Line data    Source code

       1           0 : // Distributed under the MIT License.
       2             : // See LICENSE.txt for details.
       3             : 
       4             : #pragma once
       5             : 
       6             : #include <cstddef>
       7             : #include <limits>
       8             : #include <memory>
       9             : #include <pup.h>
      10             : 
      11             : #include "DataStructures/Tensor/TypeAliases.hpp"
      12             : #include "Options/String.hpp"
      13             : #include "PointwiseFunctions/Elasticity/ConstitutiveRelations/ConstitutiveRelation.hpp"
      14             : #include "Utilities/Serialization/CharmPupable.hpp"
      15             : #include "Utilities/TMPL.hpp"
      16             : 
      17             : /// \cond
      18             : class DataVector;
      19             : /// \endcond
      20             : 
      21             : namespace Elasticity::ConstitutiveRelations {
      22             : 
      23             : /*!
      24             :  * \brief A cubic crystalline material
      25             :  *
      26             :  * \details For a cubic crystalline material the Elasticity tensor in the linear
      27             :  * constitutive relation \f$T^{ij}=-Y^{ijkl}S_{kl}\f$ reduces to
      28             :  *
      29             :  * \f[
      30             :  * Y^{ijkl} =
      31             :  * \begin{cases}
      32             :  * c_{11} & \mathrm{for}\; i=j=k=l \\
      33             :  * c_{12} & \mathrm{for}\; i=j,k=l,i \neq k \\
      34             :  * c_{44} & \mathrm{for}\; i=k,j=l,i \neq j \;\mathrm{or}\; i=l,j=k,i\neq j \\
      35             :  * \end{cases}
      36             :  * \f]
      37             :  *
      38             :  * with the three independent parameters: the \f$\mathrm{Lam\acute{e}}\f$
      39             :  * parameter \f$\lambda\f$, the Shear modulus \f$\mu\f$ and the %Poisson
      40             :  * ratio \f$\nu\f$. In the parametrization chosen in this implementation we use
      41             :  * the experimental group parameters \f$c_{11}\f$, \f$c_{12}\f$ and
      42             :  * \f$c_{44}\f$, related by;
      43             :  *
      44             :  * \f[
      45             :  * c_{11} = \frac{1 - \nu}{\nu} \lambda = \frac{(1 - \nu)E}{(1 + \nu)(1 -
      46             :  * 2\nu)}, \quad
      47             :  * c_{12} = \lambda = \frac{E\nu}{(1 + \nu)(1 - 2\nu)}, \quad
      48             :  * c_{44} = \mu
      49             :  * \f]
      50             :  *
      51             :  * and inversely;
      52             :  *
      53             :  * \f[
      54             :  * E = \frac{(c_{11} + 2c_{12})(c_{11} - c_{12})}{c_{11} + c_{12}}, \quad
      55             :  * \nu = \left(1 + \frac{c_{11}}{c_{12}}\right)^{-1}, \quad
      56             :  * \mu = c_{44}
      57             :  * \f]
      58             :  *
      59             :  * The stress-strain relation then reduces to
      60             :  *
      61             :  * \f[
      62             :  * T^{ij} =
      63             :  * \begin{cases}
      64             :  * -(c_{11} - c_{12}) S^{ij} - c_{12} \mathrm{Tr}(S) & \mathrm{for}\; i=j \\
      65             :  * -2 c_{44} S^{ij} & \mathrm{for}\; i \neq j \\
      66             :  * \end{cases}
      67             :  * \f]
      68             :  *
      69             :  * In the case where the shear modulus satisfies \f$c_{44} =
      70             :  * \frac{c_{11}-c_{12}}{2}\f$ the constitutive relation is that of an isotropic
      71             :  * material (see `Elasticity::ConstitutiveRelations::IsotropicHomogeneous`).
      72             :  */
      73             : 
      74           1 : class CubicCrystal : public ConstitutiveRelation<3> {
      75             :  public:
      76           0 :   static constexpr size_t volume_dim = 3;
      77             : 
      78           0 :   struct C_11 {
      79           0 :     using type = double;
      80           0 :     static constexpr Options::String help = {
      81             :         "c_11 parameter for a cubic crystal"};
      82           0 :     static type lower_bound() { return 0.0; }
      83             :   };
      84             : 
      85           0 :   struct C_12 {
      86           0 :     using type = double;
      87           0 :     static constexpr Options::String help = {
      88             :         "c_12 parameter for a cubic crystal"};
      89           0 :     static type lower_bound() { return 0.0; }
      90             :   };
      91             : 
      92           0 :   struct C_44 {
      93           0 :     using type = double;
      94           0 :     static constexpr Options::String help = {
      95             :         "c_44 parameter for a cubic crystal"};
      96           0 :     static type lower_bound() { return 0.0; }
      97             :   };
      98             : 
      99           0 :   using options = tmpl::list<C_11, C_12, C_44>;
     100             : 
     101           0 :   static constexpr Options::String help = {
     102             :       "A constitutive relation that describes a cubic, crystalline material in "
     103             :       "terms of the three independent group paremeters. The parameters "
     104             :       "are measured in units of stress, typically Pascals."};
     105             : 
     106           0 :   CubicCrystal() = default;
     107           0 :   CubicCrystal(const CubicCrystal&) = default;
     108           0 :   CubicCrystal& operator=(const CubicCrystal&) = default;
     109           0 :   CubicCrystal(CubicCrystal&&) = default;
     110           0 :   CubicCrystal& operator=(CubicCrystal&&) = default;
     111           0 :   ~CubicCrystal() override = default;
     112             : 
     113           0 :   CubicCrystal(double c_11, double c_12, double c_44);
     114             : 
     115           1 :   std::unique_ptr<ConstitutiveRelation<3>> get_clone() const override;
     116             : 
     117             :   /// The constitutive relation that characterizes the elastic properties of a
     118             :   /// material
     119           1 :   void stress(gsl::not_null<tnsr::II<DataVector, 3>*> stress,
     120             :               const tnsr::ii<DataVector, 3>& strain,
     121             :               const tnsr::I<DataVector, 3>& x) const override;
     122             : 
     123             :   /// The 1st group parameter \f$c_{11} = \frac{1 - \nu}{\nu} \lambda\f$
     124           1 :   double c_11() const;
     125             :   /// The 2nd group parameter; the \f$\mathrm{Lam\acute{e}}\f$ parameter
     126             :   /// \f$c_{12} = \lambda\f$
     127           1 :   double c_12() const;
     128             :   /// The 3rd group parameter; the shear modulus (rigidity) \f$c_{44} = \mu\f$
     129           1 :   double c_44() const;
     130             :   /// The Young's modulus \f$E\f$
     131           1 :   double youngs_modulus() const;
     132             :   /// The %Poisson ratio \f$\nu\f$
     133           1 :   double poisson_ratio() const;
     134             : 
     135             :   // clang-tidy: no runtime references
     136           0 :   void pup(PUP::er& /*p*/) override;  //  NOLINT
     137             : 
     138           0 :   explicit CubicCrystal(CkMigrateMessage* /*unused*/) {}
     139             : 
     140           0 :   WRAPPED_PUPable_decl_base_template(  // NOLINT
     141             :       SINGLE_ARG(ConstitutiveRelation<3>), CubicCrystal);
     142             : 
     143             :  private:
     144           0 :   double c_11_ = std::numeric_limits<double>::signaling_NaN();
     145           0 :   double c_12_ = std::numeric_limits<double>::signaling_NaN();
     146           0 :   double c_44_ = std::numeric_limits<double>::signaling_NaN();
     147             : };  // namespace ConstitutiveRelations
     148             : 
     149           0 : bool operator==(const CubicCrystal& lhs, const CubicCrystal& rhs);
     150           0 : bool operator!=(const CubicCrystal& lhs, const CubicCrystal& rhs);
     151             : 
     152             : }  // namespace Elasticity::ConstitutiveRelations