A symmetric 2nd order tensor. More...

#include <symtensor.h>

Public Member Functions
	SymTensor ()
	Default constructor, no data initialization.

	SymTensor (const SymTensor &s)
	Copy constructor.

	SymTensor (const double &i11, const double &i22=0.0, const double &i33=0.0, const double &i12=0.0, const double &i13=0.0, const double &i23=0.0)

const SymTensor &	operator= (const SymTensor &s)
	Assignment operator.

bool	operator== (const SymTensor &s) const
	Equality operator.

bool	operator< (const SymTensor &s) const

const double &	s11 () const
	Component access, note that s12 is equivalent to s21 (for instance).

const double &	s22 () const
	Component access, note that s12 is equivalent to s21 (for instance).

const double &	s33 () const
	Component access, note that s12 is equivalent to s21 (for instance).

const double &	s12 () const
	Component access, note that s12 is equivalent to s21 (for instance).

const double &	s13 () const
	Component access, note that s12 is equivalent to s21 (for instance).

const double &	s23 () const
	Component access, note that s12 is equivalent to s21 (for instance).

const double &	s21 () const
	Component access, note that s12 is equivalent to s21 (for instance).

const double &	s31 () const
	Component access, note that s12 is equivalent to s21 (for instance).

const double &	s32 () const
	Component access, note that s12 is equivalent to s21 (for instance).

double &	rs11 ()
	Reference access to components, note that s12 is equivalent to s21 (for instance).

double &	rs22 ()
	Reference access to components, note that s12 is equivalent to s21 (for instance).

double &	rs33 ()
	Reference access to components, note that s12 is equivalent to s21 (for instance).

double &	rs12 ()
	Reference access to components, note that s12 is equivalent to s21 (for instance).

double &	rs13 ()
	Reference access to components, note that s12 is equivalent to s21 (for instance).

double &	rs23 ()
	Reference access to components, note that s12 is equivalent to s21 (for instance).

double &	rs21 ()
	Reference access to components, note that s12 is equivalent to s21 (for instance).

double &	rs31 ()
	Reference access to components, note that s12 is equivalent to s21 (for instance).

double &	rs32 ()
	Reference access to components, note that s12 is equivalent to s21 (for instance).

const double &	operator[] (unsigned int i) const
	Allows Index access to tensor components.

double &	operator[] (unsigned int i)

const double &	operator() (unsigned int i, unsigned int j) const
	Allows 2D index access to tensor components - base 0.

double &	operator() (unsigned int i, unsigned int j)
	Allows 2D index access to tensor components - base 0.

DVect3	getEigenInfo (SymTensorInfo *si=0) const
	Returns the eigenvalues (principal components) and eigenvectors (principal directions). The information necessary to regenerate the tensor from eigenvalues is placed in the helper class si. x = minimum (most negative), y = intermediate, z = maximum (most positive)

double	getTrace () const
	Returns the trace of the tensor (11+22+33). I1.

SymTensor	getDeviatoric () const
	Returns the deviatoric tensor.

double	getI1 () const
	Same as getTrace() - returns the first invariant.

double	getI2 () const
	Returns the second invariant.

double	getI3 () const
	Returns the third invariant, or I3.

double	getJ2 () const
	Returns the second invariant of the deviatoric – J2.

double	getJ2 (SymTensor dev, double I1=nullptr)
	Returns the second invariant of the deviatoric – J2.

double	getJ3 () const
	returns the third invariant of the deviatoric – J3

double	getLode (double I1=nullptr, double J2=nullptr, double *J3=nullptr)
	returns the Lode's angle in rad, TX = pi/6, TE = -pi/6

double	getDeterminate () const
	Returns the determinate of the tensor.

double	getNorm2 () const
	Returns a scalar norm (magnitude) value for the tensor, can be used for tolerance checking, etc.

double	getTotalMeasure () const

SymTensor	toGlobal (const Axes3D &a) const
	Transforms tensor from local (a) to global system.

DVect3	operator* (const DVect3 &input) const
	Performs the linear mapping represented by the tensor on the vector input.

DVect2	operator* (const DVect2 &input) const

SymTensor	operator* (const double &mul) const

const SymTensor &	*operator=** (const double &mul)

SymTensor	operator/ (const double &mul) const

const SymTensor &	operator/= (const double &mul)

SymTensor	mul (const double &d) const
	Returns a SymTensor with every component multiplied by a scalar value.

const SymTensor &	operator+= (const SymTensor &s)
	+= operator for a SymTensor

const SymTensor &	operator-= (const SymTensor &s)

SymTensor	operator+ (const SymTensor &s) const

SymTensor	operator- (const SymTensor &s) const

bool	isDiagonal (double tol=std::numeric_limits< double >::epsilon() *1000.0) const
	Determines whether or not the SymTensor is diagonal.

bool	isIsotropic (double tol=std::numeric_limits< double >::epsilon() *1000.0) const

void	adjustTrace (const double &newTrace)

void	incrementDiagonal (const double &increment)

void	rotate (const DVect3 &rot)

double	maxAbs () const

bool	zero () const

Static Public Member Functions
static SymTensor	fromPrincipal (const DVect3 &prin, const Axes3D &axes)
	Creates a full SymTensor given principal vectors (in a DVect3) and an Axes3D for orientation.

static SymTensor	fromForceNormal (const DVect3 &normal, const DVect3 &force)

static uint32	doubleToSingleComponent (uint32 dof1, uint32 dof2)

Detailed Description

A symmetric 2nd order tensor.

Includes helper functions for converting to and from eigenvalues and eigenvectors.

Constructor & Destructor Documentation

◆ SymTensor()

SymTensor::SymTensor	(	const double &	i11,
		const double &	i22 = 0.0,
		const double &	i33 = 0.0,
		const double &	i12 = 0.0,
		const double &	i13 = 0.0,
		const double &	i23 = 0.0 )

inlineexplicit

Explicit constructor, from the six components.
The diagonal components are optional.

Member Function Documentation

◆ fromForceNormal()

SymTensor SymTensor::fromForceNormal	(	const DVect3 &	normal,
		const DVect3 &	force )

static

Find a stress that produces the given force when multiplied by the given normal There is not a unique solution to to this - uses the max normal abs component. Note does not check normal.