Various tensor transformation utilities. More...

Functions
double	vonMises (int N, const double *S)
	Returns the von Mises value of a symmetric stress/strain tensor. More...

double	vonMises (double s11, double s22, double s12)
	Returns the von Mises value of a 2D stress/strain tensor. More...

double	vonMises (double s11, double s22, double s33, double s12, double s13, double s23)
	Returns the von Mises value of a 3D stress/strain tensor. More...

int	principalDirs (int N, const double S, double pVals, double *pDirs)
	Calculates the principal directions and values of a tensor. More...

int	principalDirs (const double S, double pVal, double p1Dir, double p2Dir)
	Calculates the principal directions and values of a 2D tensor. More...

int	principalDirs (const double S, double pVal, double p1Dir, double p2Dir, double *p3Dir)
	Calculates the principal directions and values of a 3D tensor. More...

bool	principalValues (int N, const double S, double P)
	Calculates the principal values of a tensor. More...

bool	principalVals2D (double s11, double s22, double s12, double *pVal)
	Calculates the principal values of a 2D tensor. More...

bool	principalVals3D (double s11, double s22, double s33, double s12, double s13, double s23, double *pVal)
	Calculates the principal values of a 3D tensor. More...

bool	principalValues (double s11, double s22, double s12, double &p1, double &p2)

bool	principalValues (double s11, double s22, double s33, double s12, double s13, double s23, double &p1, double &p2, double &p3)

double	maxShearValue (double pMax, double pMin)
	Returns the maximum shear value. More...

void	maxShearDir (int N, const double pMaxDir, const double pMinDir, double *maxShearDir)
	Returns the direction of maximum shear. More...

void	rotate2D (const double inTensor, const double rotMx, double *outTensor)
	Coordinate transformation for a 2D tensor. More...

void	rotate (const double inTensor, const double eX, const double eY, double outTensor)
	Coordinate transformation for a 2D tensor. More...

void	rotate3D (const double inTensor, const double rotMx, double *outTensor)
	Coordinate transformation for a 3D tensor. More...

void	rotate (const double inTensor, const double eX, const double eY, const double eZ, double *outTensor)
	Coordinate transformation for a 3D tensor. More...

void	from2Dto3D (const double tensor2D, double tensor3D)
	Plain 2D-to-3D tensor conversion. More...

void	from3Dto2D (const double tensor3D, double tensor2D)
	Plain 3D-to-2D tensor conversion. More...

Detailed Description

Various tensor transformation utilities.

Function Documentation

◆ from2Dto3D()

void FFaTensorTransforms::from2Dto3D	(	const double *	S2D,
		double *	S3D
	)

Plain 2D-to-3D tensor conversion.

Padding with zeros to fit the 3D tensor.

◆ from3Dto2D()

void FFaTensorTransforms::from3Dto2D	(	const double *	S3D,
		double *	S2D
	)

Plain 3D-to-2D tensor conversion.

Just cutting off whats needed to fit the 2D tensor.

◆ maxShearDir()

void FFaTensorTransforms::maxShearDir	(	int	N,
		const double *	pMaxDir,
		const double *	pMinDir,
		double *	maxShearDir
	)

Returns the direction of maximum shear.

Parameters

[in]	N	Vector dimension (1, 2 or 3)
[in]	pMaxDir	Direction of the max principal value
[in]	pMinDir	Direction of the min principal value
[out]	maxShearDir	Direction of the max shear value, this is 45 degrees on the max and min directions pointing from min to max

◆ maxShearValue()

double FFaTensorTransforms::maxShearValue	(	double	pMax,
		double	pMin
	)

Returns the maximum shear value.

Parameters

[in]	pMax	Max principal value
[in]	pMin	Min principal value

Returns: Max shear value

◆ principalDirs() [1/3]

int FFaTensorTransforms::principalDirs	(	const double *	S,
		double *	pVal,
		double *	p1Dir,
		double *	p2Dir
	)

Calculates the principal directions and values of a 2D tensor.

Parameters

[in]	S	Tensor values, {s11, s22, s12}
[out]	pVal	Principal values, {pMax,pMin}
[out]	p1Dir	Direction vector for the first principal value
[out]	p2Dir	Direction vector for the second principal value

Returns: Negative value on error, otherwise zero

◆ principalDirs() [2/3]

int FFaTensorTransforms::principalDirs	(	const double *	S,
		double *	pVal,
		double *	p1Dir,
		double *	p2Dir,
		double *	p3Dir
	)

Calculates the principal directions and values of a 3D tensor.

Parameters

[in]	S	Tensor values, {s11, s22, s33, s12, s13, s23}
[out]	pVal	Principal values, {pMax,pMid,pMin}
[out]	p1Dir	Direction vector for the first principal value
[out]	p2Dir	Direction vector for the second principal value
[out]	p3Dir	Direction vector for the third principal value

Returns: Negative value on error, otherwise zero

◆ principalDirs() [3/3]

int FFaTensorTransforms::principalDirs	(	int	N,
		const double *	S,
		double *	pVal,
		double *	pDir
	)

Calculates the principal directions and values of a tensor.

Parameters

[in]	N	Tensor dimension (1, 2 or 3)
[in]	S	Tensor values, upper triangle of the symmetric tensor
[out]	pVal	Principal values in descending order, i.e., {P1,P2,P3}
[out]	pDir	Associated principal direction vectors, e.g., in 3D: dir1 = pDir[0:2] dir2 = pDir[3:5] dir3 = pDir[6:8]

Returns: Negative value on error, otherwise zero

The tensor values are assumed laid out as follows

N = 1: S = {s11}
N = 2: S = {s11, s22, s12}
N = 3: S = {s11, s22, s33, s12, s13, s23}

This function uses the LAPACK eigenvalue solver DSYEV.

◆ principalVals2D()

bool FFaTensorTransforms::principalVals2D	(	double	s11,
		double	s22,
		double	s12,
		double *	pVal
	)

Calculates the principal values of a 2D tensor.

◆ principalVals3D()

bool FFaTensorTransforms::principalVals3D	(	double	s11,
		double	s22,
		double	s33,
		double	s12,
		double	s13,
		double	s23,
		double *	pVal
	)

Calculates the principal values of a 3D tensor.

◆ principalValues() [1/3]

bool FFaTensorTransforms::principalValues	(	double	s11,
		double	s22,
		double	s12,
		double &	p1,
		double &	p2
	)

inline

◆ principalValues() [2/3]

bool FFaTensorTransforms::principalValues	(	double	s11,
		double	s22,
		double	s33,
		double	s12,
		double	s13,
		double	s23,
		double &	p1,
		double &	p2,
		double &	p3
	)

inline

◆ principalValues() [3/3]

bool FFaTensorTransforms::principalValues	(	int	N,
		const double *	S,
		double *	P
	)

Calculates the principal values of a tensor.

Parameters

[in]	N	Tensor dimension (1, 2 or 3)
[in]	S	Tensor values, upper triangle of the symmetric tensor
[out]	P	Principal values in descending order, i.e., {P1,P2,P3}

The tensor values are assumed laid out as follows

N = 1: S = {s11}
N = 2: S = {s11, s22, s12}
N = 3: S = {s11, s22, s33, s12, s13, s23}

◆ rotate() [1/2]

void FFaTensorTransforms::rotate	(	const double *	S,
		const double *	eX,
		const double *	eY,
		const double *	eZ,
		double *	S_transformed
	)

Coordinate transformation for a 3D tensor.

Parameters

[in]	S	Symmetric input tensor, S = {s11, s22, s33, s12, s13, s23}
[in]	eX	Unit X-direction vector
[in]	eY	Unit Y-direction vector
[in]	eZ	Unit Z-direction vector
[out]	S_transformed	The transformed tensor

◆ rotate() [2/2]

void FFaTensorTransforms::rotate	(	const double *	S,
		const double *	eX,
		const double *	eY,
		double *	S_transformed
	)

Coordinate transformation for a 2D tensor.

Parameters

[in]	S	Symmetric input tensor, S = {s11, s22, s12}
[in]	eX	Unit X-direction vector
[in]	eY	Unit Y-direction vector
[out]	S_transformed	The transformed tensor

◆ rotate2D()

void FFaTensorTransforms::rotate2D	(	const double *	inTensor,
		const double *	rotMx,
		double *	outTensor
	)

Coordinate transformation for a 2D tensor.

Parameters

[in]	inTensor	Symmetric input tensor, {s11, s22, s12}
[in]	rotMx	Transformation matrix, [eX, eY]
[out]	outTensor	The transformed tensor

◆ rotate3D()

void FFaTensorTransforms::rotate3D	(	const double *	inTensor,
		const double *	rotMx,
		double *	outTensor
	)

Coordinate transformation for a 3D tensor.

Parameters

[in]	inTensor	Symmetric input tensor, {s11, s22, s33, s12, s13, s23}
[in]	rotMx	Transformation matrix, [eX, eY, eZ]
[out]	outTensor	The transformed tensor

◆ vonMises() [1/3]

double FFaTensorTransforms::vonMises	(	double	s11,
		double	s22,
		double	s12
	)

Returns the von Mises value of a 2D stress/strain tensor.

◆ vonMises() [2/3]

double FFaTensorTransforms::vonMises	(	double	s11,
		double	s22,
		double	s33,
		double	s12,
		double	s13,
		double	s23
	)

Returns the von Mises value of a 3D stress/strain tensor.

◆ vonMises() [3/3]

double FFaTensorTransforms::vonMises	(	int	N,
		const double *	S
	)

Returns the von Mises value of a symmetric stress/strain tensor.

Parameters

[in]	N	Tensor dimension (1, 2 or 3)
[in]	S	Tensor values, upper triangle of the symmetric tensor

The tensor values are assumed laid out as follows

N = 1: S = {s11}
N = 2: S = {s11, s22, s12}
N = 3: S = {s11, s22, s33, s12, s13, s23}

Functions

Detailed Description

Function Documentation

◆ from2Dto3D()

◆ from3Dto2D()

◆ maxShearDir()

◆ maxShearValue()

◆ principalDirs() [1/3]

◆ principalDirs() [2/3]

◆ principalDirs() [3/3]

◆ principalVals2D()

◆ principalVals3D()

◆ principalValues() [1/3]

◆ principalValues() [2/3]

◆ principalValues() [3/3]

◆ rotate() [1/2]

◆ rotate() [2/2]

◆ rotate2D()

◆ rotate3D()

◆ vonMises() [1/3]

◆ vonMises() [2/3]

◆ vonMises() [3/3]