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

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 $S_{ij}={\mathrm{\nabla }}_{(i}{u}_{j)}$ 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 [194]) 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

get_clone()

template<size_t Dim>

virtual std::unique_ptr< ConstitutiveRelation< Dim > > Elasticity::ConstitutiveRelations::ConstitutiveRelation< Dim >::get_clone ( ) const

pure virtual

Returns a std::unique_ptr pointing to a copy of the ConstitutiveRelation.

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

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 virtual

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 >.

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The documentation for this class was generated from the following file:

• src/PointwiseFunctions/Elasticity/ConstitutiveRelations/ConstitutiveRelation.hpp