Class for the 2nd-order tensor (3, 3) representation. More...

#include <tensor.hpp>

Collaboration diagram for constitutive::Tensor2< T >:

Public Member Functions
	Tensor2 (const Eigen::Matrix< T, 3, 3 > &data)
	Constructor for the tensor.
Eigen::Matrix< T, 6, 1 >	toVector () const
	Convert the tensor to a vector.
void	clearCaches () const
	Clear caches.
const Eigen::Matrix< T, 3, 3 > &	mean () const
	Calculate the mean tensor.
const Eigen::Matrix< T, 3, 3 > &	deviatoric () const
	Calculate the deviatoric tensor.
T	I1 () const
	Calculate the first invariant of the tensor.
T	I2 () const
	Calculate the second invariant of the tensor.
T	I3 () const
	Calculate the third invariant of the tensor.
T	J2 () const
	Calculate the second deviatoric invariant of the tensor.
T	J3 () const
	Calculate the third deviatoric invariant of the tensor.
T	p () const
	Calculate the mean value of the tensor.
T	q () const
	Calculate the deviatoric value of the tensor.
T	eta () const
	Calculate the eta value of the tensor.
const Eigen::Matrix< T, 3, 1 > &	principals () const
	Calculate the principal values of the tensor.
T	p1 () const
	Calculate the maximum principal value of the tensor.
T	p2 () const
	Calculate the median principal value of the tensor.
T	p3 () const
	Calculate the minimum principal value of the tensor.
T	b () const
	Calculate the b-value of the tensor.
T	R () const
	Calculate the R-value of the tensor.
T	cos3theta () const
	Calculate the cosine of 3 times of the Lode angle of the tensor.
T	theta () const
	Calculate the Lode angle (0, pi/3) of the tensor.
T	lode () const
	Calculate the Lode angle (-pi/6, pi/6) of the tensor.
T	norm () const
	Calculate the norm of the tensor.
const Eigen::Matrix< T, 3, 3 > &	normalized () const
	Calculate the normalized tensor.
Tensor2	operator+ (const Tensor2 &other) const
	Add two tensors.
Tensor2	operator+ (const Eigen::Matrix< T, 3, 3 > &other) const
	Add a matrix to the tensor.
Tensor2	operator+ (const T &other) const
	Add a scalar to the tensor.
Tensor2	operator- (const Tensor2 &other) const
	Subtract two tensors.
Tensor2	operator- (const Eigen::Matrix< T, 3, 3 > &other) const
	Subtract a matrix from the tensor.
Tensor2	operator- (const T &other) const
	Subtract a scalar from the tensor.
Tensor2	operator* (const Tensor2 &other) const
	Multiply the tensor by a tensor.
Tensor2	operator* (const Eigen::Matrix< T, 3, 3 > &other) const
	Multiply the tensor by a matrix.
Eigen::Matrix< T, 3, 1 >	operator* (const Eigen::Matrix< T, 3, 1 > &other) const
	Multiply the tensor by a vector.
Tensor2	operator* (const T &other) const
	Multiply the tensor by a scalar.
Tensor2	operator/ (const T &other) const
	Divide the tensor by a scalar.

Static Public Member Functions
static Tensor2	fromVector (const Eigen::Matrix< T, 6, 1 > &vec)
	Static method to create a tensor from a vector.

Public Attributes
Eigen::Matrix< T, 3, 3 >	matrix
	Matrix representation of the tensor.

Detailed Description

template<typename T>
struct constitutive::Tensor2< T >

Class for the 2nd-order tensor (3, 3) representation.

Constructor & Destructor Documentation

◆ Tensor2()

template<typename T>

constitutive::Tensor2< T >::Tensor2 ( const Eigen::Matrix< T, 3, 3 > & data )

inlineexplicit

Constructor for the tensor.

Warning: Please ensure that the input matrix is symmetric, as the tensor is expected to be symmetric.

Parameters

data	Matrix representation of the tensor.

References matrix.

Referenced by constitutive::FabricTensor< T >::evolve(), fromVector(), constitutive::operator*(), constitutive::operator*(), operator*(), operator*(), operator*(), constitutive::operator+(), constitutive::operator+(), operator+(), operator+(), operator+(), constitutive::operator-(), constitutive::operator-(), operator-(), operator-(), operator-(), and operator/().

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Member Function Documentation

◆ b()

template<typename T>

T constitutive::Tensor2< T >::b ( ) const

inline

Calculate the b-value of the tensor.

References constitutive::CachedVariable< T >::cached, constitutive::CachedScalar< T >::initialize(), p1(), p2(), p3(), principals(), and constitutive::CachedVariable< T >::value().

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◆ clearCaches()

template<typename T>

void constitutive::Tensor2< T >::clearCaches ( ) const

inline

Clear caches.

References constitutive::CachedVariable< T >::cached.

◆ cos3theta()

template<typename T>

T constitutive::Tensor2< T >::cos3theta ( ) const

inline

Calculate the cosine of 3 times of the Lode angle of the tensor.

Returns: Cosine of 3 times of the Lode angle of the tensor.

References constitutive::CachedVariable< T >::cached, cos3theta(), constitutive::CachedScalar< T >::initialize(), J2(), J3(), and constitutive::CachedVariable< T >::value().

Referenced by cos3theta(), and theta().

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◆ deviatoric()

template<typename T>

const Eigen::Matrix< T, 3, 3 > & constitutive::Tensor2< T >::deviatoric ( ) const

inline

Calculate the deviatoric tensor.

Returns: Deviatoric tensor.

References constitutive::CachedVariable< T >::cached, constitutive::CachedMatrix33< T >::initialize(), mean(), and constitutive::CachedVariable< T >::value().

Referenced by J2(), and J3().

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◆ eta()

template<typename T>

T constitutive::Tensor2< T >::eta ( ) const

inline

Calculate the eta value of the tensor.

Returns: eta value of the tensor.

References constitutive::CachedVariable< T >::cached, constitutive::CachedScalar< T >::initialize(), p(), q(), and constitutive::CachedVariable< T >::value().

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◆ fromVector()

template<typename T>

Tensor2 constitutive::Tensor2< T >::fromVector ( const Eigen::Matrix< T, 6, 1 > & vec )

inlinestatic

Static method to create a tensor from a vector.

Parameters

vec	Vector representation of the tensor.

Returns: Tensor representation of the vector.

References matrix, and Tensor2().

Referenced by constitutive::StateVariable< T >::strain(), and constitutive::StateVariable< T >::strainp().

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◆ I1()

template<typename T>

T constitutive::Tensor2< T >::I1 ( ) const

inline

Calculate the first invariant of the tensor.

Returns: First invariant of the tensor.

References constitutive::CachedVariable< T >::cached, constitutive::CachedScalar< T >::initialize(), and constitutive::CachedVariable< T >::value().

Referenced by p().

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◆ I2()

template<typename T>

T constitutive::Tensor2< T >::I2 ( ) const

inline

Calculate the second invariant of the tensor.

Returns: Second invariant of the tensor.

References constitutive::CachedVariable< T >::cached, constitutive::CachedScalar< T >::initialize(), and constitutive::CachedVariable< T >::value().

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◆ I3()

template<typename T>

T constitutive::Tensor2< T >::I3 ( ) const

inline

Calculate the third invariant of the tensor.

Returns: Third invariant of the tensor.

References constitutive::CachedVariable< T >::cached, constitutive::CachedScalar< T >::initialize(), and constitutive::CachedVariable< T >::value().

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◆ J2()

template<typename T>

T constitutive::Tensor2< T >::J2 ( ) const

inline

Calculate the second deviatoric invariant of the tensor.

Returns: Second deviatoric invariant of the tensor.

References constitutive::CachedVariable< T >::cached, deviatoric(), constitutive::CachedScalar< T >::initialize(), and constitutive::CachedVariable< T >::value().

Referenced by cos3theta(), and q().

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◆ J3()

template<typename T>

T constitutive::Tensor2< T >::J3 ( ) const

inline

Calculate the third deviatoric invariant of the tensor.

Returns: Third deviatoric invariant of the tensor.

References constitutive::CachedVariable< T >::cached, deviatoric(), constitutive::CachedScalar< T >::initialize(), and constitutive::CachedVariable< T >::value().

Referenced by cos3theta().

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◆ lode()

template<typename T>

T constitutive::Tensor2< T >::lode ( ) const

inline

Calculate the Lode angle (-pi/6, pi/6) of the tensor.

Returns: Lode angle of the tensor.

References constitutive::CachedVariable< T >::cached, constitutive::CachedScalar< T >::initialize(), PI, theta(), and constitutive::CachedVariable< T >::value().

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◆ mean()

template<typename T>

const Eigen::Matrix< T, 3, 3 > & constitutive::Tensor2< T >::mean ( ) const

inline

Calculate the mean tensor.

Returns: Mean tensor.

References constitutive::CachedVariable< T >::cached, constitutive::CachedMatrix33< T >::initialize(), and constitutive::CachedVariable< T >::value().

Referenced by deviatoric().

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◆ norm()

template<typename T>

T constitutive::Tensor2< T >::norm ( ) const

inline

Calculate the norm of the tensor.

Returns: Norm of the tensor.

References constitutive::CachedVariable< T >::cached, constitutive::CachedScalar< T >::initialize(), and constitutive::CachedVariable< T >::value().

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◆ normalized()

template<typename T>

const Eigen::Matrix< T, 3, 3 > & constitutive::Tensor2< T >::normalized ( ) const

inline

Calculate the normalized tensor.

Returns: Normalized tensor.

References constitutive::CachedVariable< T >::cached, constitutive::CachedMatrix33< T >::initialize(), and constitutive::CachedVariable< T >::value().

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◆ operator*() [1/4]

template<typename T>

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

inline

Multiply the tensor by a vector.

Parameters

other Vector to be multiplied.

Returns: Product of the tensor and the vector.

◆ operator*() [2/4]

template<typename T>

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

inline

Multiply the tensor by a matrix.

Parameters

other Matrix to be multiplied.

Returns: Product of the tensor and the matrix.

References Tensor2().

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◆ operator*() [3/4]

template<typename T>

Tensor2 constitutive::Tensor2< T >::operator* ( const T & other ) const

inline

Multiply the tensor by a scalar.

Parameters

other Scalar to be multiplied.

Returns: Product of the tensor and the scalar.

References Tensor2().

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◆ operator*() [4/4]

template<typename T>

Tensor2 constitutive::Tensor2< T >::operator* ( const Tensor2< T > & other ) const

inline

Multiply the tensor by a tensor.

Parameters

other Scalar to be multiplied.

Returns: Product of the tensor and the scalar.

References matrix, and Tensor2().

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◆ operator+() [1/3]

template<typename T>

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

inline

Add a matrix to the tensor.

Parameters

other Matrix to be added.

Returns: Sum of the tensor and the matrix.

References Tensor2().

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◆ operator+() [2/3]

template<typename T>

Tensor2 constitutive::Tensor2< T >::operator+ ( const T & other ) const

inline

Add a scalar to the tensor.

Parameters

other Scalar to be added.

Returns: Sum of the tensor and the scalar.

References Tensor2().

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◆ operator+() [3/3]

template<typename T>

Tensor2 constitutive::Tensor2< T >::operator+ ( const Tensor2< T > & other ) const

inline

Add two tensors.

Parameters

other Tensor to be added.

Returns: Sum of the two tensors.

References matrix, and Tensor2().

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◆ operator-() [1/3]

template<typename T>

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

inline

Subtract a matrix from the tensor.

Parameters

other Matrix to be subtracted.

Returns: Difference of the tensor and the matrix.

References Tensor2().

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◆ operator-() [2/3]

template<typename T>

Tensor2 constitutive::Tensor2< T >::operator- ( const T & other ) const

inline

Subtract a scalar from the tensor.

Parameters

other Scalar to be subtracted.

Returns: Difference of the tensor and the scalar.

References Tensor2().

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◆ operator-() [3/3]

template<typename T>

Tensor2 constitutive::Tensor2< T >::operator- ( const Tensor2< T > & other ) const

inline

Subtract two tensors.

Parameters

other Tensor to be subtracted.

Returns: Difference of the two tensors.

References matrix, and Tensor2().

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◆ operator/()

template<typename T>

Tensor2 constitutive::Tensor2< T >::operator/ ( const T & other ) const

inline

Divide the tensor by a scalar.

Parameters

other Scalar to be divided.

Returns: Quotient of the tensor and the scalar.

References Tensor2().

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◆ p()

template<typename T>

T constitutive::Tensor2< T >::p ( ) const

inline

Calculate the mean value of the tensor.

Returns: Mean value of the tensor.

References constitutive::CachedVariable< T >::cached, I1(), constitutive::CachedScalar< T >::initialize(), and constitutive::CachedVariable< T >::value().

Referenced by eta().

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◆ p1()

template<typename T>

T constitutive::Tensor2< T >::p1 ( ) const

inline

Calculate the maximum principal value of the tensor.

References constitutive::CachedVariable< T >::cached, constitutive::CachedScalar< T >::initialize(), principals(), and constitutive::CachedVariable< T >::value().

Referenced by b(), and R().

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◆ p2()

template<typename T>

T constitutive::Tensor2< T >::p2 ( ) const

inline

Calculate the median principal value of the tensor.

References constitutive::CachedVariable< T >::cached, constitutive::CachedScalar< T >::initialize(), principals(), and constitutive::CachedVariable< T >::value().

Referenced by b().

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◆ p3()

template<typename T>

T constitutive::Tensor2< T >::p3 ( ) const

inline

Calculate the minimum principal value of the tensor.

References constitutive::CachedVariable< T >::cached, constitutive::CachedScalar< T >::initialize(), principals(), and constitutive::CachedVariable< T >::value().

Referenced by b(), and R().

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◆ principals()

template<typename T>

const Eigen::Matrix< T, 3, 1 > & constitutive::Tensor2< T >::principals ( ) const

inline

Calculate the principal values of the tensor.

Returns: Principal values of the tensor.

References constitutive::CachedVariable< T >::cached, constitutive::CachedVector3< T >::initialize(), and constitutive::CachedVariable< T >::value().

Referenced by b(), p1(), p2(), and p3().

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◆ q()

template<typename T>

T constitutive::Tensor2< T >::q ( ) const

inline

Calculate the deviatoric value of the tensor.

Returns: Deviatoric value of the tensor.

References constitutive::CachedVariable< T >::cached, constitutive::CachedScalar< T >::initialize(), J2(), and constitutive::CachedVariable< T >::value().

Referenced by eta().

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◆ R()

template<typename T>

T constitutive::Tensor2< T >::R ( ) const

inline

Calculate the R-value of the tensor.

References constitutive::CachedVariable< T >::cached, constitutive::CachedScalar< T >::initialize(), p1(), p3(), and constitutive::CachedVariable< T >::value().

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◆ theta()

template<typename T>

T constitutive::Tensor2< T >::theta ( ) const

inline

Calculate the Lode angle (0, pi/3) of the tensor.

Returns: Lode angle of the tensor.

References constitutive::CachedVariable< T >::cached, cos3theta(), constitutive::CachedScalar< T >::initialize(), and constitutive::CachedVariable< T >::value().

Referenced by lode().

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◆ toVector()

template<typename T>

Eigen::Matrix< T, 6, 1 > constitutive::Tensor2< T >::toVector ( ) const

inline

Convert the tensor to a vector.

Returns: Vector representation of the tensor.

References matrix.

Member Data Documentation

◆ matrix

template<typename T>

Eigen::Matrix<T, 3, 3> constitutive::Tensor2< T >::matrix

Matrix representation of the tensor.

Referenced by fromVector(), constitutive::operator*(), constitutive::operator*(), constitutive::operator*(), operator*(), constitutive::operator+(), constitutive::operator+(), operator+(), constitutive::operator-(), constitutive::operator-(), operator-(), Tensor2(), and toVector().

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

include/constitutive/tensor.hpp

Public Member Functions

Static Public Member Functions

Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Tensor2()

Member Function Documentation

◆ b()

◆ clearCaches()

◆ cos3theta()

◆ deviatoric()

◆ eta()

◆ fromVector()

◆ I1()

◆ I2()

◆ I3()

◆ J2()

◆ J3()

◆ lode()

◆ mean()

◆ norm()

◆ normalized()

◆ operator*() [1/4]

◆ operator*() [2/4]

◆ operator*() [3/4]

◆ operator*() [4/4]

◆ operator+() [1/3]

◆ operator+() [2/3]

◆ operator+() [3/3]

◆ operator-() [1/3]

◆ operator-() [2/3]

◆ operator-() [3/3]

◆ operator/()

◆ p()

◆ p1()

◆ p2()

◆ p3()

◆ principals()

◆ q()

◆ R()

◆ theta()

◆ toVector()

Member Data Documentation

◆ matrix