mandel_notation.h

// Copyright 2024, UChicago Argonne, LLC
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// Software Name: NEML2 -- the New Engineering material Model Library, version 2
// By: Argonne National Laboratory
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#pragma once
 
#include <array>
 
#include "neml2/misc/types.h"
#include "neml2/misc/defaults.h"
 
namespace neml2
{
class Tensor;
 
constexpr std::array<std::array<Size, 3>, 3> mandel_reverse_index{
    std::array<Size, 3>{0, 5, 4}, std::array<Size, 3>{5, 1, 3}, std::array<Size, 3>{4, 3, 2}};
constexpr std::array<std::array<Size, 2>, 6> mandel_index{std::array<Size, 2>{0, 0},
                                                          std::array<Size, 2>{1, 1},
                                                          std::array<Size, 2>{2, 2},
                                                          std::array<Size, 2>{1, 2},
                                                          std::array<Size, 2>{0, 2},
                                                          std::array<Size, 2>{0, 1}};
 
constexpr std::array<std::array<Size, 3>, 3> skew_reverse_index{
    std::array<Size, 3>{0, 2, 1}, std::array<Size, 3>{2, 0, 0}, std::array<Size, 3>{1, 0, 0}};
constexpr std::array<std::array<double, 3>, 3> skew_factor{std::array<double, 3>{0.0, -1.0, 1.0},
                                                           std::array<double, 3>{1.0, 0.0, -1.0},
                                                           std::array<double, 3>{-1.0, 1.0, 0.0}};
 
inline constexpr double
mandel_factor(Size i)
{
  return i < 3 ? 1.0 : sqrt2;
}
 
const Tensor & full_to_mandel_map(const TensorOptions & opt = default_integer_tensor_options());
const Tensor & mandel_to_full_map(const TensorOptions & opt = default_integer_tensor_options());
const Tensor & full_to_mandel_factor(const TensorOptions & opt = default_tensor_options());
const Tensor & mandel_to_full_factor(const TensorOptions & opt = default_tensor_options());
const Tensor & full_to_skew_map(const TensorOptions & opt = default_integer_tensor_options());
const Tensor & skew_to_full_map(const TensorOptions & opt = default_integer_tensor_options());
const Tensor & full_to_skew_factor(const TensorOptions & opt = default_tensor_options());
const Tensor & skew_to_full_factor(const TensorOptions & opt = default_tensor_options());
 
Tensor
full_to_reduced(const Tensor & full, const Tensor & rmap, const Tensor & rfactors, Size dim = 0);
 
Tensor
reduced_to_full(const Tensor & reduced, const Tensor & rmap, const Tensor & rfactors, Size dim = 0);
 
Tensor full_to_mandel(const Tensor & full, Size dim = 0);
 
Tensor mandel_to_full(const Tensor & mandel, Size dim = 0);
 
Tensor full_to_skew(const Tensor & full, Size dim = 0);
 
Tensor skew_to_full(const Tensor & skew, Size dim = 0);
} // namespace neml2