Interface classf or materials. More...

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

Inheritance diagram for Ikarus::Materials::Material< MI >:

Public Types
using	MaterialImpl = MI
	Type of material implementation. More...

Public Member Functions
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...

template<StrainTags tag, typename Derived > requires CorrectStrainSize<MaterialImpl, Derived>
auto	storedEnergy (const Eigen::MatrixBase< Derived > &Eraw) const
	Return the stored potential energy of the material. More...

template<StrainTags tag, bool voigt = true, typename Derived > requires CorrectStrainSize<MaterialImpl, Derived>
auto	stresses (const Eigen::MatrixBase< Derived > &Eraw) const
	Get the stresses of the material. More...

template<StrainTags tag, bool voigt = true, typename Derived > requires CorrectStrainSize<MaterialImpl, Derived>
auto	tangentModuli (const Eigen::MatrixBase< Derived > &Eraw) const
	Get the tangentModuli of the material. More...

template<StrainTags tag, bool voigt = true, bool useNumeric = false, typename Derived > requires CorrectStrainSize<MaterialImpl, Derived>
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...

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

Static Public Member Functions
static constexpr std::string	name ()
	Get the name of the implemented material. More...

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

static constexpr bool	isLinear = MI::strainTag == StrainTags::linear

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

Detailed Description

template<class MI>
struct Ikarus::Materials::Material< MI >

Consider a hyper elastic material with the free Helmholtz energy

\[\require{cases}\psi: \begin{cases}\mathbb{R}^{3\times 3} &\rightarrow \mathbb{R} \\ \BC &\mapsto \psi(\BC) \end{cases}.\]

Then, the value of this potential energy is return by storedEnergy and its first derivative (the stresses) by stresses and the second derivatives (the tangent moduli) by tangentModuli .

The passed strains can be in several formats, i.e., $\BC$ can be the right Cauchy-Green tensor, the deformation gradient $\mathbf{F}$ or linear strains. The current supported tags are given by Ikarus::StrainTags.

Template Parameters

MI	Type of the underlying material implementation.

Member Typedef Documentation

◆ MaterialImpl

template<class MI >

using Ikarus::Materials::Material< MI >::MaterialImpl = MI

Member Function Documentation

◆ impl() [1/2]

template<class MI >

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

inlineconstexpr

Returns: Reference to the underlying material.

◆ impl() [2/2]

template<class MI >

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

inlineconstexpr

Returns: Const reference to the underlying material.

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◆ materialInversion()

template<class MI >

template<StrainTags tag, bool voigt = true, bool useNumeric = false, typename Derived >
requires CorrectStrainSize<MaterialImpl, Derived>

auto Ikarus::Materials::Material< 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

inline

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()

template<class MI >

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

inline

Returns: Material parameter.

◆ name()

template<class MI >

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

inlinestaticconstexpr

Returns: Name of the material.

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◆ rebind()

template<class MI >

template<typename STO >

auto Ikarus::Materials::Material< MI >::rebind ( ) const

inline

Useful for using automatic differentiation.

Template Parameters

STO	The scalar type to rebind to.

Returns: Rebound material.

◆ storedEnergy()

template<class MI >

template<StrainTags tag, typename Derived >
requires CorrectStrainSize<MaterialImpl, Derived>

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

inline

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.

◆ stresses()

template<class MI >

template<StrainTags tag, bool voigt = true, typename Derived >
requires CorrectStrainSize<MaterialImpl, Derived>

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

inline

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.

◆ tangentModuli()

template<class MI >

template<StrainTags tag, bool voigt = true, typename Derived >
requires CorrectStrainSize<MaterialImpl, Derived>

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

inline

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.

Member Data Documentation

◆ derivativeFactor

template<class MI >

constexpr double Ikarus::Materials::Material< MI >::derivativeFactor = MI::derivativeFactorImpl

staticconstexpr

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

◆ isLinear

template<class MI >

constexpr bool Ikarus::Materials::Material< MI >::isLinear = MI::strainTag == StrainTags::linear

staticconstexpr

◆ isReduced

template<class MI >

constexpr bool Ikarus::Materials::Material< MI >::isReduced

staticconstexpr

Initial value:

= traits::isSpecializationNonTypeAndTypes<VanishingStress, MaterialImpl>::value or

traits::isSpecializationNonTypeAndTypes<VanishingStrain, MaterialImpl>::value

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

finiteelements/mechanics/materials/interface.hh

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Detailed Description

Member Typedef Documentation

◆ MaterialImpl

Member Function Documentation

◆ impl() [1/2]

◆ impl() [2/2]

◆ materialInversion()

◆ materialParameters()

◆ name()

◆ rebind()

◆ storedEnergy()

◆ stresses()

◆ tangentModuli()

Member Data Documentation

◆ derivativeFactor

◆ isLinear

◆ isReduced