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 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. | |
| tnsr::II< DataVector, Dim > | stress (const tnsr::iJ< DataVector, Dim > &grad_displacement, const tnsr::I< DataVector, Dim > &x) const noexcept |
| Symmmetrize the displacement gradient to compute the strain, then pass it to the constitutive relation. | |
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 [63]) 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.