CompressibleExponentialLaw< DIM > Class Template Reference

#include <CompressibleExponentialLaw.hpp>

Inherits AbstractCompressibleMaterialLaw< DIM >.

Collaboration diagram for CompressibleExponentialLaw< DIM >:

Public Member Functions
	CompressibleExponentialLaw ()
void	ComputeStressAndStressDerivative (c_matrix< double, DIM, DIM > &rC, c_matrix< double, DIM, DIM > &rInvC, double pressure, c_matrix< double, DIM, DIM > &rT, FourthOrderTensor< DIM, DIM, DIM, DIM > &rDTdE, bool computeDTdE)
double	GetA ()
std::vector< std::vector < double > >	GetB ()
double	GetCompressibilityParam ()
Private Attributes
double	mA
std::vector< std::vector < double > >	mB
double	mCompressibilityParam
c_matrix< double, DIM, DIM >	mIdentity
Friends
class	TestCompressibleLawTransverselyIsotropic

Detailed Description

template<unsigned DIM>
class CompressibleExponentialLaw< DIM >

The compressible exponential material law implemented in

Uysk, Effect of Laminar Orthotropic Myofiber Architecture on Regional Stress and Strain in the Canine Left Ventricle, Journal of Elasticity, 2000.

W = a[exp(Q)-1]/2 + c (J ln(J) - J + 1) where Q = sum b_{MN} E_{MN}^2

The exponential term is the same form as in the SchmidCosta law, although the parameters here are those given in the paper cited above, not the same as in the SchmidCosta class.

Note, by default, the fibre direction is assumed to be THE X-DIRECTION, and the sheet direction the Y-DIRECTION (ie sheets in the XY plane). Call SetChangeOfBasisMatrix() before ComputeStressAndStressDerivative(), with the matrix P = [fibre_vec, sheet_vec, normal_vec] if this is not the case.

Definition at line 59 of file CompressibleExponentialLaw.hpp.

Constructor & Destructor Documentation

template<unsigned DIM>

CompressibleExponentialLaw< DIM >::CompressibleExponentialLaw ( ) [inline]

Constructor.

Definition at line 39 of file CompressibleExponentialLaw.cpp.

References CompressibleExponentialLaw< DIM >::mA, CompressibleExponentialLaw< DIM >::mB, CompressibleExponentialLaw< DIM >::mCompressibilityParam, and CompressibleExponentialLaw< DIM >::mIdentity.

Member Function Documentation

template<unsigned DIM>

void CompressibleExponentialLaw< DIM >::ComputeStressAndStressDerivative	(	c_matrix< double, DIM, DIM > &	rC,
		c_matrix< double, DIM, DIM > &	rInvC,
		double	pressure,
		c_matrix< double, DIM, DIM > &	rT,
		FourthOrderTensor< DIM, DIM, DIM, DIM > &	rDTdE,
		bool	computeDTdE
	)			`[inline, virtual]`

Compute the (2nd Piola Kirchoff) stress T and the stress derivative dT/dE for a given strain.

NOTE: the strain E is not expected to be passed in, instead the Lagrangian deformation tensor C is required (recall, E = 0.5(C-I))

dT/dE is a fourth-order tensor, where dT/dE[M][N][P][Q] = dT^{MN}/dE_{PQ}

Parameters:

	rC	The Lagrangian deformation tensor (F^T F)
	rInvC	The inverse of C. Should be computed by the user. (Change this?)
	pressure	the current pressure
	rT	the stress will be returned in this parameter
	rDTdE	the stress derivative will be returned in this parameter, assuming the final parameter is true
	computeDTdE	a boolean flag saying whether the stress derivative is required or not.