Elasticity::ConstitutiveRelations::ConstitutiveRelation< Dim > Class Template Reference

Base class for constitutive (stress-strain) relations that characterize the elastic properties of a material. More...

#include <ConstitutiveRelation.hpp>

Public Types
using	creatable_classes = tmpl::list< CubicCrystal, IsotropicHomogeneous< Dim > >

Public Member Functions
	ConstitutiveRelation (const ConstitutiveRelation &)=default
ConstitutiveRelation &	operator= (const ConstitutiveRelation &)=default
	ConstitutiveRelation (ConstitutiveRelation &&)=default
ConstitutiveRelation &	operator= (ConstitutiveRelation &&)=default
	WRAPPED_PUPable_abstract (ConstitutiveRelation)
virtual void	stress (gsl::not_null< tnsr::II< DataVector, Dim > * > stress, const tnsr::ii< DataVector, Dim > &strain, const tnsr::I< DataVector, Dim > &x) const noexcept=0
	The constitutive relation that characterizes the elastic properties of a material. More...
void	stress (gsl::not_null< tnsr::IJ< DataVector, Dim > * > stress, const tnsr::ii< DataVector, Dim > &strain, const tnsr::I< DataVector, Dim > &x) const noexcept
	The constitutive relation that characterizes the elastic properties of a material.

Static Public Attributes
static constexpr size_t	volume_dim = Dim

Detailed Description

template<size_t Dim>
class Elasticity::ConstitutiveRelations::ConstitutiveRelation< Dim >

Base class for constitutive (stress-strain) relations that characterize the elastic properties of a material.

Details

A constitutive relation, in the context of elasticity, relates the Stress \(T^{ij}\) and Strain \(S_{ij}=\nabla_{(i}u_{j)}\) within an elastic material (see Elasticity). For small stresses it is approximated by the linear relation

\[ T^{ij} = -Y^{ijkl}S_{kl} \]

(Eq. 11.17 in [106]) that is referred to as Hooke's law. The constitutive relation in this linear approximation is determined by the elasticity (or Young's) tensor \(Y^{ijkl}=Y^{(ij)(kl)}=Y^{klij}\) that generalizes a simple proportionality to a three-dimensional and (possibly) anisotropic material.

Note

We assume a Euclidean metric in Cartesian coordinates here (for now).

Member Function Documentation

stress()

template<size_t Dim>

virtual void Elasticity::ConstitutiveRelations::ConstitutiveRelation< Dim >::stress ( gsl::not_null< tnsr::II< DataVector, Dim > * >  stress, const tnsr::ii< DataVector, Dim > &  strain, const tnsr::I< DataVector, Dim > &  x  ) const

pure virtualnoexcept

The constitutive relation that characterizes the elastic properties of a material.

Implemented in Elasticity::ConstitutiveRelations::IsotropicHomogeneous< Dim >, Elasticity::ConstitutiveRelations::IsotropicHomogeneous< 2 >, and Elasticity::ConstitutiveRelations::IsotropicHomogeneous< 3 >.