constitutive Namespace Reference

helper functions for mathematical operations More...

Classes
struct	CachedMatrix33
struct	CachedScalar
struct	CachedTensor2
struct	CachedVariable
struct	CachedVector3
struct	CachedVector6
struct	ConstitutiveModelBase
	Base class for constitutive models. More...
struct	DebugVariable
struct	ElastoplasticModelBase
struct	FabricTensor
	Fabric tensor for the directional density function. More...
struct	FabricTensorChanged
struct	Load
	Load. More...
struct	LoadPhase
	load phase More...
struct	MaterialBase
	Material properties. More...
struct	Options
	Options for constitutive models. More...
struct	Scalar
struct	StateVariable
	State variables for constitutive models. More...
struct	Tensor2
	Class for the 2nd-order tensor (3, 3) representation. More...
struct	Vector

Functions
template<typename T>
auto	butcherTableau (int n, T alpha, T beta, const std::string &fourth_order_type="classic")
	Construct Butcher tableau for the Runge-Kutta method, a[i, j] = 0 for j >= i, c[0] = 0.
template auto	butcherTableau (int n, float alpha, float beta, const std::string &fourth_order_type)
template auto	butcherTableau (int n, double alpha, double beta, const std::string &fourth_order_type)
template<typename T>
Eigen::Matrix< T, 3, 3 >	orthogonalDirection (const Eigen::Matrix< T, 3, 3 > &F, const Eigen::Matrix< T, 3, 3 > &n)
	Orthogonal direction.
template Eigen::Matrix< float, 3, 3 >	orthogonalDirection (const Eigen::Matrix< float, 3, 3 > &F, const Eigen::Matrix< float, 3, 3 > &n)
template Eigen::Matrix< double, 3, 3 >	orthogonalDirection (const Eigen::Matrix< double, 3, 3 > &F, const Eigen::Matrix< double, 3, 3 > &n)
template<typename T>
Eigen::Matrix< T, 3, 3 >	nonCoaxialDirection (const Eigen::Matrix< T, 3, 3 > &F, const Eigen::Matrix< T, 3, 3 > &n, const Eigen::Matrix< T, 3, 3 > &m)
	Non-coaxial direction.
template Eigen::Matrix< float, 3, 3 >	nonCoaxialDirection (const Eigen::Matrix< float, 3, 3 > &F, const Eigen::Matrix< float, 3, 3 > &n, const Eigen::Matrix< float, 3, 3 > &m)
template Eigen::Matrix< double, 3, 3 >	nonCoaxialDirection (const Eigen::Matrix< double, 3, 3 > &F, const Eigen::Matrix< double, 3, 3 > &n, const Eigen::Matrix< double, 3, 3 > &m)
template<typename T>
Tensor2< T >	operator+ (const T &scalar, const Tensor2< T > &tensor)
	Add a tensor to a scalar.
template Tensor2< float >	operator+ (const float &scalar, const Tensor2< float > &tensor)
template Tensor2< double >	operator+ (const double &scalar, const Tensor2< double > &tensor)
template<typename T>
Tensor2< T >	operator+ (const Eigen::Matrix< T, 3, 3 > &matrix, const Tensor2< T > &tensor)
	Add a matrix to a tensor.
template Tensor2< float >	operator+ (const Eigen::Matrix< float, 3, 3 > &matrix, const Tensor2< float > &tensor)
template Tensor2< double >	operator+ (const Eigen::Matrix< double, 3, 3 > &matrix, const Tensor2< double > &tensor)
template<typename T>
Tensor2< T >	operator- (const T &scalar, const Tensor2< T > &tensor)
	Subtract a tensor from a scalar.
template Tensor2< float >	operator- (const float &scalar, const Tensor2< float > &tensor)
template Tensor2< double >	operator- (const double &scalar, const Tensor2< double > &tensor)
template<typename T>
Tensor2< T >	operator- (const Eigen::Matrix< T, 3, 3 > &matrix, const Tensor2< T > &tensor)
	Subtract a tensor from a matrix.
template Tensor2< float >	operator- (const Eigen::Matrix< float, 3, 3 > &matrix, const Tensor2< float > &tensor)
template Tensor2< double >	operator- (const Eigen::Matrix< double, 3, 3 > &matrix, const Tensor2< double > &tensor)
template<typename T>
Tensor2< T >	operator* (const Eigen::Matrix< T, 3, 3 > &matrix, const Tensor2< T > &tensor)
	Multiply a tensor by a matrix.
template Tensor2< float >	operator* (const Eigen::Matrix< float, 3, 3 > &matrix, const Tensor2< float > &tensor)
template Tensor2< double >	operator* (const Eigen::Matrix< double, 3, 3 > &matrix, const Tensor2< double > &tensor)
template<typename T>
Eigen::Matrix< T, 1, 3 >	operator* (const Eigen::Matrix< T, 1, 3 > &vector, const Tensor2< T > &tensor)
	Multiply a tensor by a vector.
template Eigen::Matrix< float, 1, 3 >	operator* (const Eigen::Matrix< float, 1, 3 > &vector, const Tensor2< float > &tensor)
template Eigen::Matrix< double, 1, 3 >	operator* (const Eigen::Matrix< double, 1, 3 > &vector, const Tensor2< double > &tensor)
template<typename T>
Tensor2< T >	operator* (const T &scalar, const Tensor2< T > &tensor)
	Multiply a tensor by a scalar.
template Tensor2< float >	operator* (const float &scalar, const Tensor2< float > &tensor)
template Tensor2< double >	operator* (const double &scalar, const Tensor2< double > &tensor)
template<typename T>
Eigen::Matrix< T, 3, 3 >	vec2mat (const Eigen::Matrix< T, 6, 1 > &vector)
	Convert a 6x1 vector to a 3x3 matrix.
template Eigen::Matrix< float, 3, 3 >	vec2mat (const Eigen::Matrix< float, 6, 1 > &vector)
template Eigen::Matrix< double, 3, 3 >	vec2mat (const Eigen::Matrix< double, 6, 1 > &vector)
template<typename T>
Eigen::Matrix< T, 6, 1 >	mat2vec (const Eigen::Matrix< T, 3, 3 > &matrix)
	Convert a 3x3 matrix to a 6x1 vector.
template Eigen::Matrix< float, 6, 1 >	mat2vec (const Eigen::Matrix< float, 3, 3 > &matrix)
template Eigen::Matrix< double, 6, 1 >	mat2vec (const Eigen::Matrix< double, 3, 3 > &matrix)
template<typename T>
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic >	ignoreDistractions (Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > data, const T &ignored_value=0.0, const T &tol=1e-15)
	Ignore data distractions.
template Eigen::Matrix< float, Eigen::Dynamic, Eigen::Dynamic >	ignoreDistractions (Eigen::Matrix< float, Eigen::Dynamic, Eigen::Dynamic > data, const float &ignored_value, const float &tol)
template Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic >	ignoreDistractions (Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > data, const double &ignored_value, const double &tol)
std::vector< std::string >	split (const std::string &string, const std::string &delimiter)
	Split a string by a delimiter.

Detailed Description

helper functions for mathematical operations

Function Documentation

butcherTableau() [1/3]

template auto constitutive::butcherTableau	(	int	n,
		double	alpha,
		double	beta,
		const std::string &	fourth_order_type )

References butcherTableau().

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butcherTableau() [2/3]

template auto constitutive::butcherTableau	(	int	n,
		float	alpha,
		float	beta,
		const std::string &	fourth_order_type )

References butcherTableau().

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butcherTableau() [3/3]

template<typename T>

auto constitutive::butcherTableau	(	int	n,
		T	alpha,
		T	beta,
		const std::string &	fourth_order_type = "classic" )

Construct Butcher tableau for the Runge-Kutta method, a[i, j] = 0 for j >= i, c[0] = 0.

Parameters

n	Order of the Runge-Kutta method, only 1, 2, 3, and 4 are supported.
alpha	Parameter for 2nd- and 3rd-order Runge-Kutta methods
beta	Parameter for 2nd- and 3rd-order Runge-Kutta methods
fourth_order_type	Type of fourth-order Runge-Kutta method, only 'classic', '3/8-rule', and 'ralston' are supported.

Returns

Butcher tableau (a, b, c)

References butcherTableau().

Referenced by butcherTableau(), butcherTableau(), butcherTableau(), and constitutive::ElastoplasticModelBase< T >::RKn().

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ignoreDistractions() [1/3]

template Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > constitutive::ignoreDistractions	(	Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic >	data,
		const double &	ignored_value,
		const double &	tol )

References ignoreDistractions().

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ignoreDistractions() [2/3]

template Eigen::Matrix< float, Eigen::Dynamic, Eigen::Dynamic > constitutive::ignoreDistractions	(	Eigen::Matrix< float, Eigen::Dynamic, Eigen::Dynamic >	data,
		const float &	ignored_value,
		const float &	tol )

References ignoreDistractions().

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ignoreDistractions() [3/3]

template<typename T>

Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > constitutive::ignoreDistractions	(	Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic >	data,
		const T &	ignored_value = 0.0,
		const T &	tol = 1e-15 )

Ignore data distractions.

Parameters

data	A 2D matrix
ignored_value	The value to be set for distractions
tol	The tolerance

Returns

A 2D matrix

References ignoreDistractions().

Referenced by ignoreDistractions(), ignoreDistractions(), ignoreDistractions(), and micromechanical::ChangHicher< T >::stressStrainIntegrate1().

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mat2vec() [1/3]

template Eigen::Matrix< double, 6, 1 > constitutive::mat2vec

(

const Eigen::Matrix< double, 3, 3 > &

matrix

)

References mat2vec().

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mat2vec() [2/3]

template Eigen::Matrix< float, 6, 1 > constitutive::mat2vec

(

const Eigen::Matrix< float, 3, 3 > &

matrix

)

References mat2vec().

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mat2vec() [3/3]

template<typename T>

Eigen::Matrix< T, 6, 1 > constitutive::mat2vec

(

const Eigen::Matrix< T, 3, 3 > &

matrix

)

Convert a 3x3 matrix to a 6x1 vector.

Parameters

matrix

A 3x3 matrix

Returns

A 6x1 vector

References mat2vec().

Referenced by micromechanical::core::BestFitAveraging< T >::averageStrain(), micromechanical::core::LoveWeberAveraging< T >::averageStress(), elastoplastic::J2Yang< T >::beginConstantStressStateScope(), elastoplastic::SIMSAND< T >::beginConstantStressStateScope(), elastoplastic::J2Yang< T >::dfdeps(), elastoplastic::SIMSAND< T >::dfdeps(), elastoplastic::J2Yang< T >::dfdsig(), elastoplastic::SIMSAND< T >::dfdsig(), elastoplastic::core::StressDilatancy< T >::dgdsig(), constitutive::ConstitutiveModelBase< T >::increment(), elastoplastic::core::ElastoplasticModel< T >::initialize(), micromechanical::core::MicromechanicalBase< T > *::initialize(), constitutive::ElastoplasticModelBase< T >::interpolateFabricTensor(), mat2vec(), mat2vec(), mat2vec(), elastoplastic::core::ElastoplasticModel< T >::postIncrement(), and micromechanical::core::MicromechanicalBase< T > *::postIncrement().

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nonCoaxialDirection() [1/3]

template Eigen::Matrix< double, 3, 3 > constitutive::nonCoaxialDirection	(	const Eigen::Matrix< double, 3, 3 > &	F,
		const Eigen::Matrix< double, 3, 3 > &	n,
		const Eigen::Matrix< double, 3, 3 > &	m )

References nonCoaxialDirection().

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nonCoaxialDirection() [2/3]

template Eigen::Matrix< float, 3, 3 > constitutive::nonCoaxialDirection	(	const Eigen::Matrix< float, 3, 3 > &	F,
		const Eigen::Matrix< float, 3, 3 > &	n,
		const Eigen::Matrix< float, 3, 3 > &	m )

References nonCoaxialDirection().

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nonCoaxialDirection() [3/3]

template<typename T>

Eigen::Matrix< T, 3, 3 > constitutive::nonCoaxialDirection	(	const Eigen::Matrix< T, 3, 3 > &	F,
		const Eigen::Matrix< T, 3, 3 > &	n,
		const Eigen::Matrix< T, 3, 3 > &	m )

Non-coaxial direction.

References nonCoaxialDirection().

Referenced by constitutive::FabricTensor< T >::evolve(), constitutive::ElastoplasticModelBase< T >::nonCoaxialDirection(), nonCoaxialDirection(), nonCoaxialDirection(), and nonCoaxialDirection().

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operator*() [1/9]

template Tensor2< double > constitutive::operator*	(	const double &	scalar,
		const Tensor2< double > &	tensor )

References operator*().

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operator*() [2/9]

template Eigen::Matrix< double, 1, 3 > constitutive::operator*	(	const Eigen::Matrix< double, 1, 3 > &	vector,
		const Tensor2< double > &	tensor )

References operator*().

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operator*() [3/9]

template Tensor2< double > constitutive::operator*	(	const Eigen::Matrix< double, 3, 3 > &	matrix,
		const Tensor2< double > &	tensor )

References operator*().

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operator*() [4/9]

template Eigen::Matrix< float, 1, 3 > constitutive::operator*	(	const Eigen::Matrix< float, 1, 3 > &	vector,
		const Tensor2< float > &	tensor )

References operator*().

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operator*() [5/9]

template Tensor2< float > constitutive::operator*	(	const Eigen::Matrix< float, 3, 3 > &	matrix,
		const Tensor2< float > &	tensor )

References operator*().

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operator*() [6/9]

template<typename T>

Eigen::Matrix< T, 1, 3 > constitutive::operator*	(	const Eigen::Matrix< T, 1, 3 > &	vector,
		const Tensor2< T > &	tensor )

Multiply a tensor by a vector.

Parameters

vector	Vector to be multiplied.
tensor	Tensor to be multiplied.

Returns

Product of the vector and the tensor.

References constitutive::Tensor2< T >::matrix, and operator*().

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operator*() [7/9]

template<typename T>

Tensor2< T > constitutive::operator*	(	const Eigen::Matrix< T, 3, 3 > &	matrix,
		const Tensor2< T > &	tensor )

Multiply a tensor by a matrix.

Parameters

matrix	Matrix to be multiplied.
tensor	Tensor to be multiplied.

Returns

Product of the matrix and the tensor.

References constitutive::Tensor2< T >::matrix, operator*(), and constitutive::Tensor2< T >::Tensor2().

Referenced by operator*(), operator*(), operator*(), operator*(), operator*(), operator*(), operator*(), operator*(), and operator*().

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operator*() [8/9]

template Tensor2< float > constitutive::operator*	(	const float &	scalar,
		const Tensor2< float > &	tensor )

References operator*().

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operator*() [9/9]

template<typename T>

Tensor2< T > constitutive::operator*	(	const T &	scalar,
		const Tensor2< T > &	tensor )

Multiply a tensor by a scalar.

Parameters

scalar	Scalar to be multiplied.
tensor	Tensor to be multiplied.

Returns

Product of the scalar and the tensor.

References constitutive::Tensor2< T >::matrix, operator*(), and constitutive::Tensor2< T >::Tensor2().

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operator+() [1/6]

template Tensor2< double > constitutive::operator+	(	const double &	scalar,
		const Tensor2< double > &	tensor )

References operator+().

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operator+() [2/6]

template Tensor2< double > constitutive::operator+	(	const Eigen::Matrix< double, 3, 3 > &	matrix,
		const Tensor2< double > &	tensor )

References operator+().

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operator+() [3/6]

template Tensor2< float > constitutive::operator+	(	const Eigen::Matrix< float, 3, 3 > &	matrix,
		const Tensor2< float > &	tensor )

References operator+().

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operator+() [4/6]

template<typename T>

Tensor2< T > constitutive::operator+	(	const Eigen::Matrix< T, 3, 3 > &	matrix,
		const Tensor2< T > &	tensor )

Add a matrix to a tensor.

Parameters

matrix	Matrix to be added.
tensor	Tensor to be added.

Returns

Sum of the matrix and the tensor.

References constitutive::Tensor2< T >::matrix, operator+(), and constitutive::Tensor2< T >::Tensor2().

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operator+() [5/6]

template Tensor2< float > constitutive::operator+	(	const float &	scalar,
		const Tensor2< float > &	tensor )

References operator+().

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operator+() [6/6]

template<typename T>

Tensor2< T > constitutive::operator+	(	const T &	scalar,
		const Tensor2< T > &	tensor )

Add a tensor to a scalar.

Parameters

scalar	Scalar to be added.
tensor	Tensor to be added.

Returns

Sum of the scalar and the tensor.

References constitutive::Tensor2< T >::matrix, operator+(), and constitutive::Tensor2< T >::Tensor2().

Referenced by operator+(), operator+(), operator+(), operator+(), operator+(), and operator+().

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operator-() [1/6]

template Tensor2< double > constitutive::operator-	(	const double &	scalar,
		const Tensor2< double > &	tensor )

References operator-().

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operator-() [2/6]

template Tensor2< double > constitutive::operator-	(	const Eigen::Matrix< double, 3, 3 > &	matrix,
		const Tensor2< double > &	tensor )

References operator-().

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operator-() [3/6]

template Tensor2< float > constitutive::operator-	(	const Eigen::Matrix< float, 3, 3 > &	matrix,
		const Tensor2< float > &	tensor )

References operator-().

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operator-() [4/6]

template<typename T>

Tensor2< T > constitutive::operator-	(	const Eigen::Matrix< T, 3, 3 > &	matrix,
		const Tensor2< T > &	tensor )

Subtract a tensor from a matrix.

Parameters

matrix	Matrix to be subtracted.
tensor	Tensor to be subtracted.

Returns

Difference of the matrix and the tensor.

References constitutive::Tensor2< T >::matrix, operator-(), and constitutive::Tensor2< T >::Tensor2().

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operator-() [5/6]

template Tensor2< float > constitutive::operator-	(	const float &	scalar,
		const Tensor2< float > &	tensor )

References operator-().

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operator-() [6/6]

template<typename T>

Tensor2< T > constitutive::operator-	(	const T &	scalar,
		const Tensor2< T > &	tensor )

Subtract a tensor from a scalar.

Parameters

scalar	Scalar to be subtracted.
tensor	Tensor to be subtracted.

Returns

Difference of the scalar and the tensor.

References constitutive::Tensor2< T >::matrix, operator-(), and constitutive::Tensor2< T >::Tensor2().

Referenced by operator-(), operator-(), operator-(), operator-(), operator-(), and operator-().

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orthogonalDirection() [1/3]

template Eigen::Matrix< double, 3, 3 > constitutive::orthogonalDirection	(	const Eigen::Matrix< double, 3, 3 > &	F,
		const Eigen::Matrix< double, 3, 3 > &	n )

References orthogonalDirection().

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orthogonalDirection() [2/3]

template Eigen::Matrix< float, 3, 3 > constitutive::orthogonalDirection	(	const Eigen::Matrix< float, 3, 3 > &	F,
		const Eigen::Matrix< float, 3, 3 > &	n )

References orthogonalDirection().

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orthogonalDirection() [3/3]

template<typename T>

Eigen::Matrix< T, 3, 3 > constitutive::orthogonalDirection	(	const Eigen::Matrix< T, 3, 3 > &	F,
		const Eigen::Matrix< T, 3, 3 > &	n )

Orthogonal direction.

References orthogonalDirection().

Referenced by constitutive::FabricTensor< T >::evolve(), constitutive::ElastoplasticModelBase< T >::orthogonalDirection(), orthogonalDirection(), orthogonalDirection(), and orthogonalDirection().

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split()

std::vector< std::string > constitutive::split ( const std::string & string, const std::string & delimiter )

inline

Split a string by a delimiter.

Parameters

string	string to split
delimiter	delimiter

Returns

vector of strings

References split().

Referenced by constitutive::FabricTensor< T >::evolve(), constitutive::FabricTensor< T >::requiresEvolution(), constitutive::FabricTensor< T >::setupDefaultParameters(), and split().

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vec2mat() [1/3]

template Eigen::Matrix< double, 3, 3 > constitutive::vec2mat

(

const Eigen::Matrix< double, 6, 1 > &

vector

)

References vec2mat().

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vec2mat() [2/3]

template Eigen::Matrix< float, 3, 3 > constitutive::vec2mat

(

const Eigen::Matrix< float, 6, 1 > &

vector

)

References vec2mat().

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vec2mat() [3/3]

template<typename T>

Eigen::Matrix< T, 3, 3 > constitutive::vec2mat

(

const Eigen::Matrix< T, 6, 1 > &

vector

)

Convert a 6x1 vector to a 3x3 matrix.

Parameters

vector

A 6x1 vector

Returns

A 3x3 matrix

References vec2mat().

Referenced by constitutive::Load< T >::addUndrainedTrueTriaxialWithAxialStrainPhase(), constitutive::StateVariable< T >::epsm(), constitutive::StateVariable< T >::epspm(), constitutive::StateVariable< T >::Fij(), constitutive::StateVariable< T >::FNij(), elastoplastic::core::ElastoplasticModel< T >::fromAbaqus(), micromechanical::core::MicromechanicalBase< T > *::fromAbaqus(), constitutive::StateVariable< T >::FTij(), constitutive::ConstitutiveModelBase< T >::increment(), micromechanical::core::KinematicHypothesisLocalization< T >::localizeStrain(), micromechanical::core::StaticHypothesisLocalization< T >::localizeStress(), vec2mat(), vec2mat(), and vec2mat().

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