
//
Fad eqps_rateF = 0.0;
if (delta_time(0) > 0) eqps_rateF = sq23 * dgamF / delta_time(0);
Fad rate_termF = 1.0 + std::asinh( std::pow(eqps_rateF / f, n));
Fad kappaF = two_mubarF * eps_ssF;
Fad PhiF = sq32 * (smagF - two_mubarF * dgamF) - ( Y + kappaF ) * rate_termF;
// compute the hardening residual
//
Fad eps_resF = eps_ssF - eps_ss_old - (H - Rd*eps_ssF) * dgamF;
// for convenience put the residuals into a container
//
RFad[0] = PhiF;
RFad[1] = eps_resF;
// extract the values of the residuals
//
for (int i = 0; i < 2; ++i)
R[i] = RFad[i].val();
// extract the sensitivities of the residuals
//
for (int i = 0; i < 2; ++i)
for (int j = 0; j < 2; ++j)
dRdX[i + 2 * j] = RFad[i].dx(j);
// this call invokes the solver and updates the solution in X
//
solver.solve(dRdX, X, R);
// compute the norm of the residual
//
RealType R0 = Sacado::ScalarValue<ScalarT>::eval(R[0]);
RealType R1 = Sacado::ScalarValue<ScalarT>::eval(R[1]);
RealType norm_res = std::sqrt(R0*R0 + R1*R1);
max_norm = std::max(norm_res, max_norm);
// check against too many inerations
//
TEUCHOS_TEST_FOR_EXCEPTION(iter == 30, std::runtime_error,
std::endl <<
"Error in ElastoViscoplastic return mapping\n" <<
"iter count = " << iter << "\n" << std::endl);
// check for a sufficiently small residual
//
std::cout << "======== norm_res : " << norm_res << std::endl;
if ( (norm_res/max_norm < 1.e-12) || (norm_res < 1.e-12) )
converged = true;
// increment the iteratio counter
//
iter++;
}
solver.computeFadInfo(dRdX, X, R);
ScalarT dgam = X[0];
ScalarT eps_ss = X[1];
ScalarT kappa = 2.0 * mubar * eps_ss;
std::cout << "======== dgam : " << dgam << std::endl;
std::cout << "======== e_ss : " << eps_ss << std::endl;
std::cout << "======== kapp : " << kappa << std::endl;
// plastic direction
N = (1 / smag) * s;
// update s
s -= 2 * mubar * dgam * N;
// update state variables
eps_ss_field(cell, pt) = eps_ss;
eqps_field(cell,pt) = eqps_old + sq23 * dgam;
kappa_field(cell,pt) = kappa;
// mechanical source
// FIXME this is not correct, just a placeholder
//
if (have_temperature_ && delta_time(0) > 0) {
source_field(cell, pt) = (sq23 * dgam / delta_time(0))
* (Y + kappa) / (density_ * heat_capacity_);
}
// exponential map to get Fpnew
//
A = dgam * N;
expA = Intrepid::exp(A);
Fpnew = expA * Fpn;
for (std::size_t i(0); i < num_dims_; ++i) {
for (std::size_t j(0); j < num_dims_; ++j) {
Fp_field(cell, pt, i, j) = Fpnew(i, j);
}
}
} else {
// we are not yielding, variables do not evolve
//
eps_ss_field(cell, pt) = eps_ss_old;
eqps_field(cell,pt) = eqps_old;
kappa_field(cell,pt) = kappa_old;
if (have_temperature_) source_field(cell, pt) = 0.0;
for (std::size_t i(0); i < num_dims_; ++i) {
for (std::size_t j(0); j < num_dims_; ++j) {
Fp_field(cell, pt, i, j) = Fpn(i, j);
}
}
}
// compute pressure
ScalarT p = 0.5 * bulk * (J(cell, pt) - 1. / (J(cell, pt)));
// compute stress
sigma = p * I + s / J(cell, pt);
for (std::size_t i(0); i < num_dims_; ++i) {
for (std::size_t j(0); j < num_dims_; ++j) {
stress_field(cell, pt, i, j) = sigma(i, j);
}
}
}
}
if (have_temperature_) {
for (std::size_t cell(0); cell < workset.numCells; ++cell) {
for (std::size_t pt(0); pt < num_pts_; ++pt) {
F.fill(&def_grad_field(cell,pt,0,0));
ScalarT J = Intrepid::det(F);
sigma.fill(&stress_field(cell,pt,0,0));
sigma -= 3.0 * expansion_coeff_ * (1.0 + 1.0 / (J*J))
* (temperature_(cell,pt) - ref_temperature_) * I;
for (std::size_t i = 0; i < num_dims_; ++i) {
for (std::size_t j = 0; j < num_dims_; ++j) {
stress_field(cell, pt, i, j) = sigma(i, j);
}
}
}
}
}
}
