Classes
struct	ArrudaBoyceT
	Implementation of the ArrudaBoyce material model (also referred as Eight-Chain model). More...

struct	BlatzKoT
	Implementation of the Blatz-Ko material model. More...

struct	Deviatoric
	This is the interface implementation for the deviatoric part of a hyperelastic material. It is intended to be used with the hyperelastic material model. More...

struct	DeviatoricInvariants
	Implementation of the deviatoric invariants and its derivatives. More...

struct	GentT
	Implementation of the Gent material model. More...

struct	Hyperelastic
	Implementation of a general Hyperelastic Material material model. More...

struct	InvariantBasedT
	Implementation of the InvariantBased material model. More...

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

struct	Material
	Interface classf or materials. More...

struct	MatrixIndexPair
	Represents a pair of stress or strain matrix indices (row and column). More...

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

struct	OgdenT
	Implementation of the Ogden material model. More...

struct	StVenantKirchhoffT
	Implementation of the Saint Venant-Kirchhoff material model.The energy is computed as. More...

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

struct	VanishingStress
	VanishingStress material model that enforces stress components to be zero. More...

struct	VF0
	Default volumetric function. More...

struct	VF1
	Volumetric function No. 1 found in [5] Tab. 4. More...

struct	VF10
	Volumetric function No. 10 found in [5] Tab. 4. More...

struct	VF11
	Volumetric function No. 11 found in [5] Tab. 4. More...

struct	VF2
	Volumetric function No. 2 found in [5] Tab. 4. More...

struct	VF3
	Volumetric function No. 3 found in [5] Tab. 4. More...

struct	VF4
	Volumetric function No. 4 found in [5] Tab. 4. More...

struct	VF5
	Volumetric function No. 5 found in [5] Tab. 4. More...

struct	VF6
	Volumetric function No. 6 found in [5] Tab. 4. More...

struct	VF7
	Volumetric function No. 7 found in [5] Tab. 4. More...

struct	VF8
	Volumetric function No. 8 found in [5] Tab. 4. More...

struct	VF9
	Volumetric function No. 9 found in [5] Tab. 4. More...

struct	Volumetric
	Interface for the volumetric part of a hyperelastic material. Has to be parametrized with a volumetric function. More...

Concepts
concept	CorrectStrainSize
	Template concept for ensuring correct strain size.

Typedefs
using	ArrudaBoyce = ArrudaBoyceT< double >
	Alias for ArrudaBoyceT with double as the default scalar type. More...

using	BlatzKo = BlatzKoT< double >
	Alias for BlatzKoT with double as the default scalar type. More...

using	Gent = GentT< double >
	Alias for GentT with double as the default scalar type. More...

template<int n>
using	InvariantBased = InvariantBasedT< double, n >
	Alias for InvariantBasedT with double as the default scalar type. More...

template<int n, PrincipalStretchTags tag>
using	Ogden = OgdenT< double, n, tag >
	Alias for OgdenT with double as the default scalar type. More...

using	NeoHooke = NeoHookeT< double >
	Alias for NeoHookeT with double as the default scalar type. More...

using	NoVolumetricPart = Volumetric< VF0 >

using	LinearElasticity = LinearElasticityT< double >
	Convenience typedef for LinearElasticity with double as ScalarType. More...

using	StVenantKirchhoff = StVenantKirchhoffT< double >
	Alias for StVenantKirchhoffT with double as the default scalar type. More...

Functions
auto	makeBlatzKo (double mu)
	A helper function to create a hyperelastic material model, where the deviatoric part is according to the Blatz-Ko model. More...

template<int n, PrincipalStretchTags tag, typename VolumetricFunction = VF0>
auto	makeOgden (const typename Ogden< n, tag >::MaterialParameters &mu, const typename Ogden< n, tag >::MaterialExponents alpha, double K=0.0, const VolumetricFunction &vf=VolumetricFunction{})
	A helper function to create a hyperelastic material model, where the deviatoric part is according to the Ogden model. More...

template<int n, typename VolumetricFunction = VF0>
auto	makeInvariantBased (const typename InvariantBased< n >::MaterialParameters &mu, const typename InvariantBased< n >::Exponents pex, const typename InvariantBased< n >::Exponents qex, double K=0.0, const VolumetricFunction &vf=VolumetricFunction{})
	A helper function to create a hyperelastic material model, where the deviatoric part is according to the general invariant-based model. More...

template<typename VolumetricFunction = VF0>
auto	makeMooneyRivlin (const typename InvariantBased< 2 >::MaterialParameters &mu, double K=0.0, const VolumetricFunction &vf=VolumetricFunction{})
	A helper function to create a hyperelastic material model, where the deviatoric part is according to the Mooney-Rivlin model (InvariantBased model with n = 2). More...

template<typename VolumetricFunction = VF0>
auto	makeYeoh (const typename InvariantBased< 3 >::MaterialParameters &mu, double K=0.0, const VolumetricFunction &vf=VolumetricFunction{})
	A helper function to create a hyperelastic material model, where the deviatoric part is according to the Yeoh model (InvariantBased model with n = 3). More...

template<typename VolumetricFunction = VF0>
auto	makeArrudaBoyce (const ArrudaBoyceMatParameters &matPar, double K=0.0, const VolumetricFunction &vf=VolumetricFunction{})
	A helper function to create a hyperelastic material model, where the deviatoric part is according to the Arruda-Boyce model. More...

template<typename VolumetricFunction = VF0>
auto	makeGent (const GentMatParameters &matPar, double K=0.0, const VolumetricFunction &vf=VolumetricFunction{})
	A helper function to create a hyperelastic material model, where the deviatoric part is according to the Gent model. More...

template<typename MAT , typename S >
consteval bool	hasCorrectSize ()
	Template function for checking if the strain size is correct. More...

template<MatrixIndexPair... stressIndexPair, typename MaterialImpl >
auto	makeVanishingStrain (MaterialImpl mat)
	Factory function to create a VanishingStrain material with specified strain indices. More...

template<typename MaterialImpl >
auto	planeStrain (const MaterialImpl &mat)
	Factory function to create a VanishingStrain material for plane strain conditions. More...

template<MatrixIndexPair... stressIndexPair, typename MaterialImpl >
auto	makeVanishingStress (MaterialImpl mat, typename MaterialImpl::ScalarType p_tol=1e-12)
	Factory function to create a VanishingStress material with specified stress indices. More...

template<typename MaterialImpl >
auto	planeStress (const MaterialImpl &mat, typename MaterialImpl::ScalarType tol=1e-8)
	Factory function to create a VanishingStress material for plane stress conditions. More...

template<typename MaterialImpl >
auto	shellMaterial (const MaterialImpl &mat, typename MaterialImpl::ScalarType tol=1e-8)
	Factory function to create a VanishingStress material for a shell material with zero normal stress condition. More...

template<typename MaterialImpl >
auto	beamMaterial (const MaterialImpl &mat, typename MaterialImpl::ScalarType tol=1e-8)
	Factory function to create a VanishingStress material for a beam material with two zero normal stress condition. More...

Typedef Documentation

◆ ArrudaBoyce

using Ikarus::Materials::ArrudaBoyce = typedef ArrudaBoyceT<double>

◆ BlatzKo

using Ikarus::Materials::BlatzKo = typedef BlatzKoT<double>

◆ Gent

using Ikarus::Materials::Gent = typedef GentT<double>

◆ InvariantBased

template<int n>

using Ikarus::Materials::InvariantBased = typedef InvariantBasedT<double, n>

◆ LinearElasticity

using Ikarus::Materials::LinearElasticity = typedef LinearElasticityT<double>

◆ NeoHooke

using Ikarus::Materials::NeoHooke = typedef NeoHookeT<double>

◆ NoVolumetricPart

using Ikarus::Materials::NoVolumetricPart = typedef Volumetric<VF0>

◆ Ogden

template<int n, PrincipalStretchTags tag>

using Ikarus::Materials::Ogden = typedef OgdenT<double, n, tag>

◆ StVenantKirchhoff

using Ikarus::Materials::StVenantKirchhoff = typedef StVenantKirchhoffT<double>

Function Documentation

◆ beamMaterial()

template<typename MaterialImpl >

auto Ikarus::Materials::beamMaterial	(	const MaterialImpl &	mat,
		typename MaterialImpl::ScalarType	tol = `1e-8`
	)

Template Parameters

MaterialImpl The underlying material model.

Parameters

mat	The underlying material model.
p_tol	Tolerance for stress reduction.

Returns: VanishingStress The created VanishingStress material for plane stress.

◆ hasCorrectSize()

template<typename MAT , typename S >

consteval bool Ikarus::Materials::hasCorrectSize ( )

The given strain quantity has to be a Eigen::Vector6 or a Eigen::Matrix3

Template Parameters

MAT	Type of the material.
S	Type of the strains.

◆ makeArrudaBoyce()

template<typename VolumetricFunction = VF0>

auto Ikarus::Materials::makeArrudaBoyce	(	const ArrudaBoyceMatParameters &	matPar,
		double	K = `0.0`,
		const VolumetricFunction &	vf = `VolumetricFunction{}`
	)

inline

Template Parameters

VolumetricFunction Type of the volumetric function.

Parameters

matPar	The Arruda-Boyce material parameters (C and lambdaM).
K	Bulk modulus (or) Lamé's first parameter.
vf	The volumetric function.

Returns: A hyperelastic material model.

◆ makeBlatzKo()

auto Ikarus::Materials::makeBlatzKo ( double mu )

inline

Parameters

mu	The shear modulus.

Returns: A hyperelastic material model.

◆ makeGent()

template<typename VolumetricFunction = VF0>

auto Ikarus::Materials::makeGent	(	const GentMatParameters &	matPar,
		double	K = `0.0`,
		const VolumetricFunction &	vf = `VolumetricFunction{}`
	)

inline

Template Parameters

VolumetricFunction Type of the volumetric function.

Parameters

matPar	The Gent material parameters (mu and Jm).
K	Bulk modulus (or) Lamé's first parameter.
vf	The volumetric function.

Returns: A hyperelastic material model.

◆ makeInvariantBased()

template<int n, typename VolumetricFunction = VF0>

auto Ikarus::Materials::makeInvariantBased	(	const typename InvariantBased< n >::MaterialParameters &	mu,
		const typename InvariantBased< n >::Exponents	pex,
		const typename InvariantBased< n >::Exponents	qex,
		double	K = `0.0`,
		const VolumetricFunction &	vf = `VolumetricFunction{}`
	)

inline

Template Parameters

n	Number of material parameters.
VolumetricFunction	Type of the volumetric function.

Parameters

mu	The shear parameters (mu_i).
pex	The exponents related to the first invariant.
qex	The exponents related to the second invariant.
K	Bulk modulus (or) Lamé's first parameter.
vf	The volumetric function.

Returns: A hyperelastic material model.

◆ makeMooneyRivlin()

template<typename VolumetricFunction = VF0>

auto Ikarus::Materials::makeMooneyRivlin	(	const typename InvariantBased< 2 >::MaterialParameters &	mu,
		double	K = `0.0`,
		const VolumetricFunction &	vf = `VolumetricFunction{}`
	)

inline

Template Parameters

VolumetricFunction Type of the volumetric function.

Parameters

mu	The shear parameters (mu_i).
K	Bulk modulus (or) Lamé's first parameter.
vf	The volumetric function.

Returns: A hyperelastic material model.

◆ makeOgden()

template<int n, PrincipalStretchTags tag, typename VolumetricFunction = VF0>

auto Ikarus::Materials::makeOgden	(	const typename Ogden< n, tag >::MaterialParameters &	mu,
		const typename Ogden< n, tag >::MaterialExponents	alpha,
		double	K = `0.0`,
		const VolumetricFunction &	vf = `VolumetricFunction{}`
	)

inline

Template Parameters

n	Number of Ogden material parameters.
PrincipalStretchTags	Type of the principal stretches, either total or deviatoric.
VolumetricFunction	Type of the volumetric function.

Parameters

mu	The shear parameters (mu_i).
alpha	The (exponential) parameters (alpha_i).
K	Bulk modulus (or) Lamé's first parameter.
vf	The volumetric function.

Returns: A hyperelastic material model.

◆ makeVanishingStrain()

template<MatrixIndexPair... stressIndexPair, typename MaterialImpl >

auto Ikarus::Materials::makeVanishingStrain ( MaterialImpl mat )

Template Parameters

matrixIndexPair	The array of MatrixIndexPair representing fixed strain components.
MaterialImpl	The underlying material model.

Parameters

mat	The underlying material model.
p_tol	Tolerance for stress reduction.

Returns: VanishingStress The created VanishingStress material.

Here is the caller graph for this function:

◆ makeVanishingStress()

template<MatrixIndexPair... stressIndexPair, typename MaterialImpl >

auto Ikarus::Materials::makeVanishingStress	(	MaterialImpl	mat,
		typename MaterialImpl::ScalarType	p_tol = `1e-12`
	)

Template Parameters

matrixIndexPair	The array of MatrixIndexPair representing fixed stress components.
MaterialImpl	The underlying material model.

Parameters

mat	The underlying material model.
p_tol	Tolerance for stress reduction.

Returns: VanishingStress The created VanishingStress material.

Here is the caller graph for this function:

◆ makeYeoh()

template<typename VolumetricFunction = VF0>

auto Ikarus::Materials::makeYeoh	(	const typename InvariantBased< 3 >::MaterialParameters &	mu,
		double	K = `0.0`,
		const VolumetricFunction &	vf = `VolumetricFunction{}`
	)

inline

Template Parameters

VolumetricFunction Type of the volumetric function.

Parameters

mu	The shear parameters (mu_i).
K	Bulk modulus (or) Lamé's first parameter.
vf	The volumetric function.

Returns: A hyperelastic material model.

◆ planeStrain()

template<typename MaterialImpl >

auto Ikarus::Materials::planeStrain ( const MaterialImpl & mat )

The output is as follows for the stress and material tangent (in Voigt notation):

\[ \BS(\BE) \rightarrow \begin{bmatrix} S_{11} \\ S_{22} \\ S_{12} \end{bmatrix}, \quad \BBC(\BE) \rightarrow \begin{bmatrix} C_{11} & C_{12} & C_{13} \\ C_{21} & C_{22} & C_{23} \\ C_{31} & C_{32} & C_{33} \end{bmatrix} \]

Template Parameters

MaterialImpl The underlying material model.

Parameters

mat	The underlying material model.

Returns: VanishingStrain The created VanishingStrain material for plane strain case.

◆ planeStress()

template<typename MaterialImpl >

auto Ikarus::Materials::planeStress	(	const MaterialImpl &	mat,
		typename MaterialImpl::ScalarType	tol = `1e-8`
	)

Template Parameters

MaterialImpl The underlying material model.

Parameters

mat	The underlying material model.
tol	Tolerance for stress reduction.

Returns: VanishingStress The created VanishingStress material for plane stress.

◆ shellMaterial()

template<typename MaterialImpl >

auto Ikarus::Materials::shellMaterial	(	const MaterialImpl &	mat,
		typename MaterialImpl::ScalarType	tol = `1e-8`
	)

Template Parameters

MaterialImpl The underlying material model.

Parameters

mat	The underlying material model.
tol	Tolerance for stress reduction.

Returns: VanishingStress The created VanishingStress material for plane stress.

Classes

Concepts

Typedefs

Functions

Typedef Documentation

◆ ArrudaBoyce

◆ BlatzKo

◆ Gent

◆ InvariantBased

◆ LinearElasticity

◆ NeoHooke

◆ NoVolumetricPart

◆ Ogden

◆ StVenantKirchhoff

Function Documentation

◆ beamMaterial()

◆ hasCorrectSize()

◆ makeArrudaBoyce()

◆ makeBlatzKo()

◆ makeGent()

◆ makeInvariantBased()

◆ makeMooneyRivlin()

◆ makeOgden()

◆ makeVanishingStrain()

◆ makeVanishingStress()

◆ makeYeoh()

◆ planeStrain()

◆ planeStress()

◆ shellMaterial()