Implementation of the Neo-Hookean material model.The energy is computed as. More...

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

Inheritance diagram for Ikarus::NeoHookeT< ST >:

Public Types
using	ScalarType = ST

using	StrainMatrix = Eigen::Matrix< ScalarType, worldDimension, worldDimension >

using	StressMatrix = StrainMatrix

using	MaterialImpl = NeoHookeT< ST >
	Type of material implementation. More...

Public Member Functions
constexpr std::string	nameImpl () const noexcept

	NeoHookeT (const LamesFirstParameterAndShearModulus &mpt)
	Constructor for NeoHookeT. More...

template<typename Derived >
ScalarType	storedEnergyImpl (const Eigen::MatrixBase< Derived > &C) const noexcept
	Computes the stored energy in the Neo-Hookean material model. More...

template<bool voigt, typename Derived >
auto	stressesImpl (const Eigen::MatrixBase< Derived > &C) const
	Computes the stresses in the Neo-Hookean material model. More...

template<bool voigt, typename Derived >
auto	tangentModuliImpl (const Eigen::MatrixBase< Derived > &C) const
	Computes the tangent moduli in the Neo-Hookean material model. More...

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

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

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

constexpr std::string	name () const
	Get the name of 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...

Static Public Attributes
static constexpr int	worldDimension = 3

static constexpr auto	strainTag = StrainTags::rightCauchyGreenTensor

static constexpr auto	stressTag = StressTags::PK2

static constexpr auto	tangentModuliTag = TangentModuliTags::Material

static constexpr bool	energyAcceptsVoigt = false

static constexpr bool	stressToVoigt = false

static constexpr bool	stressAcceptsVoigt = false

static constexpr bool	moduliToVoigt = false

static constexpr bool	moduliAcceptsVoigt = false

static constexpr double	derivativeFactor = 2

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

Detailed Description

template<typename ST>
struct Ikarus::NeoHookeT< ST >

\[ \psi(\BC) = \frac{\mu}{2} (\tr \BC-3- 2 \log \sqrt{\det \BC}) + \frac{\lambda}{2} (\log \sqrt{\det \BC})^2 ,\]

where \( \BC \) denotes the right Cauchy-Green strain tensor.

The second Piola-Kirchhoff stresses are computed as

\[ \BS(\BC) =\fracpt{\psi(\BC)}{\BC} = \mu (\BI-\BC^{-1}) + \lambda \log \sqrt{\det \BC} \BC^{-1},\]

and the material tangent moduli are computed as

\[ \BBC(\BC) =\fracpt{^2\psi(\BC)}{\BC^2} = \lambda \BC^{-1} \otimes \BC^{-1} + 2 (\mu- \lambda \log \sqrt{\det \BC} ) \CI,\]

where \( \CI_{IJKL} = \frac{1}{2}({(\BC^{-1})}^{IK}{(\BC^{-1})}^{JL}+{(\BC^{-1})}^{IL} {(\BC^{-1})}^{JK}).\)

Remarks: See [1], Section 6.4.3 for a discussion of this material

Template Parameters

ST	The scalar type for the strains and stresses,....

Member Typedef Documentation

◆ MaterialImpl

using Ikarus::Material< NeoHookeT< ST > >::MaterialImpl = NeoHookeT< ST >

inherited

◆ ScalarType

template<typename ST >

using Ikarus::NeoHookeT< ST >::ScalarType = ST

◆ StrainMatrix

template<typename ST >

using Ikarus::NeoHookeT< ST >::StrainMatrix = Eigen::Matrix<ScalarType, worldDimension, worldDimension>

◆ StressMatrix

template<typename ST >

using Ikarus::NeoHookeT< ST >::StressMatrix = StrainMatrix

Constructor & Destructor Documentation

◆ NeoHookeT()

template<typename ST >

Ikarus::NeoHookeT< ST >::NeoHookeT ( const LamesFirstParameterAndShearModulus & mpt )

inlineexplicit

Parameters

mpt	The Lame's parameters (first parameter and shear modulus).

Member Function Documentation

◆ impl() [1/2]

constexpr MaterialImpl & Ikarus::Material< NeoHookeT< ST > >::impl ( )

inlineconstexprinherited

Returns: Reference to the underlying material.

◆ impl() [2/2]

constexpr const MaterialImpl & Ikarus::Material< NeoHookeT< ST > >::impl ( ) const

inlineconstexprinherited

Returns: Const reference to the underlying material.

◆ name()

constexpr std::string Ikarus::Material< NeoHookeT< ST > >::name ( ) const

inlineconstexprinherited

Returns: Name of the material.

◆ nameImpl()

template<typename ST >

constexpr std::string Ikarus::NeoHookeT< ST >::nameImpl ( ) const

inlineconstexprnoexcept

◆ rebind()

template<typename ST >

template<typename STO >

auto Ikarus::NeoHookeT< ST >::rebind ( ) const

inline

Template Parameters

STO	The target scalar type.

Returns: NeoHookeT<ScalarTypeOther> The rebound NeoHooke material.

◆ storedEnergy()

auto Ikarus::Material< NeoHookeT< ST > >::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<typename ST >

template<typename Derived >

ScalarType Ikarus::NeoHookeT< ST >::storedEnergyImpl ( const Eigen::MatrixBase< Derived > & C ) const

inlinenoexcept

Template Parameters

Derived The derived type of the input matrix.

Parameters

C	The right Cauchy-Green tensor.

Returns: ScalarType The stored energy.

◆ stresses()

auto Ikarus::Material< NeoHookeT< ST > >::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<typename ST >

template<bool voigt, typename Derived >

auto Ikarus::NeoHookeT< ST >::stressesImpl ( const Eigen::MatrixBase< Derived > & C ) const

inline

Template Parameters

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

Parameters

C	The right Cauchy-Green tensor.

Returns: StressMatrix The stresses.

◆ tangentModuli()

auto Ikarus::Material< NeoHookeT< ST > >::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<typename ST >

template<bool voigt, typename Derived >

auto Ikarus::NeoHookeT< ST >::tangentModuliImpl ( const Eigen::MatrixBase< Derived > & C ) 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

C	The right Cauchy-Green tensor.

Returns: Eigen::TensorFixedSize<ScalarType, Eigen::Sizes<3, 3, 3, 3>> The tangent moduli.

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

neohooke.hh

Public Types

Public Member Functions

Static Public Attributes

Detailed Description

Member Typedef Documentation

◆ MaterialImpl

◆ ScalarType

◆ StrainMatrix

◆ StressMatrix

Constructor & Destructor Documentation

◆ NeoHookeT()

Member Function Documentation

◆ impl() [1/2]

◆ impl() [2/2]

◆ name()

◆ nameImpl()

◆ rebind()

◆ storedEnergy()

◆ storedEnergyImpl()

◆ stresses()

◆ stressesImpl()

◆ tangentModuli()

◆ tangentModuliImpl()

Member Data Documentation

◆ derivativeFactor

◆ energyAcceptsVoigt

◆ isReduced

◆ moduliAcceptsVoigt

◆ moduliToVoigt

◆ strainTag

◆ stressAcceptsVoigt

◆ stressTag

◆ stressToVoigt

◆ tangentModuliTag

◆ worldDimension