physicshelper.hh

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// SPDX-FileCopyrightText: 2021-2024 The Ikarus Developers mueller@ibb.uni-stuttgart.de
// SPDX-License-Identifier: LGPL-3.0-or-later
 
#pragma once
#include <dune/common/float_cmp.hh>
 
#include <Eigen/Core>
namespace Ikarus {
 
inline Eigen::Matrix3d planeStressLinearElasticMaterialTangent(double E, double nu) {
  Eigen::Matrix3d C;
  C.setZero();
  C(0, 0) = C(1, 1) = 1;
  C(0, 1) = C(1, 0) = nu;
  C(2, 2)           = (1 - nu) / 2;
  C *= E / (1 - nu * nu);
  return C;
}
 
inline Eigen::Matrix<double, 6, 6> linearElasticMaterialTangent3D(double E, double nu) {
  Eigen::Matrix<double, 6, 6> C;
  C.setZero();
  C(0, 0) = C(1, 1) = C(2, 2) = 1 - nu;
  C(0, 1) = C(1, 0) = C(2, 0) = C(0, 2) = C(1, 2) = C(2, 1) = nu;
  C(3, 3) = C(4, 4) = C(5, 5) = (1 - 2 * nu) / 2;
  C *= E / ((1 + nu) * (1 - 2 * nu));
  return C;
}
 
struct YoungsModulusAndPoissonsRatio
{
  double emodul;
  double nu;
};
 
struct YoungsModulusAndShearModulus
{
  double emodul;
  double mu;
};
 
struct YoungsModulusAndBulkModulus
{
  double emodul;
  double K;
};
 
struct YoungsModulusAndLamesFirstParameter
{
  double emodul;
  double lambda;
};
 
struct BulkModulusAndLamesFirstParameter
{
  double K;
  double lambda;
};
 
struct LamesFirstParameterAndShearModulus
{
  double lambda;
  double mu;
};
 
template <typename MP>
concept MPTuple =
    std::is_same_v<MP, YoungsModulusAndPoissonsRatio> or std::is_same_v<MP, YoungsModulusAndBulkModulus> or
    std::is_same_v<MP, YoungsModulusAndLamesFirstParameter> or std::is_same_v<MP, BulkModulusAndLamesFirstParameter> or
    std::is_same_v<MP, LamesFirstParameterAndShearModulus> or std::is_same_v<MP, YoungsModulusAndShearModulus>;
 
template <typename ValuePair>
struct ConvertLameConstants
{
  constexpr double toLamesFirstParameter()
  requires(!std::is_same_v<ValuePair, YoungsModulusAndLamesFirstParameter> and
           !std::is_same_v<ValuePair, BulkModulusAndLamesFirstParameter> and
           !std::is_same_v<ValuePair, LamesFirstParameterAndShearModulus>)
  {
    if constexpr (std::is_same_v<ValuePair, YoungsModulusAndPoissonsRatio>) {
      const auto& E  = vp_.emodul;
      const auto& nu = vp_.nu;
      return Dune::FloatCmp::eq(nu, 0.5) ? std::numeric_limits<double>::infinity()
                                         : E * nu / ((1.0 + nu) * (1.0 - 2.0 * nu));
    } else if constexpr (std::is_same_v<ValuePair, YoungsModulusAndShearModulus>) {
      const auto& E  = vp_.emodul;
      const auto& mu = vp_.mu;
      return mu * (E - 2.0 * mu) / (3.0 * mu - E);
    } else if constexpr (std::is_same_v<ValuePair, YoungsModulusAndBulkModulus>) {
      const auto& E = vp_.emodul;
      const auto& K = vp_.K;
      return 3.0 * K * (3.0 * K - E) / (9.0 * K - E);
    } else
      assert(false && "Your LameParameter request is not implemented");
  }
 
  constexpr double toBulkModulus()
  requires(!std::is_same_v<ValuePair, YoungsModulusAndBulkModulus> and
           !std::is_same_v<ValuePair, BulkModulusAndLamesFirstParameter>)
  {
    if constexpr (std::is_same_v<ValuePair, YoungsModulusAndPoissonsRatio>) {
      const auto& E  = vp_.emodul;
      const auto& nu = vp_.nu;
      return E / (3.0 * (1.0 - 2.0 * nu));
    } else if constexpr (std::is_same_v<ValuePair, YoungsModulusAndShearModulus>) {
      const auto& E  = vp_.emodul;
      const auto& mu = vp_.mu;
      return E * mu / (3.0 * (3.0 * mu - E));
    } else if constexpr (std::is_same_v<ValuePair, YoungsModulusAndLamesFirstParameter>) {
      const auto& E      = vp_.emodul;
      const auto& lambda = vp_.lambda;
      return (E + 3.0 * lambda + calcR(vp_)) / 6.0;
    } else if constexpr (std::is_same_v<ValuePair, LamesFirstParameterAndShearModulus>) {
      const auto& lambda = vp_.lambda;
      const auto& mu     = vp_.mu;
      return lambda + 2.0 * mu / 3.0;
    } else
      assert(false && "Your LameParameter request is not implemented");
  }
 
  constexpr double toShearModulus()
  requires(!std::is_same_v<ValuePair, YoungsModulusAndShearModulus> and
           !std::is_same_v<ValuePair, LamesFirstParameterAndShearModulus>)
  {
    if constexpr (std::is_same_v<ValuePair, YoungsModulusAndPoissonsRatio>) {
      const auto& E  = vp_.emodul;
      const auto& nu = vp_.nu;
      return E / (2.0 * (1.0 + nu));
    } else if constexpr (std::is_same_v<ValuePair, YoungsModulusAndBulkModulus>) {
      const auto& E = vp_.emodul;
      const auto& K = vp_.K;
      return 3.0 * K * E / (9.0 * K - E);
    } else if constexpr (std::is_same_v<ValuePair, YoungsModulusAndLamesFirstParameter>) {
      const auto& E      = vp_.emodul;
      const auto& lambda = vp_.lambda;
      return (E - 3.0 * lambda + calcR(vp_)) / 4.0;
    } else if constexpr (std::is_same_v<ValuePair, BulkModulusAndLamesFirstParameter>) {
      const auto& K      = vp_.K;
      const auto& lambda = vp_.lambda;
      return 3.0 * (K - lambda) / 2.0;
    } else
      assert(false && "Your LameParameter request is not implemented");
  }
 
  constexpr double toPWaveModulus() {
    if constexpr (std::is_same_v<ValuePair, YoungsModulusAndPoissonsRatio>) {
      const auto& E  = vp_.emodul;
      const auto& nu = vp_.nu;
      return E * (1.0 - nu) / ((1.0 + nu) * (1.0 - 2.0 * nu));
    } else if constexpr (std::is_same_v<ValuePair, YoungsModulusAndShearModulus>) {
      const auto& E  = vp_.emodul;
      const auto& mu = vp_.mu;
      return mu * (4.0 * mu - E) / (3.0 * mu - E);
    } else if constexpr (std::is_same_v<ValuePair, YoungsModulusAndBulkModulus>) {
      const auto& E = vp_.emodul;
      const auto& K = vp_.K;
      return 3.0 * K * (3.0 * K + E) / (9.0 * K - E);
    } else if constexpr (std::is_same_v<ValuePair, YoungsModulusAndLamesFirstParameter>) {
      const auto& E      = vp_.emodul;
      const auto& lambda = vp_.lambda;
      return (E - lambda + calcR(vp_)) / 2.0;
    } else if constexpr (std::is_same_v<ValuePair, BulkModulusAndLamesFirstParameter>) {
      const auto& K      = vp_.K;
      const auto& lambda = vp_.lambda;
      return 3.0 * K - 2.0 * lambda;
    } else if constexpr (std::is_same_v<ValuePair, LamesFirstParameterAndShearModulus>) {
      const auto& lambda = vp_.lambda;
      const auto& mu     = vp_.mu;
      return lambda + 2.0 * mu;
    } else
      assert(false && "Your LameParameter request is not implemented");
  }
 
  constexpr double toPoissonsRatio()
  requires(!std::is_same_v<ValuePair, YoungsModulusAndPoissonsRatio>)
  {
    if constexpr (std::is_same_v<ValuePair, YoungsModulusAndShearModulus>) {
      const auto& E  = vp_.emodul;
      const auto& mu = vp_.mu;
      return E / (2.0 * mu) - 1.0;
    } else if constexpr (std::is_same_v<ValuePair, YoungsModulusAndBulkModulus>) {
      const auto& E = vp_.emodul;
      const auto& K = vp_.K;
      return (3.0 * K - E) / (6.0 * K);
    } else if constexpr (std::is_same_v<ValuePair, YoungsModulusAndLamesFirstParameter>) {
      const auto& E      = vp_.emodul;
      const auto& lambda = vp_.lambda;
      return 2.0 * lambda / (E + lambda + calcR(vp_));
    } else if constexpr (std::is_same_v<ValuePair, BulkModulusAndLamesFirstParameter>) {
      const auto& K      = vp_.K;
      const auto& lambda = vp_.lambda;
      return lambda / (3 * K - lambda);
    } else if constexpr (std::is_same_v<ValuePair, LamesFirstParameterAndShearModulus>) {
      const auto& lambda = vp_.lambda;
      const auto& mu     = vp_.mu;
      return lambda / (2.0 * (lambda + mu));
    } else
      assert(false && "Your LameParameter request is not implemented");
  }
 
  constexpr double toYoungsModulus()
  requires(!std::is_same_v<ValuePair, YoungsModulusAndPoissonsRatio> and
           !std::is_same_v<ValuePair, YoungsModulusAndShearModulus> and
           !std::is_same_v<ValuePair, YoungsModulusAndBulkModulus> and
           !std::is_same_v<ValuePair, YoungsModulusAndLamesFirstParameter>)
  {
    if constexpr (std::is_same_v<ValuePair, BulkModulusAndLamesFirstParameter>) {
      return 9.0 * vp_.K * (vp_.K - vp_.lambda) / (3.0 * vp_.K - vp_.lambda);
    } else if constexpr (std::is_same_v<ValuePair, LamesFirstParameterAndShearModulus>) {
      const auto& lambda = vp_.lambda;
      const auto& mu     = vp_.mu;
      return mu * (3.0 * lambda + 2.0 * mu) / (lambda + mu);
    } else
      assert(false && "Your LameParameter request is not implemented");
  }
 
private:
  friend ConvertLameConstants<YoungsModulusAndPoissonsRatio> convertLameConstants(
      const YoungsModulusAndPoissonsRatio& valuePair);
  friend ConvertLameConstants<YoungsModulusAndShearModulus> convertLameConstants(
      const YoungsModulusAndShearModulus& valuePair);
 
  friend ConvertLameConstants<YoungsModulusAndBulkModulus> convertLameConstants(
      const YoungsModulusAndBulkModulus& valuePair);
 
  friend ConvertLameConstants<LamesFirstParameterAndShearModulus> convertLameConstants(
      const LamesFirstParameterAndShearModulus& valuePair);
 
  friend ConvertLameConstants<BulkModulusAndLamesFirstParameter> convertLameConstants(
      const BulkModulusAndLamesFirstParameter& valuePair);
  ConvertLameConstants(ValuePair&& valuePair)
      : vp_(valuePair) {}
  ConvertLameConstants(const ValuePair& valuePair)
      : vp_(valuePair) {}
 
  double calcR(const YoungsModulusAndLamesFirstParameter& valuePair) {
    const auto& E      = valuePair.emodul;
    const auto& lambda = valuePair.lambda;
    return std::sqrt(E * E + 9 * lambda * lambda + 2 * E * lambda);
  }
  ValuePair vp_;
};
inline ConvertLameConstants<YoungsModulusAndPoissonsRatio> convertLameConstants(
    const YoungsModulusAndPoissonsRatio& valuePair) {
  return {valuePair};
}
inline ConvertLameConstants<YoungsModulusAndShearModulus> convertLameConstants(
    const YoungsModulusAndShearModulus& valuePair) {
  return {valuePair};
}
inline ConvertLameConstants<YoungsModulusAndBulkModulus> convertLameConstants(
    const YoungsModulusAndBulkModulus& valuePair) {
  return {valuePair};
}
inline ConvertLameConstants<LamesFirstParameterAndShearModulus> convertLameConstants(
    const LamesFirstParameterAndShearModulus& valuePair) {
  return {valuePair};
}
inline ConvertLameConstants<BulkModulusAndLamesFirstParameter> convertLameConstants(
    const BulkModulusAndLamesFirstParameter& valuePair) {
  return {valuePair};
}
 
inline auto toLamesFirstParameterAndShearModulus(const YoungsModulusAndPoissonsRatio& matParameter) {
  auto lambda = convertLameConstants(matParameter).toLamesFirstParameter();
  auto mu     = convertLameConstants(matParameter).toShearModulus();
 
  return LamesFirstParameterAndShearModulus{.lambda = lambda, .mu = mu};
}
 
inline auto toYoungsModulusAndPoissonsRatio(const LamesFirstParameterAndShearModulus& matParameter) {
  auto emod = convertLameConstants(matParameter).toYoungsModulus();
  auto nu   = convertLameConstants(matParameter).toPoissonsRatio();
 
  return YoungsModulusAndPoissonsRatio{.emodul = emod, .nu = nu};
}
 
} // namespace Ikarus