Building blocks for stationary elasticity problems (linear elasticity and hyperelasticity) More...

Classes
class	Kaskade::Elastomechanics::ElasticModulus
	Material parameters for isotropic linearly elastic materials. More...

class	Kaskade::Elastomechanics::DetIpm1< dim, Scalar >
	A class for computing determinants and their derivatives. More...

class	Kaskade::Elastomechanics::Pstable
	Numerically stable evaluation of \( (x+1)^p -1 \). More...

class	Kaskade::Elastomechanics::ShiftedInvariants< dim, Scalar >
	A class for shifted invariants of a tensor. More...

class	Kaskade::Elastomechanics::LinearizedGreenLagrangeTensor< Scalar, dim, byValue >
	Linearized (right) Green-Lagrange strain tensor, the workhorse of linear elastomechanics. More...

class	Kaskade::Elastomechanics::GreenLagrangeTensor< Scalar, dim, byValue >
	Full (right) Green-Lagrange strain tensor, the workhorse of hyperelasticity. More...

class	Kaskade::Elastomechanics::SurfaceGreenLagrangeTensor< Scalar, dim, byValue >
	Full (right) Green-Lagrange strain tensor for displacements from dim-1 to dim. More...

class	Kaskade::Elastomechanics::ExtendedGreenLagrangeTensor< Scalar, dim, byValue >
	Full (right) Green-Lagrange strain tensor for displacements from dim-1 to dim. More...

class	Kaskade::Elastomechanics::IsochoricGreenLagrangeTensor< dim, Scalar >
	Isochoric part of the full (right) Green-Lagrange strain tensor, used in compressible hyperelasticity. More...

class	Kaskade::Elastomechanics::StrainView< Displacement, StrainTensor >
	A function view that provides on the fly computed strain tensors of displacemnts. More...

class	Kaskade::Elastomechanics::HyperelasticVariationalFunctional< HyperelasticEnergy, StrainTensor >
	General base class for variational functionals defined in terms of hyperelastic stored energies. More...

class	Kaskade::Elastomechanics::LameNavier< dim_, Scalar_ >
	Convenience class for handling linear elastomechanics. More...

class	Kaskade::Elastomechanics::OrthotropicLameNavier< Scalar, dim >
	Convenience class for handling orthotropic materials in linear elastomechanics. More...

class	Kaskade::Elastomechanics::FirstPiolaKirchhoffStress< HyperelasticEnergy, StrainTensor >
	Represents the first Piola Kirchhoff stress as known in nonlinear elasticity. The Piola-Kirchhoff stress is \( T = F\sigma = (I+u_x) \sigma(u) \). More...

class	Kaskade::Elastomechanics::MaterialLaws::MaterialLawBase< dim_, Scalar_, MaterialLaw >
	Base class for hyperelastic material laws, providing default implementations of the stress and the tangent stiffness tensor \( C \). More...

class	Kaskade::Elastomechanics::MaterialLaws::InvariantsMaterialLaw< Material >
	Adaptor for hyperelastic material laws, providing an easy way to formulate incompressible material laws in terms of the invariants of the Cauchy-Green strain tensor \( C = I+2E\). More...

class	Kaskade::Elastomechanics::MaterialLaws::CompressibleInvariantsMaterialLaw< Material, DeviatoricPenalty >
	Adaptor for hyperelastic material laws, providing an easy way to formulate compressible material laws in terms of the invariants of the isochoric part \( \bar C = C/(det C)^(1/d) \) of the Cauchy-Green strain tensor and a penalization of the deviatoric part \( I_d \). More...

class	Kaskade::Elastomechanics::MaterialLaws::StVenantKirchhoff< dim, Scalar >
	The St. Venant-Kirchhoff material, foundation of linear elastomechanics. More...

class	Kaskade::Elastomechanics::MaterialLaws::OrthotropicLinearMaterial< dim, Scalar >
	Orthotropic linear material law. More...

class	Kaskade::Elastomechanics::MaterialLaws::MooneyRivlin< dimension >
	Mooney-Rivlin material law formulated in terms of the (shifted) invariants \( i_1, i_2, i_3 \) of the doubled Green-Lagrange strain tensor \( 2E \). More...

class	Kaskade::Elastomechanics::MaterialLaws::NeoHookean< dimension >
	Neo-Hookean material law formulated in terms of the shifted invariants \( i_1, i_2, i_3 \) of the doubled Green-Lagrange strain tensor \( 2E \). More...

class	Kaskade::Elastomechanics::MaterialLaws::BlatzKo< dimension >
	Blatz-Ko material law for rubber foams in terms of the shifted invariants \( i_1, i_2, i_3 \) of the doubled Green-Lagrange strain tensor \( 2E \). More...

Functions
template<class Displacement >
auto	Kaskade::Elastomechanics::makeLinearizedGreenLagrangeStrainView (Displacement const &u)
	A convenience function for creating function views for linearized Green-Lagrange strain tensors. More...

template<class Displacement >
auto	Kaskade::Elastomechanics::makeGreenLagrangeStrainView (Displacement const &u)
	A convenience function for creating function views for full Green-Lagrange strain tensors. More...

template<class Real , int dim>
std::array< Dune::FieldVector< Real, dim >, dim >	Kaskade::Elastomechanics::principalDirections (Dune::FieldMatrix< Real, dim, dim > const &A)
	Computes the dim principal directions of the symmetric positive definite tensor A. More...

template<class Function >
double	Kaskade::Elastomechanics::orientationPreservingStepsize (Function const &y, Function const &dy, double epsilon)
	Computes the maximal orientation preserving stepsize. More...

Detailed Description

Building blocks for stationary elasticity problems (linear elasticity and hyperelasticity)

Function Documentation

◆ makeGreenLagrangeStrainView()

template<class Displacement >

auto Kaskade::Elastomechanics::makeGreenLagrangeStrainView ( Displacement const & u )

A convenience function for creating function views for full Green-Lagrange strain tensors.

Definition at line 664 of file elasto.hh.

◆ makeLinearizedGreenLagrangeStrainView()

template<class Displacement >

auto Kaskade::Elastomechanics::makeLinearizedGreenLagrangeStrainView ( Displacement const & u )

A convenience function for creating function views for linearized Green-Lagrange strain tensors.

Definition at line 654 of file elasto.hh.

◆ orientationPreservingStepsize()

template<class Function >

double Kaskade::Elastomechanics::orientationPreservingStepsize	(	Function const &	y,
		Function const &	dy,
		double	epsilon
	)

Computes the maximal orientation preserving stepsize.

Given two FE functions \( y, \delta y \) with \( \det (I+y_x) > 0 \), computes the maximum step size \( \alpha \le 1 \) such that \( \det(I+y_x+\alpha \delta y_x) \ge \epsilon \det (I+y_x) \).

Parameters

epsilon (<1)

Definition at line 734 of file elasto.hh.

◆ principalDirections()

template<class Real , int dim>

std::array< Dune::FieldVector< Real, dim >, dim > Kaskade::Elastomechanics::principalDirections ( Dune::FieldMatrix< Real, dim, dim > const & A )

Computes the dim principal directions of the symmetric positive definite tensor A.

The vectors are orthogonal to each other and have a length of the corresponding eigenvalue.