Implementation of the Linear Elasticity material model.The energy is computed as. More...

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

Inheritance diagram for Ikarus::LinearElasticityT< ScalarType_ >:

Public Types
using	ScalarType = ScalarType_

using	Base = StVenantKirchhoffT< ScalarType >

using	field_type = ScalarType

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

using	StressMatrix = StrainMatrix

using	MaterialImplType = LinearElasticityT< ScalarType_ >
	Type of material implementation. More...

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

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

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

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

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

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

constexpr const LinearElasticityT< ScalarType_ > &	impl () const
	Const accessor to the underlying material (CRTP). More...

constexpr LinearElasticityT< ScalarType_ > &	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...

Public Attributes
StVenantKirchhoffT< ScalarType >	svk

Static Public Attributes
static constexpr int	worldDimension = 3

static constexpr auto	strainTag = StrainTags::linear

static constexpr auto	stressTag = StressTags::linear

static constexpr auto	tangentModuliTag = TangentModuliTags::Material

static constexpr bool	energyAcceptsVoigt = Base::energyAcceptsVoigt

static constexpr bool	stressToVoigt = Base::stressToVoigt

static constexpr bool	stressAcceptsVoigt = Base::stressAcceptsVoigt

static constexpr bool	moduliToVoigt = Base::moduliToVoigt

static constexpr bool	moduliAcceptsVoigt = Base::moduliAcceptsVoigt

static constexpr double	derivativeFactor = 1

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

Detailed Description

template<typename ScalarType_>
struct Ikarus::LinearElasticityT< ScalarType_ >

\[ \psi(\Bvep) = \frac{\lambda}{2} (\tr \Bvep)^2 +\mu \tr (\Bvep^2) ,\]

where \( \Bvep \) denotes the linear strain tensor.

The second Piola-Kirchhoff stresses are computed as

\[ \BS(\Bvep) =\fracpt{\psi(\Bvep)}{\Bvep} = \lambda \tr \Bvep \BI +2 \mu \Bvep,\]

and the material tangent moduli are computed as

\[ \BBC(\Bvep) =\fracpt{^2\psi(\Bvep)}{\Bvep^2} = \lambda \tr \Bvep \CI +2 \mu \CI^{\mathrm{sym}},\]

where \( \CI_{IJKL} = \de_{IJ}\de_{KL}\) and \( \CI_{IJKL}^\mathrm{sym} = \frac{1}{2}(\de_{IK}\de_{JL}+ \de_{IL}\de_{JK})\).

Template Parameters

ScalarType_ The scalar type used in the material.

Member Typedef Documentation

◆ Base

template<typename ScalarType_ >

using Ikarus::LinearElasticityT< ScalarType_ >::Base = StVenantKirchhoffT<ScalarType>

◆ field_type

template<typename ScalarType_ >

using Ikarus::LinearElasticityT< ScalarType_ >::field_type = ScalarType

◆ MaterialImplType

using Ikarus::Material< LinearElasticityT< ScalarType_ > >::MaterialImplType = LinearElasticityT< ScalarType_ >

inherited

◆ ScalarType

template<typename ScalarType_ >

using Ikarus::LinearElasticityT< ScalarType_ >::ScalarType = ScalarType_

◆ StrainMatrix

template<typename ScalarType_ >

using Ikarus::LinearElasticityT< ScalarType_ >::StrainMatrix = Eigen::Matrix<ScalarType, worldDimension, worldDimension>

◆ StressMatrix

template<typename ScalarType_ >

using Ikarus::LinearElasticityT< ScalarType_ >::StressMatrix = StrainMatrix

Constructor & Destructor Documentation

◆ LinearElasticityT()

template<typename ScalarType_ >

Ikarus::LinearElasticityT< ScalarType_ >::LinearElasticityT ( const LamesFirstParameterAndShearModulus & mpt )

inlineexplicit

Parameters

mpt	The LamesFirstParameterAndShearModulus object.

Member Function Documentation

◆ impl() [1/2]

constexpr LinearElasticityT< ScalarType_ > & Ikarus::Material< LinearElasticityT< ScalarType_ > >::impl ( )

inlineconstexprinherited

Returns: Reference to the underlying material.

◆ impl() [2/2]

constexpr const LinearElasticityT< ScalarType_ > & Ikarus::Material< LinearElasticityT< ScalarType_ > >::impl ( ) const

inlineconstexprinherited

Returns: Const reference to the underlying material.

◆ name()

constexpr std::string Ikarus::Material< LinearElasticityT< ScalarType_ > >::name ( ) const

inlineconstexprinherited

Returns: Name of the material.

◆ nameImpl()

template<typename ScalarType_ >

constexpr std::string Ikarus::LinearElasticityT< ScalarType_ >::nameImpl ( ) const

inlineconstexprnoexcept

◆ rebind()

template<typename ScalarType_ >

template<typename ScalarTypeOther >

auto Ikarus::LinearElasticityT< ScalarType_ >::rebind ( ) const

inline

Template Parameters

ScalarTypeOther The scalar type to rebind to.

Returns: Rebound material.

◆ storedEnergy()

auto Ikarus::Material< LinearElasticityT< ScalarType_ > >::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 ScalarType_ >

template<typename Derived >

ScalarType Ikarus::LinearElasticityT< ScalarType_ >::storedEnergyImpl ( const Eigen::MatrixBase< Derived > & E ) const

inline

Template Parameters

Derived The underlying Eigen type.

Parameters

E	The strain tensor components.

Returns: Scalar return of stored energy.

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◆ stresses()

auto Ikarus::Material< LinearElasticityT< ScalarType_ > >::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 ScalarType_ >

template<bool voigt, typename Derived >

auto Ikarus::LinearElasticityT< ScalarType_ >::stressesImpl ( const Eigen::MatrixBase< Derived > & E ) const

inline

Template Parameters

voigt	Boolean indicating whether to return Voigt-shaped result.
Derived	The underlying Eigen type.

Parameters

E	The strain tensor components.

Returns: Matrix valued return of stresses.

◆ tangentModuli()

auto Ikarus::Material< LinearElasticityT< ScalarType_ > >::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 ScalarType_ >

template<bool voigt, typename Derived >

auto Ikarus::LinearElasticityT< ScalarType_ >::tangentModuliImpl ( const Eigen::MatrixBase< Derived > & E ) const

inline

Template Parameters

voigt	Boolean indicating whether to return Voigt-shaped result.
Derived	The underlying Eigen type.

Parameters

E	The strain tensor components.

Returns: Tangent moduli as fourth-order tensor.

Member Data Documentation

◆ derivativeFactor

template<typename ScalarType_ >

constexpr double Ikarus::LinearElasticityT< ScalarType_ >::derivativeFactor = 1

staticconstexpr

◆ energyAcceptsVoigt

template<typename ScalarType_ >

constexpr bool Ikarus::LinearElasticityT< ScalarType_ >::energyAcceptsVoigt = Base::energyAcceptsVoigt

staticconstexpr

◆ isReduced

constexpr bool Ikarus::Material< LinearElasticityT< ScalarType_ > >::isReduced

staticconstexprinherited

◆ moduliAcceptsVoigt

template<typename ScalarType_ >

constexpr bool Ikarus::LinearElasticityT< ScalarType_ >::moduliAcceptsVoigt = Base::moduliAcceptsVoigt

staticconstexpr

◆ moduliToVoigt

template<typename ScalarType_ >

constexpr bool Ikarus::LinearElasticityT< ScalarType_ >::moduliToVoigt = Base::moduliToVoigt

staticconstexpr

◆ strainTag

template<typename ScalarType_ >

constexpr auto Ikarus::LinearElasticityT< ScalarType_ >::strainTag = StrainTags::linear

staticconstexpr

◆ stressAcceptsVoigt

template<typename ScalarType_ >

constexpr bool Ikarus::LinearElasticityT< ScalarType_ >::stressAcceptsVoigt = Base::stressAcceptsVoigt

staticconstexpr

◆ stressTag

template<typename ScalarType_ >

constexpr auto Ikarus::LinearElasticityT< ScalarType_ >::stressTag = StressTags::linear

staticconstexpr

◆ stressToVoigt

template<typename ScalarType_ >

constexpr bool Ikarus::LinearElasticityT< ScalarType_ >::stressToVoigt = Base::stressToVoigt

staticconstexpr

◆ svk

template<typename ScalarType_ >

StVenantKirchhoffT<ScalarType> Ikarus::LinearElasticityT< ScalarType_ >::svk

◆ tangentModuliTag

template<typename ScalarType_ >

constexpr auto Ikarus::LinearElasticityT< ScalarType_ >::tangentModuliTag = TangentModuliTags::Material

staticconstexpr

◆ worldDimension

template<typename ScalarType_ >

constexpr int Ikarus::LinearElasticityT< ScalarType_ >::worldDimension = 3

staticconstexpr

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

linearelasticity.hh

Public Types

Public Member Functions

Public Attributes

Static Public Attributes

Detailed Description

Member Typedef Documentation

◆ Base

◆ field_type

◆ MaterialImplType

◆ ScalarType

◆ StrainMatrix

◆ StressMatrix

Constructor & Destructor Documentation

◆ LinearElasticityT()

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

◆ svk

◆ tangentModuliTag

◆ worldDimension