SchmidCostaExponentialLaw2d Class Reference

#include <SchmidCostaExponentialLaw2d.hpp>

Inherits AbstractIncompressibleMaterialLaw< 2 >.

Collaboration diagram for SchmidCostaExponentialLaw2d:

Public Member Functions
	SchmidCostaExponentialLaw2d ()
void	ComputeStressAndStressDerivative (c_matrix< double, 2, 2 > &rC, c_matrix< double, 2, 2 > &rInvC, double pressure, c_matrix< double, 2, 2 > &rT, FourthOrderTensor< 2 > &rDTdE, bool computeDTdE)
double	GetA ()
std::vector< std::vector < double > >	GetB ()
double	GetZeroStrainPressure ()
void	SetChangeOfBasisMatrix (c_matrix< double, 2, 2 > &rChangeOfBasisMatrix)
Private Attributes
double	mA
std::vector< std::vector < double > >	mB
c_matrix< double, 2, 2 >	mIdentity
c_matrix< double, 2, 2 > *	mpChangeOfBasisMatrix

Detailed Description

A 2d version of the material law in Costa, Holmes, McCulloch "Modelling Cardiac Mechanical Properties in Three Dimensions" Philo. Trans. R. Soc.

W = aexp(Q-1) where Q = bff*Eff^2 + bfs*Efs^2 + bsf*Esf^2 + bss*Ess^2

where the parameters are taken from the fitting in Schmid,Nash,Young,Hunter "Myocardial Material Parameter Estimation - A Comparative Study for Simple Shear" Transactions of the ASME.

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 51 of file SchmidCostaExponentialLaw2d.hpp.

Constructor & Destructor Documentation

SchmidCostaExponentialLaw2d::SchmidCostaExponentialLaw2d ( )

Constructor.

Definition at line 31 of file SchmidCostaExponentialLaw2d.cpp.

References mA, mB, mIdentity, and mpChangeOfBasisMatrix.

Member Function Documentation

void SchmidCostaExponentialLaw2d::ComputeStressAndStressDerivative	(	c_matrix< double, 2, 2 > &	rC,
		c_matrix< double, 2, 2 > &	rInvC,
		double	pressure,
		c_matrix< double, 2, 2 > &	rT,
		FourthOrderTensor< 2 > &	rDTdE,
		bool	computeDTdE
	)

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.

Definition at line 60 of file SchmidCostaExponentialLaw2d.cpp.

References mA, mB, mIdentity, mpChangeOfBasisMatrix, FourthOrderTensor< DIM >::SetAsProduct(), and FourthOrderTensor< DIM >::Zero().

double SchmidCostaExponentialLaw2d::GetA ( )

Get method for mA.

Definition at line 146 of file SchmidCostaExponentialLaw2d.cpp.

References mA.

std::vector< std::vector< double > > SchmidCostaExponentialLaw2d::GetB ( )

Get method for mB.

Definition at line 151 of file SchmidCostaExponentialLaw2d.cpp.

References mB.

double SchmidCostaExponentialLaw2d::GetZeroStrainPressure ( ) [virtual]

Get the pressure corresponding to E=0, ie C=identity.

Implements AbstractIncompressibleMaterialLaw< 2 >.

Definition at line 156 of file SchmidCostaExponentialLaw2d.cpp.

void SchmidCostaExponentialLaw2d::SetChangeOfBasisMatrix ( c_matrix< double, 2, 2 > & rChangeOfBasisMatrix ) [inline]

Some material laws (eg pole-zero) may have prefered directions (eg fibre direction), but be implemented to assume the prefered directions are parallel to the X-axis etc. Call this with the change of basis matrix and C will be transformed from the Euclidean coordinate system to the appropriate coordinate system before used to calculate T, which will then be transformed from the appropriate coordinate system back to the Euclidean coordinate system before being returned, as will dTdE.

The change of basis matrix for schmid-costa should be of the form: [ fibre_vec sheet_vec normal_vec ]

Parameters:

rChangeOfBasisMatrix

Change of basis matrix.

Definition at line 123 of file SchmidCostaExponentialLaw2d.hpp.

References mpChangeOfBasisMatrix.