Implementation of the InvariantBased material model. More...

#include <ikarus/finiteelements/mechanics/materials/hyperelastic/deviatoric/invariantbased.hh>

Public Types
using	ScalarType = ST_

template<typename ST = ScalarType>
using	PrincipalStretches = Eigen::Vector< ST, 3 >

template<typename ST = ScalarType>
using	Invariants = PrincipalStretches< ST >

using	Exponents = std::array< std::size_t, numMatParameters >

using	MaterialParameters = std::array< double, numMatParameters >

template<typename ST = ScalarType>
using	FirstDerivative = Eigen::Vector< ST, dim >

template<typename ST = ScalarType>
using	SecondDerivative = Eigen::Matrix< ST, dim, dim >

Public Member Functions
MaterialParameters	materialParametersImpl () const

const Exponents &	pExponents () const

const Exponents &	qExponents () const

	InvariantBasedT (const Exponents &pex, const Exponents &qex, const MaterialParameters &matParameters)
	Constructor for InvariantBasedT. More...

template<typename ST = ScalarType>
ST	storedEnergyImpl (const PrincipalStretches< ST > &lambda) const
	Computes the stored energy in the InvariantBased material model. More...

template<typename ST = ScalarType>
FirstDerivative< ST >	firstDerivativeImpl (const PrincipalStretches< ST > &lambda) const
	Computes the first derivative of the stored energy function w.r.t. the total principal stretches. More...

template<typename ST = ScalarType>
SecondDerivative< ST >	secondDerivativeImpl (const PrincipalStretches< ST > &lambda) const
	Computes the second derivatives of the stored energy function w.r.t. the total principal stretches. More...

template<typename STO >
auto	rebind () const
	Rebinds the material to a different scalar type. More...

Static Public Member Functions
static constexpr std::string	name () noexcept

Static Public Attributes
static constexpr int	dim = 3

static constexpr int	numMatParameters = n

static constexpr auto	stretchTag = PrincipalStretchTags::deviatoric

Detailed Description

template<typename ST_, int n>
struct Ikarus::Materials::InvariantBasedT< ST_, n >

This is a general model based on deviatoric invariants. It can be used to derive other specific material models, for instance Mooney-Rivlin and Yeoh models. The energy is computed as

\[ \hat{\Psi}(\la_1, \la_2, \la_3) = \sum_{p+q=1}^n{C_{pq} (W_1 - 3)^p (W_2 - 3)^q}, \quad p,q \geq 0. \]

Remarks: See [1] for details on this material. For information on the deviatoric invariants \( W_1, W_2 \), see DeviatoricInvariants.

Template Parameters

ST_	The underlying scalar type.
n	Number of material parameters

Member Typedef Documentation

◆ Exponents

template<typename ST_ , int n>

using Ikarus::Materials::InvariantBasedT< ST_, n >::Exponents = std::array<std::size_t, numMatParameters>

◆ FirstDerivative

template<typename ST_ , int n>

template<typename ST = ScalarType>

using Ikarus::Materials::InvariantBasedT< ST_, n >::FirstDerivative = Eigen::Vector<ST, dim>

◆ Invariants

template<typename ST_ , int n>

template<typename ST = ScalarType>

using Ikarus::Materials::InvariantBasedT< ST_, n >::Invariants = PrincipalStretches<ST>

◆ MaterialParameters

template<typename ST_ , int n>

using Ikarus::Materials::InvariantBasedT< ST_, n >::MaterialParameters = std::array<double, numMatParameters>

◆ PrincipalStretches

template<typename ST_ , int n>

template<typename ST = ScalarType>

using Ikarus::Materials::InvariantBasedT< ST_, n >::PrincipalStretches = Eigen::Vector<ST, 3>

◆ ScalarType

template<typename ST_ , int n>

using Ikarus::Materials::InvariantBasedT< ST_, n >::ScalarType = ST_

◆ SecondDerivative

template<typename ST_ , int n>

template<typename ST = ScalarType>

using Ikarus::Materials::InvariantBasedT< ST_, n >::SecondDerivative = Eigen::Matrix<ST, dim, dim>

Constructor & Destructor Documentation

◆ InvariantBasedT()

template<typename ST_ , int n>

Ikarus::Materials::InvariantBasedT< ST_, n >::InvariantBasedT	(	const Exponents &	pex,
		const Exponents &	qex,
		const MaterialParameters &	matParameters
	)

inlineexplicit

Parameters

pex	Array of exponents related to the first invariant.
qex	Array of exponents related to the second invariant.
matParameters	Array of material parameters.

Member Function Documentation

◆ firstDerivativeImpl()

template<typename ST_ , int n>

template<typename ST = ScalarType>

FirstDerivative< ST > Ikarus::Materials::InvariantBasedT< ST_, n >::firstDerivativeImpl ( const PrincipalStretches< ST > & lambda ) const

inline

Parameters

lambda principal stretches

Template Parameters

ST	the scalartype of the principal stretches

Returns: FirstDerivative the first derivative

◆ materialParametersImpl()

template<typename ST_ , int n>

MaterialParameters Ikarus::Materials::InvariantBasedT< ST_, n >::materialParametersImpl ( ) const

inline

◆ name()

template<typename ST_ , int n>

static constexpr std::string Ikarus::Materials::InvariantBasedT< ST_, n >::name ( )

inlinestaticconstexprnoexcept

◆ pExponents()

template<typename ST_ , int n>

const Exponents & Ikarus::Materials::InvariantBasedT< ST_, n >::pExponents ( ) const

inline

◆ qExponents()

template<typename ST_ , int n>

const Exponents & Ikarus::Materials::InvariantBasedT< ST_, n >::qExponents ( ) const

inline

◆ rebind()

template<typename ST_ , int n>

template<typename STO >

auto Ikarus::Materials::InvariantBasedT< ST_, n >::rebind ( ) const

inline

Template Parameters

STO	The target scalar type.

Returns: InvariantBasedT<ScalarTypeOther> The rebound InvariantBased material.

◆ secondDerivativeImpl()

template<typename ST_ , int n>

template<typename ST = ScalarType>

SecondDerivative< ST > Ikarus::Materials::InvariantBasedT< ST_, n >::secondDerivativeImpl ( const PrincipalStretches< ST > & lambda ) const

inline

Parameters

lambda principal stretches.

Template Parameters

ST	the scalartype of the principal stretches

Returns: SecondDerivative the second derivative

◆ storedEnergyImpl()

template<typename ST_ , int n>

template<typename ST = ScalarType>

ST Ikarus::Materials::InvariantBasedT< ST_, n >::storedEnergyImpl ( const PrincipalStretches< ST > & lambda ) const

inline

Parameters

lambda principal stretches

Template Parameters

ST	the scalartype of the principal stretches

Returns: ScalarType the energy

Member Data Documentation

◆ dim

template<typename ST_ , int n>

constexpr int Ikarus::Materials::InvariantBasedT< ST_, n >::dim = 3

staticconstexpr

◆ numMatParameters

template<typename ST_ , int n>

constexpr int Ikarus::Materials::InvariantBasedT< ST_, n >::numMatParameters = n

staticconstexpr

◆ stretchTag

template<typename ST_ , int n>

constexpr auto Ikarus::Materials::InvariantBasedT< ST_, n >::stretchTag = PrincipalStretchTags::deviatoric

staticconstexpr

The documentation for this struct was generated from the following file:

invariantbased.hh

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Detailed Description

Member Typedef Documentation

◆ Exponents

◆ FirstDerivative

◆ Invariants

◆ MaterialParameters

◆ PrincipalStretches

◆ ScalarType

◆ SecondDerivative

Constructor & Destructor Documentation

◆ InvariantBasedT()

Member Function Documentation

◆ firstDerivativeImpl()

◆ materialParametersImpl()

◆ name()

◆ pExponents()

◆ qExponents()

◆ rebind()

◆ secondDerivativeImpl()

◆ storedEnergyImpl()

Member Data Documentation

◆ dim

◆ numMatParameters

◆ stretchTag