#include <PolynomialMaterialLaw3d.hpp>

Inheritance diagram for PolynomialMaterialLaw3d:

Collaboration diagram for PolynomialMaterialLaw3d:

Public Member Functions
double	Get_dW_dI1 (double I1, double I2)

double	Get_dW_dI2 (double I1, double I2)

double	Get_d2W_dI1 (double I1, double I2)

double	Get_d2W_dI2 (double I1, double I2)

double	Get_d2W_dI1I2 (double I1, double I2)

double	GetAlpha (unsigned i, unsigned j)

	PolynomialMaterialLaw3d (unsigned n, std::vector< std::vector< double > > alpha)

Public Member Functions inherited from AbstractIsotropicIncompressibleMaterialLaw< 3 >
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)

virtual	~AbstractIsotropicIncompressibleMaterialLaw ()

double	GetZeroStrainPressure ()

Public Member Functions inherited from AbstractIncompressibleMaterialLaw< DIM >
	AbstractIncompressibleMaterialLaw ()

virtual	~AbstractIncompressibleMaterialLaw ()

Public Member Functions inherited from AbstractMaterialLaw< DIM >
	AbstractMaterialLaw ()

virtual	~AbstractMaterialLaw ()

void	ComputeCauchyStress (c_matrix< double, DIM, DIM > &rF, double pressure, c_matrix< double, DIM, DIM > &rSigma)

void	Compute1stPiolaKirchoffStress (c_matrix< double, DIM, DIM > &rF, double pressure, c_matrix< double, DIM, DIM > &rS)

void	Compute2ndPiolaKirchoffStress (c_matrix< double, DIM, DIM > &rC, double pressure, c_matrix< double, DIM, DIM > &rT)

virtual void	ScaleMaterialParameters (double scaleFactor)

void	SetChangeOfBasisMatrix (c_matrix< double, DIM, DIM > &rChangeOfBasisMatrix)

void	ResetToNoChangeOfBasisMatrix ()

Static Public Member Functions
static std::vector< std::vector< double > >	GetZeroedAlpha (unsigned n)

Private Attributes
unsigned	mN

std::vector< std::vector< double > >	mAlpha

Additional Inherited Members
Protected Member Functions inherited from AbstractMaterialLaw< DIM >
void	ComputeTransformedDeformationTensor (c_matrix< double, DIM, DIM > &rC, c_matrix< double, DIM, DIM > &rInvC, c_matrix< double, DIM, DIM > &rCTransformed, c_matrix< double, DIM, DIM > &rInvCTransformed)

void	TransformStressAndStressDerivative (c_matrix< double, DIM, DIM > &rT, FourthOrderTensor< DIM, DIM, DIM, DIM > &rDTdE, bool transformDTdE)

Protected Attributes inherited from AbstractMaterialLaw< DIM >
c_matrix< double, DIM, DIM > *	mpChangeOfBasisMatrix

Detailed Description

PolynomialMaterialLaw3d

An incompressible, isotropic, hyperelastic material law with a polynomial form

W(I_1,I_2) = Sigma_{0<p+q<=N} alpha_{pq} (I_1-3)^p (I_2-3)^q - (pressure/2) C^{-1}

For example, if N=1, this reduces to the Mooney Rivlin law W(I_1,I_2) = alpha_{10} (I_1-3) + alpha_{01} (I_2-3) - (pressure/2) C^{-1} ie the matrix alpha has the form [ 0 c1 ] [ c2 0 ] where c1 and c2 is the usual notation for the Mooney-Rivlin constants

The polynomial is specified by passing in N and the matrix (actually a std::vector of std::vector<double>s) alpha. alpha should be of size N+1 by N+1, with the bottom right hand block (ie the components such that p+q>N) all zero. alpha[0][0] should really also be 0, but, being since alpha[0][0] (I1_3)^0 (I2-3)^0 is a constant and disappears when the strain energy W is differentiated to obtain the stress, it is not used. An exception is thrown if alpha[p][q]!=0 for p+q > N though.

Definition at line 64 of file PolynomialMaterialLaw3d.hpp.