mechanics.h

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#pragma once
 
#include <deal.II/base/tensor.h>
 
#include <prismspf/config.h>
 
PRISMS_PF_BEGIN_NAMESPACE
 
namespace Mechanics
{

  template <unsigned int dim>
  constexpr unsigned int voigt_tensor_size = (2 * dim) - 1 + (dim / 3);

  template <unsigned int dim, typename T>
  inline DEAL_II_ALWAYS_INLINE void
  compute_stress(const dealii::Tensor<2, voigt_tensor_size<dim>, T> &elasticity_tensor,
                 const dealii::Tensor<1, voigt_tensor_size<dim>, T> &strain,
                 dealii::Tensor<1, voigt_tensor_size<dim>, T>       &stress)
  {
    stress = elasticity_tensor * strain;
  }

  template <unsigned int dim, typename T>
  inline DEAL_II_ALWAYS_INLINE void
  compute_stress(const dealii::Tensor<2, voigt_tensor_size<dim>, T> &elasticity_tensor,
                 const dealii::Tensor<2, dim, T>                    &strain,
                 dealii::Tensor<2, dim, T>                          &stress)
  {
    dealii::Tensor<1, voigt_tensor_size<dim>, T> sigma;
    dealii::Tensor<1, voigt_tensor_size<dim>, T> epsilon;
 
    if constexpr (dim == 3)
      {
        const int xx_dir = 0;
        const int yy_dir = 1;
        const int zz_dir = 2;
        const int yz_dir = 3;
        const int xz_dir = 4;
        const int xy_dir = 5;
 
        epsilon[xx_dir] = strain[xx_dir][xx_dir];
        epsilon[yy_dir] = strain[yy_dir][yy_dir];
        epsilon[zz_dir] = strain[zz_dir][zz_dir];
 
        // In Voigt notation: epsilon are engineering shear strains
        epsilon[yz_dir] = strain[yy_dir][zz_dir] + strain[zz_dir][yy_dir];
        epsilon[xz_dir] = strain[xx_dir][zz_dir] + strain[zz_dir][xx_dir];
        epsilon[xy_dir] = strain[xx_dir][yy_dir] + strain[yy_dir][xx_dir];
 
        // Multiply elasticity_tensor and epsilon to get sigma
        sigma = elasticity_tensor * epsilon;
 
        stress[xx_dir][xx_dir] = sigma[xx_dir];
        stress[yy_dir][yy_dir] = sigma[yy_dir];
        stress[zz_dir][zz_dir] = sigma[zz_dir];
 
        stress[yy_dir][zz_dir] = sigma[yz_dir];
        stress[zz_dir][yy_dir] = sigma[yz_dir];
 
        stress[xx_dir][zz_dir] = sigma[xz_dir];
        stress[zz_dir][xx_dir] = sigma[xz_dir];
 
        stress[xx_dir][yy_dir] = sigma[xy_dir];
        stress[yy_dir][xx_dir] = sigma[xy_dir];
      }
    else if constexpr (dim == 2)
      {
        const int xx_dir = 0;
        const int yy_dir = 1;
        const int xy_dir = 2;
 
        epsilon[xx_dir] = strain[xx_dir][xx_dir];
        epsilon[yy_dir] = strain[yy_dir][yy_dir];
 
        // In Voigt notation: epsilon are engineering shear strains
        epsilon[xy_dir] = strain[xx_dir][yy_dir] + strain[yy_dir][xx_dir];
 
        // Multiply elasticity_tensor and epsilon to get sigma
        sigma = elasticity_tensor * epsilon;
 
        stress[xx_dir][xx_dir] = sigma[xx_dir];
        stress[yy_dir][yy_dir] = sigma[yy_dir];
        stress[xx_dir][yy_dir] = sigma[xy_dir];
        stress[yy_dir][xx_dir] = sigma[xy_dir];
      }
    else
      {
        const int xx_dir = 0;
 
        stress[xx_dir][xx_dir] =
          elasticity_tensor[xx_dir][xx_dir] * strain[xx_dir][xx_dir];
      }
  }
 
} // namespace Mechanics
 
PRISMS_PF_END_NAMESPACE