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

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 |

class Elasticity::ConstitutiveRelations::ConstitutiveRelation< 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.

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

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

- src/PointwiseFunctions/Elasticity/ConstitutiveRelations/ConstitutiveRelation.hpp
- src/PointwiseFunctions/Elasticity/ConstitutiveRelations/ConstitutiveRelation.cpp

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