elastic_tensor_decomposition.h

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/*
 Copyright (C) 2023 - 2024 by the authors of the ASPECT code.
 This file is part of ASPECT.
 ASPECT 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 2, or (at your option)
 any later version.
 ASPECT 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 ASPECT; see the file LICENSE.  If not see
 <http://www.gnu.org/licenses/>.
 */
 
#ifndef _aspect_particle_property_elastic_tensor_decomposition_h
#define _aspect_particle_property_elastic_tensor_decomposition_h
 
#include <aspect/particle/property/interface.h>
#include <aspect/simulator_access.h>
 
namespace aspect
{
  namespace Particle
  {
    namespace Property
    {
      namespace Utilities
      {
        using namespace aspect::Utilities;
 
        std::array<unsigned int, 3>
        indexed_even_permutation(const unsigned int index);
 
        SymmetricTensor<2,3>
        compute_voigt_stiffness_tensor(const SymmetricTensor<2,6> &elastic_tensor);
 
        SymmetricTensor<2,3>
        compute_dilatation_stiffness_tensor(const SymmetricTensor<2,6> &elastic_tensor);
 
        Tensor<2,3> compute_unpermutated_SCCS(const SymmetricTensor<2,3> &dilatation_stiffness_tensor,
                                              const SymmetricTensor<2,3> &voigt_stiffness_tensor);
 
        std::array<std::array<double,3>,7>
        compute_elastic_tensor_SCCS_decompositions(
          const Tensor<2,3> &unpermutated_SCCS,
          const SymmetricTensor<2,6> &elastic_matrix);
 
 
        const SymmetricTensor<2,21> projection_matrix_triclinic_to_monoclinic(
          Tensor<2,21>(
        {
          {1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
          {0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
          {0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
          {0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
          {0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
          {0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
          {0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
          {0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0},
          {0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0},
          {0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0},
          {0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0},
          {0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0},
          {0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0},
          {0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0},
          {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0},
          {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0},
          {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0},
          {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0},
          {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0},
          {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0},
          {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1},
        })
        );
 
        const SymmetricTensor<2,9> projection_matrix_monoclinic_to_orthorhombic(
          Tensor<2,9>(
        {
          {1,0,0,0,0,0,0,0,0},
          {0,1,0,0,0,0,0,0,0},
          {0,0,1,0,0,0,0,0,0},
          {0,0,0,1,0,0,0,0,0},
          {0,0,0,0,1,0,0,0,0},
          {0,0,0,0,0,1,0,0,0},
          {0,0,0,0,0,0,1,0,0},
          {0,0,0,0,0,0,0,1,0},
          {0,0,0,0,0,0,0,0,1}
        })
        );
 
        const SymmetricTensor<2,9> projection_matrix_orthorhombic_to_tetragonal(
          Tensor<2,9>(
        {
          {0.5,0.5,0.0,0.0,0.0,0.0,0.0,0.0,0.0},
          {0.5,0.5,0.0,0.0,0.0,0.0,0.0,0.0,0.0},
          {0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0},
          {0.0,0.0,0.0,0.5,0.5,0.0,0.0,0.0,0.0},
          {0.0,0.0,0.0,0.5,0.5,0.0,0.0,0.0,0.0},
          {0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0},
          {0.0,0.0,0.0,0.0,0.0,0.0,0.5,0.5,0.0},
          {0.0,0.0,0.0,0.0,0.0,0.0,0.5,0.5,0.0},
          {0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0}
        })
        );
 
        const SymmetricTensor<2,9> projection_matrix_tetragonal_to_hexagonal(
          Tensor<2,9>(
        {
          {3./8.                , 3./8.                , 0.0, 0.0, 0.0, 1./(4.*std::sqrt(2.))  , 0.0, 0.0, 1./4.                 },
          {3./8.                , 3./8.                , 0.0, 0.0, 0.0, 1./(4.*std::sqrt(2.))  , 0.0, 0.0, 1./4.                 },
          {0.0                  , 0.0                  , 1.0, 0.0, 0.0, 0.0                    , 0.0, 0.0, 0.0                   },
          {0.0                  , 0.0                  , 0.0, 0.5, 0.5, 0.0                    , 0.0, 0.0, 0.0                   },
          {0.0                  , 0.0                  , 0.0, 0.5, 0.5, 0.0                    , 0.0, 0.0, 0.0                   },
          {1./(4.*std::sqrt(2.)), 1./(4.*std::sqrt(2.)), 0.0, 0.0, 0.0, 3./4.                  , 0.0, 0.0, -1./(2.*std::sqrt(2.))},
          {0.0                  , 0.0                  , 0.0, 0.0, 0.0, 0.0                    , 0.5, 0.5, 0.0                   },
          {0.0                  , 0.0                  , 0.0, 0.0, 0.0, 0.0                    , 0.5, 0.5, 0.0                   },
          {1./4.                , 1./4.                , 0.0, 0.0, 0.0, -1./(2.*std::sqrt(2.)) , 0.0, 0.0, 0.5                   }
        })
        );
 
        const SymmetricTensor<2,9> projection_matrix_hexagonal_to_isotropic(
          Tensor<2,9>(
        {
          {3./15.           , 3./15.           , 3./15.           , std::sqrt(2.)/15. , std::sqrt(2.)/15. , std::sqrt(2.)/15. , 2./15.            , 2./15.            , 2./15.             },
          {3./15.           , 3./15.           , 3./15.           , std::sqrt(2.)/15. , std::sqrt(2.)/15. , std::sqrt(2.)/15. , 2./15.            , 2./15.            , 2./15.             },
          {3./15.           , 3./15.           , 3./15.           , std::sqrt(2.)/15. , std::sqrt(2.)/15. , std::sqrt(2.)/15. , 2./15.            , 2./15.            , 2./15.             },
          {std::sqrt(2.)/15., std::sqrt(2.)/15., std::sqrt(2.)/15., 4./15.            , 4./15.            , 4./15.            , -std::sqrt(2.)/15., -std::sqrt(2.)/15., -std::sqrt(2.)/15. },
          {std::sqrt(2.)/15., std::sqrt(2.)/15., std::sqrt(2.)/15., 4./15.            , 4./15.            , 4./15.            , -std::sqrt(2.)/15., -std::sqrt(2.)/15., -std::sqrt(2.)/15. },
          {std::sqrt(2.)/15., std::sqrt(2.)/15., std::sqrt(2.)/15., 4./15.            , 4./15.            , 4./15.            , -std::sqrt(2.)/15., -std::sqrt(2.)/15., -std::sqrt(2.)/15. },
          {2./15.           , 2./15.           , 2./15.           , -std::sqrt(2.)/15., -std::sqrt(2.)/15., -std::sqrt(2.)/15., 1./5.             , 1./5.             , 1./5.         },
          {2./15.           , 2./15.           , 2./15.           , -std::sqrt(2.)/15., -std::sqrt(2.)/15., -std::sqrt(2.)/15., 1./5.             , 1./5.             , 1./5.              },
          {2./15.           , 2./15.           , 2./15.           , -std::sqrt(2.)/15., -std::sqrt(2.)/15., -std::sqrt(2.)/15., 1./5.             , 1./5.             , 1./5.              }
        })
        );
      }
 
      template <int dim>
      class ElasticTensorDecomposition : public Interface<dim>, public ::aspect::SimulatorAccess<dim>
      {
        public:
          ElasticTensorDecomposition() = default;
 
          void
          initialize () override;
 
          void
          initialize_one_particle_property (const Point<dim> &position,
                                            std::vector<double> &particle_properties) const override;
 
          void
          update_particle_properties (const ParticleUpdateInputs<dim> &inputs,
                                      typename ParticleHandler<dim>::particle_iterator_range &particles) const override;
 
          UpdateTimeFlags
          need_update () const override;
 
          std::vector<std::pair<std::string, unsigned int>>
          get_property_information() const override;
 
        private:
          unsigned int cpo_elastic_tensor_data_position;
      };
    }
  }
}
 
#endif