AnisotropicHyperelasticDamageModel_Def.hpp

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//*****************************************************************//
//    Albany 2.0:  Copyright 2012 Sandia Corporation               //
//    This Software is released under the BSD license detailed     //
//    in the file "license.txt" in the top-level Albany directory  //
//*****************************************************************//

#include <Intrepid_MiniTensor.h>
#include <Teuchos_TestForException.hpp>
#include <Phalanx_DataLayout.hpp>
#include <typeinfo>

namespace LCM
{

//----------------------------------------------------------------------------
template<typename EvalT, typename Traits>
AnisotropicHyperelasticDamageModel<EvalT, Traits>::
AnisotropicHyperelasticDamageModel(Teuchos::ParameterList* p,
    const Teuchos::RCP<Albany::Layouts>& dl) :
    LCM::ConstitutiveModel<EvalT, Traits>(p, dl),
    k_f1_(p->get<RealType>("Fiber 1 k", 1.0)),
    q_f1_(p->get<RealType>("Fiber 1 q", 1.0)),
    volume_fraction_f1_(p->get<RealType>("Fiber 1 volume fraction", 0.0)),
    max_damage_f1_(p->get<RealType>("Fiber 1 maximum damage", 1.0)),
    saturation_f1_(p->get<RealType>("Fiber 1 damage saturation", 0.0)),
    k_f2_(p->get<RealType>("Fiber 2 k", 1.0)),
    q_f2_(p->get<RealType>("Fiber 2 q", 1.0)),
    volume_fraction_f2_(p->get<RealType>("Fiber 2 volume fraction", 0.0)),
    max_damage_f2_(p->get<RealType>("Fiber 2 maximum damage", 1.0)),
    saturation_f2_(p->get<RealType>("Fiber 2 damage saturation", 0.0)),
    volume_fraction_m_(p->get<RealType>("Matrix volume fraction", 1.0)),
    max_damage_m_(p->get<RealType>("Matrix maximum damage", 1.0)),
    saturation_m_(p->get<RealType>("Matrix damage saturation", 0.0)),
    direction_f1_(p->get<Teuchos::Array<RealType> >("Fiber 1 Orientation Vector")
        .toVector()),
    direction_f2_(p->get<Teuchos::Array<RealType> >("Fiber 2 Orientation Vector")
        .toVector())
{
  std::string F_string = (*field_name_map_)["F"];
  std::string J_string = (*field_name_map_)["J"];

  // define the dependent fields
  this->dep_field_map_.insert(std::make_pair(F_string, dl->qp_tensor));
  this->dep_field_map_.insert(std::make_pair(J_string, dl->qp_scalar));
  this->dep_field_map_.insert(std::make_pair("Poissons Ratio", dl->qp_scalar));
  this->dep_field_map_.insert(std::make_pair("Elastic Modulus", dl->qp_scalar));

  // retrive appropriate field name strings
  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"];

  // define the evaluated fields
  this->eval_field_map_.insert(std::make_pair(cauchy_string, dl->qp_tensor));
  this->eval_field_map_.insert(
      std::make_pair(matrix_energy_string, dl->qp_scalar));
  this->eval_field_map_.insert(std::make_pair(f1_energy_string, dl->qp_scalar));
  this->eval_field_map_.insert(std::make_pair(f2_energy_string, dl->qp_scalar));
  this->eval_field_map_.insert(
      std::make_pair(matrix_damage_string, dl->qp_scalar));
  this->eval_field_map_.insert(std::make_pair(f1_damage_string, dl->qp_scalar));
  this->eval_field_map_.insert(std::make_pair(f2_damage_string, dl->qp_scalar));

  // define the state variables
  //
  // stress
  this->num_state_variables_++;
  this->state_var_names_.push_back(cauchy_string);
  this->state_var_layouts_.push_back(dl->qp_tensor);
  this->state_var_init_types_.push_back("scalar");
  this->state_var_init_values_.push_back(0.0);
  this->state_var_old_state_flags_.push_back(false);
  this->state_var_output_flags_.push_back(p->get<bool>("Output Cauchy Stress", false));
  //
  // matrix energy
  this->num_state_variables_++;
  this->state_var_names_.push_back(matrix_energy_string);
  this->state_var_layouts_.push_back(dl->qp_scalar);
  this->state_var_init_types_.push_back("scalar");
  this->state_var_init_values_.push_back(0.0);
  this->state_var_old_state_flags_.push_back(true);
  this->state_var_output_flags_.push_back(p->get<bool>("Output Matrix Energy", false));
  //
  // fiber 1 energy
  this->num_state_variables_++;
  this->state_var_names_.push_back(f1_energy_string);
  this->state_var_layouts_.push_back(dl->qp_scalar);
  this->state_var_init_types_.push_back("scalar");
  this->state_var_init_values_.push_back(0.0);
  this->state_var_old_state_flags_.push_back(true);
  this->state_var_output_flags_.push_back(p->get<bool>("Output Fiber 1 Energy", false));
  //
  // fiber 2 energy
  this->num_state_variables_++;
  this->state_var_names_.push_back(f2_energy_string);
  this->state_var_layouts_.push_back(dl->qp_scalar);
  this->state_var_init_types_.push_back("scalar");
  this->state_var_init_values_.push_back(0.0);
  this->state_var_old_state_flags_.push_back(true);
  this->state_var_output_flags_.push_back(p->get<bool>("Output Fiber 2 Energy", false));
  //
  // matrix damage
  this->num_state_variables_++;
  this->state_var_names_.push_back(matrix_damage_string);
  this->state_var_layouts_.push_back(dl->qp_scalar);
  this->state_var_init_types_.push_back("scalar");
  this->state_var_init_values_.push_back(0.0);
  this->state_var_old_state_flags_.push_back(true);
  this->state_var_output_flags_.push_back(p->get<bool>("Output Matrix Damage", false));
  //
  // fiber 1 damage
  this->num_state_variables_++;
  this->state_var_names_.push_back(f1_damage_string);
  this->state_var_layouts_.push_back(dl->qp_scalar);
  this->state_var_init_types_.push_back("scalar");
  this->state_var_init_values_.push_back(0.0);
  this->state_var_old_state_flags_.push_back(true);
  this->state_var_output_flags_.push_back(p->get<bool>("Output Fiber 1 Damage", false));
  //
  // fiber 2 damage
  this->num_state_variables_++;
  this->state_var_names_.push_back(f2_damage_string);
  this->state_var_layouts_.push_back(dl->qp_scalar);
  this->state_var_init_types_.push_back("scalar");
  this->state_var_init_values_.push_back(0.0);
  this->state_var_old_state_flags_.push_back(true);
  this->state_var_output_flags_.push_back(p->get<bool>("Output Fiber 2 Damage", false));

}
//----------------------------------------------------------------------------
template<typename EvalT, typename Traits>
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 (std::size_t cell = 0; cell < workset.numCells; ++cell) {
    for (std::size_t 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 (std::size_t i = 0; i < num_dims_; ++i) {
        M1(i) = direction_f1_[i];
      }
      M1 = M1 / norm(M1);

      // fiber 2
      for (std::size_t 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 (std::size_t i(0); i < num_dims_; ++i) {
        for (std::size_t 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
}
//----------------------------------------------------------------------------
}