Equation_Navier_Cauchy.h

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#ifndef Equation_Navier_Cauchy_included
#define Equation_Navier_Cauchy_included
 
#include <Operateur_Diff.h>
#include <Equation_base.h>
#include <Milieu_Elasticite.h>
#include <TRUST_Ref.h>
 
class Milieu_Elasticite;
 
/*! @brief Navier–Cauchy equation for small-strain linear elasticity.
 *
 *  Solves for the displacement field \f$\mathbf{u}\f$ of an isotropic linear elastic solid.
 *
 *  Governing equations (optionally including thermal expansion and body forces):
 *  - Balance of momentum:
 *    \f$\rho\,\ddot{\mathbf{u}} = \nabla\cdot\boldsymbol{\sigma} - 3K\alpha\,\nabla(\Delta T) + \mathbf{b}\f$
 *  - Small-strain tensor:
 *    \f$\boldsymbol{\varepsilon}=\tfrac12(\nabla\mathbf{u} + (\nabla\mathbf{u})^T)\f$
 *  - Isotropic Hooke’s law:
 *    \f$\boldsymbol{\sigma} = \mu\,(\nabla\mathbf{u}+ (\nabla\mathbf{u})^T) + \lambda\,(\nabla\cdot\mathbf{u})\,\mathbf{I}\f$
 *
 *  The Lamé parameters \f$\lambda\f$ and \f$\mu\f$, the bulk modulus \f$K\f$ and the thermal expansion
 *  coefficient \f$\alpha\f$ are provided by `Milieu_Elasticite`.
 *
 *  The operator `terme_diffusif` represents the whole divergence term
 *  \f$\nabla\cdot(\mu(\nabla\mathbf{u}+\nabla\mathbf{u}^T)+\lambda(\nabla\cdot\mathbf{u})\mathbf{I})\f$,
 *  including the volumetric contribution (\f$\lambda\f$, sometimes referred to as a “volumetric viscosity”
 *  in diffusion-like operator form).
 *
 *  Post-processing fields may be created/updated, depending on the discretization and options:
 *  stresses, strains, von Mises equivalent stress, and (when needed) nodal velocity.
 */
class Equation_Navier_Cauchy : public Equation_base
{
  Declare_instanciable(Equation_Navier_Cauchy);
 
public:
 
  int nombre_d_operateurs() const override { return 1; }
  const Operateur& operateur(int) const override;
  Operateur& operateur(int) override;
 
  const Champ_Inc_base& inconnue() const override { return deplacement_; }
  Champ_Inc_base& inconnue() override  { return deplacement_; }
  void mettre_a_jour(double temps) override;
 
  void associer_milieu_base(const Milieu_base&) override;
  const Milieu_base& milieu() const override { return milieu_.valeur(); }
  Milieu_base& milieu() override { return milieu_.valeur(); }
  void discretiser() override;
  void set_param(Param& param) const override;
  int lire_motcle_non_standard(const Motcle& mot, Entree& is) override;
  virtual const Champ_Don_base& diffusivite_pour_transport() const { return milieu_->mu_lame(); }
  virtual const Champ_base& diffusivite_pour_pas_de_temps() const { return milieu_->mu_lame(); }
  const Motcle& domaine_application() const override;
  void valider_iteration() override;
 
private:
  void update_velocity();
 
  Operateur_Diff terme_diffusif;
  OWN_PTR(Champ_Inc_base) deplacement_;
  OBS_PTR(Milieu_Elasticite) milieu_;
  OWN_PTR(Champ_Fonc_base) von_mises_, contraintes_, deformations_, vitesse_noeuds_;
};
 
#endif