EshelbianAux.hpp

Go to the documentation of this file.

/**
 * @file EshelbianAux.hpp
 * @brief Auxilary functions for Eshelbian plasticity
 * @date 2024-08-30
 *
 * @copyright Copyright (c) 2024
 *
 */
 
namespace EshelbianPlasticity {
 
inline auto diff_deviator(FTensor::Ddg<double, 3, 3> &&t_diff_stress) {
  FTensor::Index<'i', 3> i;
  FTensor::Index<'j', 3> j;
  FTensor::Index<'k', 3> k;
  FTensor::Index<'l', 3> l;
 
  FTensor::Ddg<double, 3, 3> t_diff_deviator;
  t_diff_deviator(i, j, k, l) = t_diff_stress(i, j, k, l);
 
  constexpr double third = boost::math::constants::third<double>();
 
  t_diff_deviator(0, 0, 0, 0) -= third;
  t_diff_deviator(0, 0, 1, 1) -= third;
 
  t_diff_deviator(1, 1, 0, 0) -= third;
  t_diff_deviator(1, 1, 1, 1) -= third;
 
  t_diff_deviator(2, 2, 0, 0) -= third;
  t_diff_deviator(2, 2, 1, 1) -= third;
 
  t_diff_deviator(0, 0, 2, 2) -= third;
  t_diff_deviator(1, 1, 2, 2) -= third;
  t_diff_deviator(2, 2, 2, 2) -= third;
 
  return t_diff_deviator;
}
 
constexpr static auto size_symm = (3 * (3 + 1)) / 2;
 
inline auto diff_tensor() {
  FTensor::Index<'i', 3> i;
  FTensor::Index<'j', 3> j;
  FTensor::Index<'k', 3> k;
  FTensor::Index<'l', 3> l;
  FTensor::Ddg<double, 3, 3> t_diff;
  constexpr auto t_kd = FTensor::Kronecker_Delta_symmetric<int>();
  t_diff(i, j, k, l) = (t_kd(i, k) ^ t_kd(j, l)) / 4.;
  return t_diff;
};
 
inline auto symm_L_tensor() {
  FTensor::Index<'i', 3> i;
  FTensor::Index<'j', 3> j;
  FTensor::Index<'L', size_symm> L;
  FTensor::Dg<double, 3, size_symm> t_L;
  t_L(i, j, L) = 0;
  t_L(0, 0, 0) = 1;
  t_L(1, 1, 3) = 1;
  t_L(2, 2, 5) = 1;
  t_L(1, 0, 1) = 1;
  t_L(2, 0, 2) = 1;
  t_L(2, 1, 4) = 1;
  return t_L;
}
 
inline auto diff_symmetrize() {
 
  FTensor::Index<'i', SPACE_DIM> i;
  FTensor::Index<'j', SPACE_DIM> j;
  FTensor::Index<'k', SPACE_DIM> k;
  FTensor::Index<'l', SPACE_DIM> l;
 
  FTensor::Ddg<double, SPACE_DIM, SPACE_DIM> t_diff;
 
  t_diff(i, j, k, l) = 0;
  t_diff(0, 0, 0, 0) = 1;
  t_diff(1, 1, 1, 1) = 1;
 
  t_diff(1, 0, 1, 0) = 0.5;
  t_diff(1, 0, 0, 1) = 0.5;
 
  t_diff(0, 1, 0, 1) = 0.5;
  t_diff(0, 1, 1, 0) = 0.5;
 
  if constexpr (SPACE_DIM == 3) {
    t_diff(2, 2, 2, 2) = 1;
 
    t_diff(2, 0, 2, 0) = 0.5;
    t_diff(2, 0, 0, 2) = 0.5;
    t_diff(0, 2, 0, 2) = 0.5;
    t_diff(0, 2, 2, 0) = 0.5;
 
    t_diff(2, 1, 2, 1) = 0.5;
    t_diff(2, 1, 1, 2) = 0.5;
    t_diff(1, 2, 1, 2) = 0.5;
    t_diff(1, 2, 2, 1) = 0.5;
  }
 
  return t_diff;
}
 
template <class T> struct TensorTypeExtractor {
  typedef typename std::remove_pointer<T>::type Type;
};
template <class T, int I> struct TensorTypeExtractor<FTensor::PackPtr<T, I>> {
  typedef typename std::remove_pointer<T>::type Type;
};
 
}