SpECTRE
v2023.01.13
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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 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... | |
void | stress (gsl::not_null< tnsr::IJ< DataVector, Dim > * > stress, const tnsr::ii< DataVector, Dim > &strain, const tnsr::I< DataVector, Dim > &x) const |
The constitutive relation that characterizes the elastic properties of a material. | |
Static Public Attributes | |
static constexpr size_t | volume_dim = Dim |
Base class for constitutive (stress-strain) relations that characterize the elastic properties of a material.
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 [142]) 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.
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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 >.