b2000::RightStretchTensor_3_3 Class Reference

#include "b2right_stretch_tensor.H"

Public Member Functions
	RightStretchTensor_3_3 ()
	RightStretchTensor_3_3 (const double F[3][3], const bool second=false)
void	compute (const double F[3][3], const bool second=false)

Public Attributes
double	R_3_3 [3][3]
double	U_3_3 [3][3]
double	R [9]
double	U [6]
double	DU [6][9]
double	DR [9][9]
double	DDU [6][9][9]

Detailed Description

Class to perform the polar decomposition of the 3x3 gradient deformation tensor F into the rotation tensor R and the right stretch tensor U, and to compute the first derivatives (DU) and second derivatives (DDU) of the right stretch tensor U w.r.t. gradient deformation tensor F.

The 3x3 matrices are column-major. The symmetric tensors are arranged [00, 11, 22, 01, 12, 02], and the non-symmetric tensors are arranged [00, 10, 20, 01, 11, 21, 02, 12, 22].

Constructor & Destructor Documentation

RightStretchTensor_3_3() [1/2]

b2000::RightStretchTensor_3_3::RightStretchTensor_3_3 ( )

inline

Default constructor.

RightStretchTensor_3_3() [2/2]

b2000::RightStretchTensor_3_3::RightStretchTensor_3_3 ( const double  F[3][3], const bool  second = false  )

inline

Calls compute().

Member Function Documentation

compute()

void b2000::RightStretchTensor_3_3::compute	(	const double	F[3][3],
		const bool	second = false
	)

Computes U and R with F = R * U and performs analytical differentiation of U (and R), according to Chen & Wheeler, Derivatives of the stretch and rotation tensors, Journal of Elasticity 32:175-182, 1993.

Parameters

F	The gradient deformation tensor arranged in column-major format.
second	Whether second-order differentiation should be performed. Default is false.

Member Data Documentation

DDU

double b2000::RightStretchTensor_3_3::DDU[6][9][9]

Second derivatives of the right stretch tensor U w.r.t. the components of the gradient deformation tensor F.

DR

double b2000::RightStretchTensor_3_3::DR[9][9]

Derivatives of the rotation tensor R w.r.t. the components of the gradient deformation tensor F.

DU

double b2000::RightStretchTensor_3_3::DU[6][9]

Derivatives of the right stretch tensor U w.r.t. the components of the gradient deformation tensor F.

R

double b2000::RightStretchTensor_3_3::R[9]

The rotation tensor R as a vector.

R_3_3

double b2000::RightStretchTensor_3_3::R_3_3[3][3]

The rotation tensor R as a 3 x 3 column-major matrix.

U

double b2000::RightStretchTensor_3_3::U[6]

The right stretch tensor U as a vector.

U_3_3

double b2000::RightStretchTensor_3_3::U_3_3[3][3]

The right stretch tensor U as a (symmetric) 3 x 3 column-major matrix.

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

• utils/b2right_stretch_tensor.H
• utils/b2right_stretch_tensor.C