VanishingStrain material model that enforces strain components to be zero. More...

#include <ikarus/finiteelements/mechanics/materials/vanishingstrain.hh>

Inheritance diagram for Ikarus::Materials::VanishingStrain< strainIndexPair, MI >:

Public Types
using	Underlying = MI
	The underlying material type. More...

using	ScalarType = typename Underlying::ScalarType
	Scalar type. More...

using	MaterialParameters = typename Underlying::MaterialParameters

using	StrainMatrix = typename Underlying::StrainMatrix

using	StressMatrix = typename Underlying::StressMatrix

using	MaterialTensor = typename Underlying::MaterialTensor

using	MaterialImpl = VanishingStrain< strainIndexPair, MI >
	Type of material implementation. More...

Public Member Functions
	VanishingStrain (MI mat)
	Constructor for VanishingStrain. More...

MaterialParameters	materialParametersImpl () const
	Returns the material parameters stored in the material. More...

template<typename Derived >
ScalarType	storedEnergyImpl (const Eigen::MatrixBase< Derived > &E) const
	Computes the stored energy for the VanishingStrain material. More...

template<bool voigt, typename Derived >
auto	stressesImpl (const Eigen::MatrixBase< Derived > &E) const
	Computes the stresses for the VanishingStrain material. More...

template<bool voigt, typename Derived >
auto	tangentModuliImpl (const Eigen::MatrixBase< Derived > &E) const
	Computes the tangent moduli for the VanishingStrain material. More...

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

auto &	underlying () const
	Returns a const reference to the underlying material. More...

constexpr const MaterialImpl &	impl () const
	Const accessor to the underlying material (CRTP). More...

constexpr MaterialImpl &	impl ()
	Accessor to the underlying material (CRTP). More...

auto	materialParameters () const
	Returns the material parameters stored in the implemented material. More...

auto	storedEnergy (const Eigen::MatrixBase< Derived > &Eraw) const
	Return the stored potential energy of the material. More...

auto	stresses (const Eigen::MatrixBase< Derived > &Eraw) const
	Get the stresses of the material. More...

auto	tangentModuli (const Eigen::MatrixBase< Derived > &Eraw) const
	Get the tangentModuli of the material. More...

auto	materialInversion (const Eigen::MatrixBase< Derived > &Sraw, const Eigen::MatrixBase< Derived > &EstartRaw=Derived::Zero().eval(), const double tol=1e-12, const int maxIter=20) const
	Computes the corresponding strain measure and inverse material tangent for a given stress state. More...

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

static constexpr std::string	name ()
	Get the name of the implemented material. More...

Static Public Attributes
static constexpr int	dim = Underlying::dim

static constexpr auto	fixedPairs = strainIndexPair
	Array of fixed stress components. More...

static constexpr auto	freeVoigtIndices = Impl::createfreeVoigtIndices(fixedPairs)
	Free Voigt indices. More...

static constexpr auto	fixedVoigtIndices = Impl::createFixedVoigtIndices(fixedPairs)
	Fixed Voigt indices. More...

static constexpr auto	freeStrains = freeVoigtIndices.size()
	Number of free strains. More...

static constexpr auto	strainTag = Underlying::strainTag
	Strain tag. More...

static constexpr auto	stressTag = Underlying::stressTag
	Stress tag. More...

static constexpr auto	tangentModuliTag = Underlying::tangentModuliTag
	Tangent moduli tag. More...

static constexpr bool	energyAcceptsVoigt = Underlying::energyAcceptsVoigt
	Energy accepts Voigt notation. More...

static constexpr bool	stressToVoigt = true
	Stress to Voigt notation. More...

static constexpr bool	stressAcceptsVoigt = true
	Stress accepts Voigt notation. More...

static constexpr bool	moduliToVoigt = true
	Moduli to Voigt notation. More...

static constexpr bool	moduliAcceptsVoigt = true
	Moduli accepts Voigt notation. More...

static constexpr double	derivativeFactorImpl = Underlying::derivativeFactorImpl
	Derivative factor. More...

static constexpr bool	isReduced
	Static constant for determining if the material has vanishing stress or strain components (is reduced). More...

static constexpr bool	isLinear

static constexpr double	derivativeFactor
	This factor denotes the differences between the returned stresses and moduli and the passed strain. More...

Detailed Description

template<auto strainIndexPair, typename MI>
struct Ikarus::Materials::VanishingStrain< strainIndexPair, MI >

Template Parameters

strainIndexPair	An array of MatrixIndexPair representing fixed stress components.
MI	The underlying material model.

Member Typedef Documentation

◆ MaterialImpl

using Ikarus::Materials::Material< VanishingStrain< strainIndexPair, MI > >::MaterialImpl = VanishingStrain< strainIndexPair, MI >

inherited

◆ MaterialParameters

template<auto strainIndexPair, typename MI >

using Ikarus::Materials::VanishingStrain< strainIndexPair, MI >::MaterialParameters = typename Underlying::MaterialParameters

◆ MaterialTensor

template<auto strainIndexPair, typename MI >

using Ikarus::Materials::VanishingStrain< strainIndexPair, MI >::MaterialTensor = typename Underlying::MaterialTensor

◆ ScalarType

template<auto strainIndexPair, typename MI >

using Ikarus::Materials::VanishingStrain< strainIndexPair, MI >::ScalarType = typename Underlying::ScalarType

◆ StrainMatrix

template<auto strainIndexPair, typename MI >

using Ikarus::Materials::VanishingStrain< strainIndexPair, MI >::StrainMatrix = typename Underlying::StrainMatrix

◆ StressMatrix

template<auto strainIndexPair, typename MI >

using Ikarus::Materials::VanishingStrain< strainIndexPair, MI >::StressMatrix = typename Underlying::StressMatrix

◆ Underlying

template<auto strainIndexPair, typename MI >

using Ikarus::Materials::VanishingStrain< strainIndexPair, MI >::Underlying = MI

Constructor & Destructor Documentation

◆ VanishingStrain()

template<auto strainIndexPair, typename MI >

Ikarus::Materials::VanishingStrain< strainIndexPair, MI >::VanishingStrain ( MI mat )

inlineexplicit

Parameters

mat	The underlying material model.

Member Function Documentation

◆ impl() [1/2]

constexpr MaterialImpl & Ikarus::Materials::Material< VanishingStrain< strainIndexPair, MI > >::impl ( )

inlineconstexprinherited

Returns: Reference to the underlying material.

◆ impl() [2/2]

constexpr const MaterialImpl & Ikarus::Materials::Material< VanishingStrain< strainIndexPair, MI > >::impl ( ) const

inlineconstexprinherited

Returns: Const reference to the underlying material.

◆ materialInversion()

auto Ikarus::Materials::Material< VanishingStrain< strainIndexPair, MI > >::materialInversion	(	const Eigen::MatrixBase< Derived > &	Sraw,
		const Eigen::MatrixBase< Derived > &	EstartRaw = `Derived::Zero().eval()`,
		const double	tol = `1e-12`,
		const int	maxIter = `20`
	)		const

inlineinherited

This assumes the existence of a complementary stored energy function $\chi(\BS)$, such that $$ \partial_{\BS} \chi(\BS) := \BE$$. Except for linear materials, this is not just the inverse of the material tangent, but needs the inversion of the materials stored energy function. For SVK and Linear Elasticity, the inverse of $\BC$ is taken. For NeoHooke an analytical solution exists, and for the general hyperelastic framework (and for all materials that don't implement the material inversion, for that a strain energy function exists) a numerical approach is used.

Template Parameters

tag	Strain tag indicating which strain tensor components are expected as result.
voigt	Boolean indicating whether to return Voigt-shaped result.
useNumeric	forces the function to use the generic numerical approach
Derived	the type of the stress matrix

Parameters

Sraw	input stress matrix
EstartRaw	optionally define a starting value for the numerical algorithm (applies only to numerical inversion)
tol	tolerance for the Newton-Raphson solver (applies only to numerical inversion).
maxIter	maximum number of iterations for the Newton-Raphson solver (applies only to numerical inversion).

Returns: pair of inverse material tangent and strain tensor

◆ materialParameters()

auto Ikarus::Materials::Material< VanishingStrain< strainIndexPair, MI > >::materialParameters ( ) const

inlineinherited

Returns: Material parameter.

◆ materialParametersImpl()

template<auto strainIndexPair, typename MI >

MaterialParameters Ikarus::Materials::VanishingStrain< strainIndexPair, MI >::materialParametersImpl ( ) const

inline

◆ name()

static constexpr std::string Ikarus::Materials::Material< VanishingStrain< strainIndexPair, MI > >::name ( )

inlinestaticconstexprinherited

Returns: Name of the material.

◆ nameImpl()

template<auto strainIndexPair, typename MI >

static constexpr std::string Ikarus::Materials::VanishingStrain< strainIndexPair, MI >::nameImpl ( )

inlinestaticconstexprnoexcept

◆ rebind()

template<auto strainIndexPair, typename MI >

template<typename ScalarTypeOther >

auto Ikarus::Materials::VanishingStrain< strainIndexPair, MI >::rebind ( ) const

inline

Template Parameters

ScalarTypeOther The target scalar type.

Returns: VanishingStrain The rebound VanishingStrain material.

◆ storedEnergy()

auto Ikarus::Materials::Material< VanishingStrain< strainIndexPair, MI > >::storedEnergy ( const Eigen::MatrixBase< Derived > & Eraw ) const

inlineinherited

This function return the free Helmholtz energy of the material

Template Parameters

tag	Strain tag indicating which strain tensor components are passed.
Derived	The underlying Eigen type.

Parameters

Eraw	The strain tensor components passed in Voigt notation or matrix notation.

Returns: Scalar return of stored energy.

◆ storedEnergyImpl()

template<auto strainIndexPair, typename MI >

template<typename Derived >

ScalarType Ikarus::Materials::VanishingStrain< strainIndexPair, MI >::storedEnergyImpl ( const Eigen::MatrixBase< Derived > & E ) const

inline

Template Parameters

Derived The derived type of the input matrix.

Parameters

Eraw	The strain mesasure

Returns: ScalarType The stored energy.

◆ stresses()

auto Ikarus::Materials::Material< VanishingStrain< strainIndexPair, MI > >::stresses ( const Eigen::MatrixBase< Derived > & Eraw ) const

inlineinherited

Template Parameters

tag	Strain tag indicating which strain tensor components are passed.
voigt	Boolean indicating whether to return Voigt-shaped result.
Derived	The underlying Eigen type.

Parameters

Eraw	The strain tensor components passed in Voigt notation or matrix notation.

Returns: Vectorial or Matrix return of stresses.

◆ stressesImpl()

template<auto strainIndexPair, typename MI >

template<bool voigt, typename Derived >

auto Ikarus::Materials::VanishingStrain< strainIndexPair, MI >::stressesImpl ( const Eigen::MatrixBase< Derived > & E ) const

inline

Template Parameters

voigt	A boolean indicating whether to return strains in Voigt notation.
Derived	The derived type of the input matrix.

Parameters

Eraw	The Green-Lagrangian strain.

Returns: StressMatrix The strains.

◆ tangentModuli()

auto Ikarus::Materials::Material< VanishingStrain< strainIndexPair, MI > >::tangentModuli ( const Eigen::MatrixBase< Derived > & Eraw ) const

inlineinherited

Template Parameters

tag	Strain tag indicating which strain tensor components are passed.
voigt	Boolean indicating whether to return Voigt-shaped result.
Derived	The underlying Eigen type.

Parameters

Eraw	The strain tensor components passed in Voigt notation or matrix notation.

Returns: Tangent moduli in Voigt notation or as fourth-order tensor.

◆ tangentModuliImpl()

template<auto strainIndexPair, typename MI >

template<bool voigt, typename Derived >

auto Ikarus::Materials::VanishingStrain< strainIndexPair, MI >::tangentModuliImpl ( const Eigen::MatrixBase< Derived > & E ) const

inline

Template Parameters

voigt	A boolean indicating whether to return tangent moduli in Voigt notation.
Derived	The derived type of the input matrix.

Parameters

E	The strain measure.

Returns: TangentModuli The tangent moduli.

◆ underlying()

template<auto strainIndexPair, typename MI >

auto & Ikarus::Materials::VanishingStrain< strainIndexPair, MI >::underlying ( ) const

inline

Member Data Documentation

◆ derivativeFactor

constexpr double Ikarus::Materials::Material< VanishingStrain< strainIndexPair, MI > >::derivativeFactor

staticconstexprinherited

For neoHooke the inserted quantity is $C$ the Green-Lagrangian strain tensor, the function relation between the energy and the stresses is $S = 1 \dfrac{\partial\psi(E)}{\partial E}$. This factor is the pre factor, which is the difference to the actual derivative, which is written here

◆ derivativeFactorImpl

template<auto strainIndexPair, typename MI >

constexpr double Ikarus::Materials::VanishingStrain< strainIndexPair, MI >::derivativeFactorImpl = Underlying::derivativeFactorImpl

staticconstexpr

◆ dim

template<auto strainIndexPair, typename MI >

constexpr int Ikarus::Materials::VanishingStrain< strainIndexPair, MI >::dim = Underlying::dim

staticconstexpr

◆ energyAcceptsVoigt

template<auto strainIndexPair, typename MI >

constexpr bool Ikarus::Materials::VanishingStrain< strainIndexPair, MI >::energyAcceptsVoigt = Underlying::energyAcceptsVoigt

staticconstexpr

◆ fixedPairs

template<auto strainIndexPair, typename MI >

constexpr auto Ikarus::Materials::VanishingStrain< strainIndexPair, MI >::fixedPairs = strainIndexPair

staticconstexpr

◆ fixedVoigtIndices

template<auto strainIndexPair, typename MI >

constexpr auto Ikarus::Materials::VanishingStrain< strainIndexPair, MI >::fixedVoigtIndices = Impl::createFixedVoigtIndices(fixedPairs)

staticconstexpr

◆ freeStrains

template<auto strainIndexPair, typename MI >

constexpr auto Ikarus::Materials::VanishingStrain< strainIndexPair, MI >::freeStrains = freeVoigtIndices.size()

staticconstexpr

◆ freeVoigtIndices

template<auto strainIndexPair, typename MI >

constexpr auto Ikarus::Materials::VanishingStrain< strainIndexPair, MI >::freeVoigtIndices = Impl::createfreeVoigtIndices(fixedPairs)

staticconstexpr

◆ isLinear

constexpr bool Ikarus::Materials::Material< VanishingStrain< strainIndexPair, MI > >::isLinear

staticconstexprinherited

◆ isReduced

constexpr bool Ikarus::Materials::Material< VanishingStrain< strainIndexPair, MI > >::isReduced

staticconstexprinherited

◆ moduliAcceptsVoigt

template<auto strainIndexPair, typename MI >

constexpr bool Ikarus::Materials::VanishingStrain< strainIndexPair, MI >::moduliAcceptsVoigt = true

staticconstexpr

◆ moduliToVoigt

template<auto strainIndexPair, typename MI >

constexpr bool Ikarus::Materials::VanishingStrain< strainIndexPair, MI >::moduliToVoigt = true

staticconstexpr

◆ strainTag

template<auto strainIndexPair, typename MI >

constexpr auto Ikarus::Materials::VanishingStrain< strainIndexPair, MI >::strainTag = Underlying::strainTag

staticconstexpr

◆ stressAcceptsVoigt

template<auto strainIndexPair, typename MI >

constexpr bool Ikarus::Materials::VanishingStrain< strainIndexPair, MI >::stressAcceptsVoigt = true

staticconstexpr

◆ stressTag

template<auto strainIndexPair, typename MI >

constexpr auto Ikarus::Materials::VanishingStrain< strainIndexPair, MI >::stressTag = Underlying::stressTag

staticconstexpr

◆ stressToVoigt

template<auto strainIndexPair, typename MI >

constexpr bool Ikarus::Materials::VanishingStrain< strainIndexPair, MI >::stressToVoigt = true

staticconstexpr

◆ tangentModuliTag

template<auto strainIndexPair, typename MI >

constexpr auto Ikarus::Materials::VanishingStrain< strainIndexPair, MI >::tangentModuliTag = Underlying::tangentModuliTag

staticconstexpr

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

vanishingstrain.hh

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Detailed Description

Member Typedef Documentation

◆ MaterialImpl

◆ MaterialParameters

◆ MaterialTensor

◆ ScalarType

◆ StrainMatrix

◆ StressMatrix

◆ Underlying

Constructor & Destructor Documentation

◆ VanishingStrain()

Member Function Documentation

◆ impl() [1/2]

◆ impl() [2/2]

◆ materialInversion()

◆ materialParameters()

◆ materialParametersImpl()

◆ name()

◆ nameImpl()

◆ rebind()

◆ storedEnergy()

◆ storedEnergyImpl()

◆ stresses()

◆ stressesImpl()

◆ tangentModuli()

◆ tangentModuliImpl()

◆ underlying()

Member Data Documentation

◆ derivativeFactor

◆ derivativeFactorImpl

◆ dim

◆ energyAcceptsVoigt

◆ fixedPairs

◆ fixedVoigtIndices

◆ freeStrains

◆ freeVoigtIndices

◆ isLinear

◆ isReduced

◆ moduliAcceptsVoigt

◆ moduliToVoigt

◆ strainTag

◆ stressAcceptsVoigt

◆ stressTag

◆ stressToVoigt

◆ tangentModuliTag