Elastomechanics

Predefined standard differential operators and material laws to be used as building blocks for elastomechanics problems. More...

Modules
	Stationary elasticity
	Building blocks for stationary elasticity problems (linear elasticity and hyperelasticity)
	Viscoplasticity
	Building blocks for viscoplastic problems.
	Contact Problems
	Components for defining elastomechanical contact problems.

Namespaces
namespace	Kaskade::Elastomechanics::MaterialLaws
	A namespace containing various material laws.

Classes
class	Kaskade::Elastomechanics::ShellKinematicsDerivative< dim, Real >
	A lower-dimensional kinematics ansatz useful for shell models. More...
class	Kaskade::Elastomechanics::ShellKinematics< dim, Real >
	A lower-dimensional kinematics ansatz useful for shell models. More...
class	Kaskade::Elastomechanics::ShellEnergy< Energy, Real >
	A stored energy density class for Taylor-based shell models. More...

Functions
template<class Scalar , int n>
Dune::FieldVector< Scalar, n *(n+1)/2 >	Kaskade::Elastomechanics::pack (Dune::FieldMatrix< Scalar, n, n > const &e, Scalar s=2.0)
	Returns the Voigt vector representation of a symmetric matrix (with or without doubled off-diagonal entries). More...
template<class Scalar , int n>
Dune::FieldMatrix< Scalar, ElastoDetails::dim(n), ElastoDetails::dim(n)>	Kaskade::Elastomechanics::unpack (Dune::FieldVector< Scalar, n > const &c, Scalar s=2.0)
	Returns the symmetric matrix representation of a Voigt vector with or without doubled off-diagonal entries. More...
template<int d, class Scalar >
Dune::FieldMatrix< Scalar, d, d >	Kaskade::Elastomechanics::deviatoricPart (Dune::FieldMatrix< Scalar, d, d > const &s)
	The deviatoric part of a tensor. More...

Detailed Description

Predefined standard differential operators and material laws to be used as building blocks for elastomechanics problems.

Function Documentation

deviatoricPart()

template<int d, class Scalar >

Dune::FieldMatrix< Scalar, d, d > Kaskade::Elastomechanics::deviatoricPart

(

Dune::FieldMatrix< Scalar, d, d > const &

s

)

The deviatoric part of a tensor.

This computes the deviatoric part \( \mathrm{dev}(s) = s - \frac{I_1}{d} I \) of the tensor \( s \), where \( I_1 = \mathrm{tr}(s) \) is the first invariant.

Definition at line 173 of file elasto.hh.

pack()

template<class Scalar , int n>

Dune::FieldVector< Scalar, n *(n+1)/2 > Kaskade::Elastomechanics::pack	(	Dune::FieldMatrix< Scalar, n, n > const &	e,
		Scalar	s = 2.0
	)

Returns the Voigt vector representation of a symmetric matrix (with or without doubled off-diagonal entries).

The result is

\[ \begin{bmatrix} a_{11} & a_{12} \\ * & a_{22} \end{bmatrix} \rightarrow \begin{bmatrix} a_{11} \\ a_{22} \\ s a_{12} \end{bmatrix}, \qquad \begin{bmatrix} a_{11} & a_{12} & a_{13} \\ * & a_{22} & a_{23} \\ * & * & a_{33} \end{bmatrix} \rightarrow \begin{bmatrix} a_{11} \\ a_{22} \\ a_{33} \\ sa_{23} \\ s a_{13} \\ sa_{12} \end{bmatrix} \]

Note that traditional Voigt notation treats the doubling of off-diagonal entries differently for stress and strain tensors ( \( s=2\) for strains but \( s=1 \) for stresses, such that \(\sigma:\epsilon = \sigma^T \epsilon\)).

The inverse operation is provided as unpack.

Parameters

e	the symmetric matrix
s	the off-diagonal factor (defaults to 2)

Referenced by Kaskade::Elastomechanics::MaterialLaws::OrthotropicLinearMaterial< dim, Scalar >::d0(), Kaskade::Elastomechanics::MaterialLaws::OrthotropicLinearMaterial< dim, Scalar >::d1(), and Kaskade::Elastomechanics::MaterialLaws::OrthotropicLinearMaterial< dim, Scalar >::d2().

unpack()

template<class Scalar , int n>

Dune::FieldMatrix< Scalar, ElastoDetails::dim(n), ElastoDetails::dim(n)> Kaskade::Elastomechanics::unpack	(	Dune::FieldVector< Scalar, n > const &	c,
		Scalar	s = 2.0
	)

Returns the symmetric matrix representation of a Voigt vector with or without doubled off-diagonal entries.

This is the inverse operation of pack.

Parameters

e	the symmetric matrix
s	the off-diagonal factor (defaults to 2)

Referenced by Kaskade::Elastomechanics::MaterialLaws::MaterialLawBase< dim_, Scalar_, MaterialLaw >::strainToStressMatrix().