AbstractIsotropicCompressibleMaterialLaw< DIM > Class Template Reference

#include <AbstractIsotropicCompressibleMaterialLaw.hpp>

Inheritance diagram for AbstractIsotropicCompressibleMaterialLaw< DIM >:

Collaboration diagram for AbstractIsotropicCompressibleMaterialLaw< DIM >:

List of all members.

Public Member Functions
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	~AbstractIsotropicCompressibleMaterialLaw ()
Protected Member Functions
virtual double	Get_dW_dI1 (double I1, double I2, double I3)=0
virtual double	Get_dW_dI2 (double I1, double I2, double I3)=0
virtual double	Get_dW_dI3 (double I1, double I2, double I3)=0
virtual double	Get_d2W_dI1 (double I1, double I2, double I3)=0
virtual double	Get_d2W_dI2 (double I1, double I2, double I3)=0
virtual double	Get_d2W_dI3 (double I1, double I2, double I3)=0
virtual double	Get_d2W_dI2I3 (double I1, double I2, double I3)=0
virtual double	Get_d2W_dI1I3 (double I1, double I2, double I3)=0
virtual double	Get_d2W_dI1I2 (double I1, double I2, double I3)=0

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Detailed Description

template<unsigned DIM>
class AbstractIsotropicCompressibleMaterialLaw< DIM >

AbstractIsotropicCompressibleMaterialLaw

An isotropic COMPRESSIBLE hyper-elastic material law for finite elasticity, of the form W(E) = W(I1,I2,I3) where I1,I2,I3 are the principal invariants of C, the Lagrangian deformation tensor. (NOT the deviatoric versions of these scalars), and the derivatives with respect to these invariants need to be prescribed by the concrete class.

(I1=trace(C), I2=0.5(trace(C)^2-trace(C^2)), I3=det(C)).

Definition at line 54 of file AbstractIsotropicCompressibleMaterialLaw.hpp.

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Constructor & Destructor Documentation

template<unsigned DIM>

AbstractIsotropicCompressibleMaterialLaw< DIM >::~AbstractIsotropicCompressibleMaterialLaw

(

)

[virtual]

Destructor.

Definition at line 39 of file AbstractIsotropicCompressibleMaterialLaw.cpp.

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Member Function Documentation

template<unsigned DIM>

void AbstractIsotropicCompressibleMaterialLaw< 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
	)		[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 -- NOT USED AS COMPRESSIBLE LAW
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.

This is the implemtation for an isotropic material law, so the stress etc is computed by calling methods returning dW/dI1, dW/dI2 etc.

Implements AbstractMaterialLaw< DIM >.

Definition at line 44 of file AbstractIsotropicCompressibleMaterialLaw.cpp.

References Determinant(), SecondInvariant(), and Trace().

template<unsigned DIM>

virtual double AbstractIsotropicCompressibleMaterialLaw< DIM >::Get_d2W_dI1	(	double	I1,
		double	I2,
		double	I3
	)		[protected, pure virtual]

Get the second derivative d^2W/dI1^2.

Parameters:

I1	first principal invariant of C
I2	second principal invariant of C
I3	third principal invariant of C

Implemented in CompressibleMooneyRivlinMaterialLaw< DIM >.

template<unsigned DIM>

virtual double AbstractIsotropicCompressibleMaterialLaw< DIM >::Get_d2W_dI1I2	(	double	I1,
		double	I2,
		double	I3
	)		[protected, pure virtual]

Get the second derivative d^2W/dI1dI2.

Parameters:

I1	first principal invariant of C
I2	second principal invariant of C
I3	third principal invariant of C

Implemented in CompressibleMooneyRivlinMaterialLaw< DIM >.

template<unsigned DIM>

virtual double AbstractIsotropicCompressibleMaterialLaw< DIM >::Get_d2W_dI1I3	(	double	I1,
		double	I2,
		double	I3
	)		[protected, pure virtual]

Get the second derivative d^2W/dI1dI3.

Parameters:

I1	first principal invariant of C
I2	second principal invariant of C
I3	third principal invariant of C

Implemented in CompressibleMooneyRivlinMaterialLaw< DIM >.

template<unsigned DIM>

virtual double AbstractIsotropicCompressibleMaterialLaw< DIM >::Get_d2W_dI2	(	double	I1,
		double	I2,
		double	I3
	)		[protected, pure virtual]

Get the second derivative d^2W/dI2^2.

Parameters:

I1	first principal invariant of C
I2	second principal invariant of C
I3	third principal invariant of C

Implemented in CompressibleMooneyRivlinMaterialLaw< DIM >.

template<unsigned DIM>

virtual double AbstractIsotropicCompressibleMaterialLaw< DIM >::Get_d2W_dI2I3	(	double	I1,
		double	I2,
		double	I3
	)		[protected, pure virtual]

Get the second derivative d^2W/dI2dI3.

Parameters:

I1	first principal invariant of C
I2	second principal invariant of C
I3	third principal invariant of C

Implemented in CompressibleMooneyRivlinMaterialLaw< DIM >.

template<unsigned DIM>

virtual double AbstractIsotropicCompressibleMaterialLaw< DIM >::Get_d2W_dI3	(	double	I1,
		double	I2,
		double	I3
	)		[protected, pure virtual]

Get the second derivative d^2W/dI3^2.

Parameters:

I1	first principal invariant of C
I2	second principal invariant of C
I3	third principal invariant of C

Implemented in CompressibleMooneyRivlinMaterialLaw< DIM >.

template<unsigned DIM>

virtual double AbstractIsotropicCompressibleMaterialLaw< DIM >::Get_dW_dI1	(	double	I1,
		double	I2,
		double	I3
	)		[protected, pure virtual]

Get the first derivative dW/dI1.

Parameters:

I1	first principal invariant of C
I2	second principal invariant of C
I3	third principal invariant of C

Implemented in CompressibleMooneyRivlinMaterialLaw< DIM >.

template<unsigned DIM>

virtual double AbstractIsotropicCompressibleMaterialLaw< DIM >::Get_dW_dI2	(	double	I1,
		double	I2,
		double	I3
	)		[protected, pure virtual]

Get the first derivative dW/dI2.

Parameters:

I1	first principal invariant of C
I2	second principal invariant of C
I3	third principal invariant of C

Implemented in CompressibleMooneyRivlinMaterialLaw< DIM >.

template<unsigned DIM>

virtual double AbstractIsotropicCompressibleMaterialLaw< DIM >::Get_dW_dI3	(	double	I1,
		double	I2,
		double	I3
	)		[protected, pure virtual]

Get the first derivative dW/dI3.

Parameters:

I1	first principal invariant of C
I2	second principal invariant of C
I3	third principal invariant of C

Implemented in CompressibleMooneyRivlinMaterialLaw< DIM >.

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

• continuum_mechanics/src/problem/material_laws/AbstractIsotropicCompressibleMaterialLaw.hpp
• continuum_mechanics/src/problem/material_laws/AbstractIsotropicCompressibleMaterialLaw.cpp