incompressible_neo_hookean.h

/*  ______________________________________________________________________
 *
 *  ExaDG - High-Order Discontinuous Galerkin for the Exa-Scale
 *
 *  Copyright (C) 2023 by the ExaDG authors
 *
 *  This program is free software: you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation, either version 3 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with this program. If not, see <https://www.gnu.org/licenses/>.
 *  ______________________________________________________________________
 */
 
#ifndef EXADG_STRUCTURE_MATERIAL_LIBRARY_INCOMPRESSIBLE_NEO_HOOKEAN_H_
#define EXADG_STRUCTURE_MATERIAL_LIBRARY_INCOMPRESSIBLE_NEO_HOOKEAN_H_
 
// deal.II
#include <deal.II/base/function.h>
#include <deal.II/base/point.h>
#include <deal.II/matrix_free/matrix_free.h>
 
// ExaDG
#include <exadg/matrix_free/integrators.h>
#include <exadg/operators/variable_coefficients.h>
#include <exadg/structure/material/material.h>
 
namespace ExaDG
{
namespace Structure
{
template<int dim>
struct IncompressibleNeoHookeanData : public MaterialData
{
  IncompressibleNeoHookeanData(
    MaterialType const &                         type,
    double const &                               shear_modulus,
    double const &                               bulk_modulus,
    Type2D const &                               type_two_dim,
    std::shared_ptr<dealii::Function<dim>> const shear_modulus_function = nullptr)
    : MaterialData(type),
      shear_modulus(shear_modulus),
      shear_modulus_function(shear_modulus_function),
      bulk_modulus(bulk_modulus),
      type_two_dim(type_two_dim)
  {
  }
 
  double                                 shear_modulus;
  std::shared_ptr<dealii::Function<dim>> shear_modulus_function;
 
  double bulk_modulus;
  Type2D type_two_dim;
};
 
template<int dim, typename Number>
class IncompressibleNeoHookean : public Material<dim, Number>
{
public:
  typedef typename Material<dim, Number>::VectorType     VectorType;
  typedef typename Material<dim, Number>::Range          Range;
  typedef typename Material<dim, Number>::IntegratorCell IntegratorCell;
 
  typedef typename Material<dim, Number>::scalar           scalar;
  typedef typename Material<dim, Number>::tensor           tensor;
  typedef typename Material<dim, Number>::symmetric_tensor symmetric_tensor;
 
  IncompressibleNeoHookean(dealii::MatrixFree<dim, Number> const &   matrix_free,
                           unsigned int const                        dof_index,
                           unsigned int const                        quad_index,
                           IncompressibleNeoHookeanData<dim> const & data);
 
  /*
   * The second Piola-Kirchhoff stress is defined as S = S_vol + S_iso (Flory split),
   * where we have strain energy density functions Psi_vol and Psi_iso defined as
   *
   * Psi_vol = bulk_modulus / 4 * ( J^2 - 1 - ln(J) )
   *
   * and
   *
   * Psi_iso = shear_modulus / 2 * ( I_1_bar - trace(I) )
   *
   * with the classic relations
   *
   * F = I + Grad(displacement) ,
   *
   * J = det(F) ,
   *
   * C = F^T * F ,
   *
   * I_1 = tr(C) ,
   *
   * I_1_bar = J^(-2/3) * I_1
   *
   * such that we end up with
   *
   * S_vol = bulk_modulus / 2 * (J^2 - 1) C^(-1)
   *
   * S_iso = J^(-2/3) * ( I - 1/3 * I_1 * C^(-1) )
   *
   */
  symmetric_tensor
  second_piola_kirchhoff_stress(tensor const &     gradient_displacement,
                                unsigned int const cell,
                                unsigned int const q) const final;
 
  symmetric_tensor
  second_piola_kirchhoff_stress_displacement_derivative(tensor const &     gradient_increment,
                                                        tensor const &     deformation_gradient,
                                                        unsigned int const cell,
                                                        unsigned int const q) const final;
 
private:
  /*
   * Store factors involving (potentially variable) shear modulus.
   */
  void
  cell_loop_set_coefficients(dealii::MatrixFree<dim, Number> const & matrix_free,
                             VectorType &,
                             VectorType const & src,
                             Range const &      cell_range) const;
 
  unsigned int dof_index;
  unsigned int quad_index;
 
  IncompressibleNeoHookeanData<dim> const & data;
 
  mutable scalar shear_modulus_stored;
 
  // cache coefficients for spatially varying material parameters
  bool                                 shear_modulus_is_variable;
  mutable VariableCoefficients<scalar> shear_modulus_coefficients;
 
  Number static constexpr one_third = 1.0 / 3.0;
};
} // namespace Structure
} // namespace ExaDG
 
#endif /* EXADG_STRUCTURE_MATERIAL_LIBRARY_INCOMPRESSIBLE_NEO_HOOKEAN_H_ */