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< ST >:

Public Types
using	ScalarType = ST

using	Base = StVenantKirchhoffT< ScalarType >

using	field_type = ScalarType

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

using	StressMatrix = StrainMatrix

using	MaterialParameters = typename Base::MaterialParameters

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

Public Member Functions
	LinearElasticityT (const MaterialParameters &mpt)
	Constructor for LinearElasticityT. More...

MaterialParameters	materialParametersImpl () const
	Returns the material parameters stored in the material. 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 STO >
auto	rebind () const
	Rebind 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...

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...

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	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	derivativeFactorImpl = Base::derivativeFactorImpl

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

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

Detailed Description

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

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

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

ST	The scalar type used in the material.

Member Typedef Documentation

◆ Base

template<typename ST >

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

◆ field_type

template<typename ST >

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

◆ MaterialImpl

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

inherited

◆ MaterialParameters

template<typename ST >

using Ikarus::LinearElasticityT< ST >::MaterialParameters = typename Base::MaterialParameters

◆ ScalarType

template<typename ST >

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

◆ StrainMatrix

template<typename ST >

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

◆ StressMatrix

template<typename ST >

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

Constructor & Destructor Documentation

◆ LinearElasticityT()

template<typename ST >

Ikarus::LinearElasticityT< ST >::LinearElasticityT ( const MaterialParameters & mpt )

inlineexplicit

Parameters

mpt	The LamesFirstParameterAndShearModulus object.

Member Function Documentation

◆ impl() [1/2]

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

inlineconstexprinherited

Returns: Reference to the underlying material.

◆ impl() [2/2]

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

inlineconstexprinherited

Returns: Const reference to the underlying material.

◆ materialParameters()

auto Ikarus::Material< LinearElasticityT< ST > >::materialParameters ( ) const

inlineinherited

Returns: Material parameter.

◆ materialParametersImpl()

template<typename ST >

MaterialParameters Ikarus::LinearElasticityT< ST >::materialParametersImpl ( ) const

inline

◆ name()

static constexpr std::string Ikarus::Material< LinearElasticityT< ST > >::name ( )

inlinestaticconstexprinherited

Returns: Name of the material.

◆ nameImpl()

template<typename ST >

static constexpr std::string Ikarus::LinearElasticityT< ST >::nameImpl ( )

inlinestaticconstexprnoexcept

◆ rebind()

template<typename ST >

template<typename STO >

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

inline

Template Parameters

STO	The scalar type to rebind to.

Returns: Rebound material.

◆ storedEnergy()

auto Ikarus::Material< LinearElasticityT< 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::LinearElasticityT< ST >::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.

Here is the caller graph for this function:

◆ stresses()

auto Ikarus::Material< LinearElasticityT< 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::LinearElasticityT< ST >::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< 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::LinearElasticityT< ST >::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

constexpr double Ikarus::Material< LinearElasticityT< ST > >::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<typename ST >

constexpr double Ikarus::LinearElasticityT< ST >::derivativeFactorImpl = Base::derivativeFactorImpl

staticconstexpr

◆ energyAcceptsVoigt

template<typename ST >

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

staticconstexpr

◆ isReduced

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

staticconstexprinherited

◆ moduliAcceptsVoigt

template<typename ST >

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

staticconstexpr

◆ moduliToVoigt

template<typename ST >

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

staticconstexpr

◆ strainTag

template<typename ST >

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

staticconstexpr

◆ stressAcceptsVoigt

template<typename ST >

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

staticconstexpr

◆ stressTag

template<typename ST >

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

staticconstexpr

◆ stressToVoigt

template<typename ST >

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

staticconstexpr

◆ tangentModuliTag

template<typename ST >

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

staticconstexpr

◆ worldDimension

template<typename ST >

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

staticconstexpr

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

linearelasticity.hh

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Detailed Description

Member Typedef Documentation

◆ Base

◆ field_type

◆ MaterialImpl

◆ MaterialParameters

◆ ScalarType

◆ StrainMatrix

◆ StressMatrix

Constructor & Destructor Documentation

◆ LinearElasticityT()

Member Function Documentation

◆ impl() [1/2]

◆ impl() [2/2]

◆ materialParameters()

◆ materialParametersImpl()

◆ name()

◆ nameImpl()

◆ rebind()

◆ storedEnergy()

◆ storedEnergyImpl()

◆ stresses()

◆ stressesImpl()

◆ tangentModuli()

◆ tangentModuliImpl()

Member Data Documentation

◆ derivativeFactor

◆ derivativeFactorImpl

◆ energyAcceptsVoigt

◆ isReduced

◆ moduliAcceptsVoigt

◆ moduliToVoigt

◆ strainTag

◆ stressAcceptsVoigt

◆ stressTag

◆ stressToVoigt

◆ tangentModuliTag

◆ worldDimension