Kratos::MPMStressPrincipalInvariantsUtility Class Reference

#include <mpm_stress_principal_invariants_utility.h>

Collaboration diagram for Kratos::MPMStressPrincipalInvariantsUtility:

Public Types
typedef Matrix	MatrixType
typedef Vector	VectorType
typedef unsigned int	IndexType
typedef unsigned int	SizeType

Static Public Member Functions
static void	SortPrincipalStress (Vector &rPrincipalStress, Vector &rMainStrain, Matrix &rMainDirections)
	Sort Principal Stresses, Strains, and Directions to magnitude order. More...
static void	CalculateTensorInvariants (const Vector &rVector, double &rI1, double &rJ2)
	Calculate invariants I1 and J2 of a tensor. More...
static void	CalculateTensorInvariants (const Vector &rVector, double &rI1, double &rJ2, double &rJ3)
	Calculate invariants I1, J2, and J3 of a tensor. More...
static void	CalculateTensorInvariantsDerivatives (const Vector &rVector, Vector &rDI1, Vector &rDJ2, Vector &rDJ3)
	Calculate derivatives of invariants dI1/dtensor, dJ2/dtensor, and dJ3/dtensor. More...
static void	CalculateTensorInvariantsSecondDerivatives (const Vector &rVector, Matrix &rD2I1, Matrix &rD2J2, Matrix &rD2J3)
	Calculate second derivatives of invariants d2I1/d2tensor, d2J2/d2tensor, and d2J3/d2tensor. More...
static void	CalculateStressInvariants (const Vector &rStress, double &rMeanStressP, double &rDeviatoricQ)
	Calculate stress invariants p (volumetric equivalent) and q (deviatoric equivalent). More...
static void	CalculateThirdStressInvariant (const Vector &rStress, double &rLodeAngle)
	Calculate the third stress invariants lode angle (we are using positive sine definition). More...
static void	CalculateStressInvariants (const Vector &rStress, double &rMeanStressP, double &rDeviatoricQ, double &rLodeAngle)
	Calculate stress invariants p, q, and lode angle. More...
static void	CalculateDerivativeVectors (const Vector rStress, Vector &rC1, Vector &rC2)
	Calculate stress invariant derivatives dp/dsigma (volumetric) and dq/dsigma (deviatoric). More...
static void	CalculateDerivativeVectors (const Vector rStress, Vector &rC1, Vector &rC2, Vector &rC3)
	Calculate stress invariant derivatives dp/dsigma (volumetric), dq/dsigma (deviatoric), and dlodeangle/dsigma. More...
static void	CalculateSecondDerivativeMatrices (const Vector rStress, Matrix &r2C1, Matrix &r2C2)
	Calculate second stress invariant derivatives d2p/d2sigma (volumetric) and d2q/d2sigma (deviatoric). More...
static void	CalculateSecondDerivativeMatrices (const Vector rStress, Matrix &r2C1, Matrix &r2C2, Matrix &r2C3)
	Calculate second stress invariant derivatives d2p/d2sigma (volumetric), d2q/d2sigma (deviatoric), and d2lodeangle/d2sigma. More...
static Matrix	PrincipalVectorToMatrix (const Vector &rVector, const unsigned int &rSize)
	Transform Stress or Principal stress tensor to Matrix form (fully assuming 3D space). More...
static Vector	PrincipalMatrixtoVector (const Matrix &rMatrix, const unsigned int &rSize)
	Transform Stress or Principal stress tensor to Vector form (fully assuming 3D space). More...
static double	CalculateMatrixDoubleContraction (const Matrix &rInput)
static double	CalculateMatrixTrace (const Matrix &rInput)

Static Public Attributes
static constexpr double	tolerance = 1.0e-9

Member Typedef Documentation

IndexType

typedef unsigned int Kratos::MPMStressPrincipalInvariantsUtility::IndexType

MatrixType

typedef Matrix Kratos::MPMStressPrincipalInvariantsUtility::MatrixType

SizeType

typedef unsigned int Kratos::MPMStressPrincipalInvariantsUtility::SizeType

VectorType

typedef Vector Kratos::MPMStressPrincipalInvariantsUtility::VectorType

Member Function Documentation

CalculateDerivativeVectors() [1/2]

static void Kratos::MPMStressPrincipalInvariantsUtility::CalculateDerivativeVectors ( const Vector  rStress, Vector &  rC1, Vector &  rC2  )

inlinestatic

Calculate stress invariant derivatives dp/dsigma (volumetric) and dq/dsigma (deviatoric).

Parameters

[in]	rStress	Input principal stress tensor.
[out]	rC1	Hydrostatic mean stress derivative with respect to principal stresses.
[out]	rC2	Deviatoric stress derivative with respect to principal stresses.

CalculateDerivativeVectors() [2/2]

static void Kratos::MPMStressPrincipalInvariantsUtility::CalculateDerivativeVectors ( const Vector  rStress, Vector &  rC1, Vector &  rC2, Vector &  rC3  )

inlinestatic

Calculate stress invariant derivatives dp/dsigma (volumetric), dq/dsigma (deviatoric), and dlodeangle/dsigma.

Parameters

[in]	rStress	Input principal stress tensor.
[out]	rC1	Hydrostatic mean stress derivative with respect to principal stresses.
[out]	rC2	Deviatoric stress derivative with respect to principal stresses.
[out]	rC3	Derivative of lode angle with respect to principal stresses.

CalculateMatrixDoubleContraction()

static double Kratos::MPMStressPrincipalInvariantsUtility::CalculateMatrixDoubleContraction ( const Matrix &  rInput )

inlinestatic

CalculateMatrixTrace()

static double Kratos::MPMStressPrincipalInvariantsUtility::CalculateMatrixTrace ( const Matrix &  rInput )

inlinestatic

CalculateSecondDerivativeMatrices() [1/2]

static void Kratos::MPMStressPrincipalInvariantsUtility::CalculateSecondDerivativeMatrices ( const Vector  rStress, Matrix &  r2C1, Matrix &  r2C2  )

inlinestatic

Calculate second stress invariant derivatives d2p/d2sigma (volumetric) and d2q/d2sigma (deviatoric).

Parameters

[in]	rStress	Input principal stress tensor.
[out]	r2C1	Hydrostatic mean stress second derivative with respect to principal stresses.
[out]	r2C2	Deviatoric stress second derivative with respect to principal stresses.

CalculateSecondDerivativeMatrices() [2/2]

static void Kratos::MPMStressPrincipalInvariantsUtility::CalculateSecondDerivativeMatrices ( const Vector  rStress, Matrix &  r2C1, Matrix &  r2C2, Matrix &  r2C3  )

inlinestatic

Calculate second stress invariant derivatives d2p/d2sigma (volumetric), d2q/d2sigma (deviatoric), and d2lodeangle/d2sigma.

Parameters

[in]	rStress	Input principal stress tensor.
[out]	r2C1	Hydrostatic mean stress second derivative with respect to principal stresses.
[out]	r2C2	Deviatoric stress second derivative with respect to principal stresses.
[out]	r2C3	Second Derivative of lode angle with respect to principal stresses.

CalculateStressInvariants() [1/2]

static void Kratos::MPMStressPrincipalInvariantsUtility::CalculateStressInvariants ( const Vector &  rStress, double &  rMeanStressP, double &  rDeviatoricQ  )

inlinestatic

Calculate stress invariants p (volumetric equivalent) and q (deviatoric equivalent).

Parameters

[in]	rStress	Input principal stress tensor.
[out]	rMeanStressP	Hydrostatic mean stress.
[out]	rDeviatoricQ	Deviatoric stress component.

CalculateStressInvariants() [2/2]

static void Kratos::MPMStressPrincipalInvariantsUtility::CalculateStressInvariants ( const Vector &  rStress, double &  rMeanStressP, double &  rDeviatoricQ, double &  rLodeAngle  )

inlinestatic

Calculate stress invariants p, q, and lode angle.

Parameters

[in]	rStress	Input principal stress tensor.
[out]	rMeanStressP	Hydrostatic mean stress.
[out]	rDeviatoricQ	Deviatoric stress component.
[out]	rLodeAngle	Third stress invariant direction used for non-circular octahedral profile yield surface.

CalculateTensorInvariants() [1/2]

static void Kratos::MPMStressPrincipalInvariantsUtility::CalculateTensorInvariants ( const Vector &  rVector, double &  rI1, double &  rJ2  )

inlinestatic

Calculate invariants I1 and J2 of a tensor.

Parameters

[in]	rVector	Input principal tensor.
[out]	rI1	First stress tensor invariant.
[out]	rJ2	Second stress deviator tensor invariant.

CalculateTensorInvariants() [2/2]

static void Kratos::MPMStressPrincipalInvariantsUtility::CalculateTensorInvariants ( const Vector &  rVector, double &  rI1, double &  rJ2, double &  rJ3  )

inlinestatic

Calculate invariants I1, J2, and J3 of a tensor.

Parameters

[in]	rVector	Input principal tensor.
[out]	rI1	First stress tensor invariant.
[out]	rJ2	Second stress deviator tensor invariant.
[out]	rJ3	Third stress deviator tensor invariant.

CalculateTensorInvariantsDerivatives()

static void Kratos::MPMStressPrincipalInvariantsUtility::CalculateTensorInvariantsDerivatives ( const Vector &  rVector, Vector &  rDI1, Vector &  rDJ2, Vector &  rDJ3  )

inlinestatic

Calculate derivatives of invariants dI1/dtensor, dJ2/dtensor, and dJ3/dtensor.

Parameters

[in]	rVector	Input principal tensor.
[out]	rDI1	First derivative of first stress tensor invariant.
[out]	rDJ2	First derivative of second stress deviator tensor invariant.
[out]	rDJ3	First derivative of third stress deviator tensor invariant.

CalculateTensorInvariantsSecondDerivatives()

static void Kratos::MPMStressPrincipalInvariantsUtility::CalculateTensorInvariantsSecondDerivatives ( const Vector &  rVector, Matrix &  rD2I1, Matrix &  rD2J2, Matrix &  rD2J3  )

inlinestatic

Calculate second derivatives of invariants d2I1/d2tensor, d2J2/d2tensor, and d2J3/d2tensor.

Parameters

[in]	rVector	Input principal tensor.
[out]	rD2I1	Second derivative of first stress tensor invariant.
[out]	rD2J2	Second derivative of second stress deviator tensor invariant.
[out]	rD2J3	Second derivative of third stress deviator tensor invariant.

CalculateThirdStressInvariant()

static void Kratos::MPMStressPrincipalInvariantsUtility::CalculateThirdStressInvariant ( const Vector &  rStress, double &  rLodeAngle  )

inlinestatic

Calculate the third stress invariants lode angle (we are using positive sine definition).

Parameters

[in]	rStress	Input principal tensor.
[out]	rLodeAngle	Third stress invariant direction used for non-circular octahedral profile yield surface.

PrincipalMatrixtoVector()

static Vector Kratos::MPMStressPrincipalInvariantsUtility::PrincipalMatrixtoVector ( const Matrix &  rMatrix, const unsigned int &  rSize  )

inlinestatic

Transform Stress or Principal stress tensor to Vector form (fully assuming 3D space).

Parameters

[in]	rMatrix	Matrix tensor to be transformed.
[in]	rSize	Matrix size, 3 for only principal stresses, 6 for normal stresses.

Returns

transformed vector.

PrincipalVectorToMatrix()

static Matrix Kratos::MPMStressPrincipalInvariantsUtility::PrincipalVectorToMatrix ( const Vector &  rVector, const unsigned int &  rSize  )

inlinestatic

Transform Stress or Principal stress tensor to Matrix form (fully assuming 3D space).

Parameters

[in]	rVector	Vector tensor to be transformed.
[in]	rSize	Matrix size, 3 for only principal stresses, 6 for normal stresses.

Returns

transformed matrix.

SortPrincipalStress()

static void Kratos::MPMStressPrincipalInvariantsUtility::SortPrincipalStress ( Vector &  rPrincipalStress, Vector &  rMainStrain, Matrix &  rMainDirections  )

inlinestatic

Sort Principal Stresses, Strains, and Directions to magnitude order.

Parameters

[in/out]	rPrincipalStress The principal stresses to be sorted in descending magnitude order.
[in/out]	rMainStrain The principal strain corresponding to the stresses.
[in/out]	rMainDirections The eigen directions corresponding to the stresses.

Member Data Documentation

tolerance

constexpr double Kratos::MPMStressPrincipalInvariantsUtility::tolerance = 1.0e-9

staticconstexpr

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

• /home/runner/work/Documentation/Documentation/master/applications/ParticleMechanicsApplication/custom_utilities/mpm_stress_principal_invariants_utility.h