AbstractIsotropicIncompressibleMaterialLaw< DIM > Class Template Reference

#include <AbstractIsotropicIncompressibleMaterialLaw.hpp>

Inherits AbstractIncompressibleMaterialLaw< DIM >.

Inherited by ExponentialMaterialLaw< DIM >, and MooneyRivlinMaterialLaw< DIM >.

Collaboration diagram for AbstractIsotropicIncompressibleMaterialLaw< DIM >:

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	~AbstractIsotropicIncompressibleMaterialLaw ()
double	GetZeroStrainPressure ()
template<>
double	GetZeroStrainPressure ()
Protected Member Functions
virtual double	Get_dW_dI1 (double I1, double I2)=0
virtual double	Get_dW_dI2 (double I1, double I2)=0
virtual double	Get_d2W_dI1 (double I1, double I2)=0
virtual double	Get_d2W_dI2 (double I1, double I2)=0
virtual double	Get_d2W_dI1I2 (double I1, double I2)=0

Detailed Description

template<unsigned DIM>
class AbstractIsotropicIncompressibleMaterialLaw< DIM >

AbstractIsotropicIncompressibleMaterialLaw

An isotropic incompressible hyperelastic material law for finite elastiticy

The law is given by a strain energy function W(I1,I2,I3), where I_i are the principal invariants of C, the Lagrangian deformation tensor. (I1=trace(C), I2=trace(C)^2-trace(C^2), I3=det(C)). Since it is incompressible, the full strain energy has the form W^{full} = W(I_1,I_2) - p/2 C^{-1}

Note: only dimension equals 2 or 3 should be permitted.

Definition at line 48 of file AbstractIsotropicIncompressibleMaterialLaw.hpp.

Constructor & Destructor Documentation

template<unsigned DIM>

AbstractIsotropicIncompressibleMaterialLaw< DIM >::~AbstractIsotropicIncompressibleMaterialLaw ( ) [inline, virtual]

Destructor.

Definition at line 32 of file AbstractIsotropicIncompressibleMaterialLaw.cpp.

Member Function Documentation

template<unsigned DIM>

void AbstractIsotropicIncompressibleMaterialLaw< 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.

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 37 of file AbstractIsotropicIncompressibleMaterialLaw.cpp.

References AbstractIsotropicIncompressibleMaterialLaw< DIM >::Get_d2W_dI1(), AbstractIsotropicIncompressibleMaterialLaw< DIM >::Get_d2W_dI1I2(), AbstractIsotropicIncompressibleMaterialLaw< DIM >::Get_d2W_dI2(), AbstractIsotropicIncompressibleMaterialLaw< DIM >::Get_dW_dI1(), AbstractIsotropicIncompressibleMaterialLaw< DIM >::Get_dW_dI2(), SecondInvariant(), and Trace().

template<unsigned DIM>

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

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

Todo:: The name of this method should not include underscores.

Parameters:

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

Implemented in ExponentialMaterialLaw< DIM >, MooneyRivlinMaterialLaw< DIM >, and PolynomialMaterialLaw3d.

Referenced by AbstractIsotropicIncompressibleMaterialLaw< DIM >::ComputeStressAndStressDerivative().

template<unsigned DIM>

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

Get the second derivative d^2W/dI1dI2.

Todo:: The name of this method should not include underscores.

Parameters:

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

Implemented in ExponentialMaterialLaw< DIM >, MooneyRivlinMaterialLaw< DIM >, and PolynomialMaterialLaw3d.

Referenced by AbstractIsotropicIncompressibleMaterialLaw< DIM >::ComputeStressAndStressDerivative().

template<unsigned DIM>

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

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

Todo:: The name of this method should not include underscores.

Parameters:

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

Implemented in ExponentialMaterialLaw< DIM >, MooneyRivlinMaterialLaw< DIM >, and PolynomialMaterialLaw3d.

Referenced by AbstractIsotropicIncompressibleMaterialLaw< DIM >::ComputeStressAndStressDerivative().

template<unsigned DIM>

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

Get the first derivative dW/dI1.

Todo:: The name of this method should not include underscores.

Parameters:

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

Implemented in ExponentialMaterialLaw< DIM >, MooneyRivlinMaterialLaw< DIM >, and PolynomialMaterialLaw3d.

Referenced by AbstractIsotropicIncompressibleMaterialLaw< DIM >::ComputeStressAndStressDerivative(), AbstractIsotropicIncompressibleMaterialLaw< 3 >::GetZeroStrainPressure(), and AbstractIsotropicIncompressibleMaterialLaw< DIM >::GetZeroStrainPressure().

template<unsigned DIM>

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

Get the first derivative dW/dI2.

Todo:: The name of this method should not include underscores.

Parameters:

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

Implemented in ExponentialMaterialLaw< DIM >, MooneyRivlinMaterialLaw< DIM >, and PolynomialMaterialLaw3d.

Referenced by AbstractIsotropicIncompressibleMaterialLaw< DIM >::ComputeStressAndStressDerivative(), and AbstractIsotropicIncompressibleMaterialLaw< 3 >::GetZeroStrainPressure().

template<>

double AbstractIsotropicIncompressibleMaterialLaw< 2 >::GetZeroStrainPressure ( ) [inline, virtual]

Get the pressure corresponding to zero stress given zero strain.

Implements AbstractIncompressibleMaterialLaw< DIM >.

Definition at line 136 of file AbstractIsotropicIncompressibleMaterialLaw.cpp.

References AbstractIsotropicIncompressibleMaterialLaw< DIM >::Get_dW_dI1().

template<unsigned DIM>

double AbstractIsotropicIncompressibleMaterialLaw< DIM >::GetZeroStrainPressure ( ) [virtual]

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

Since T = 2*Get_dW_dI1 identity + 4*Get_dW_dI2 (I1*identity - C) - p inverse(C), this is equal to 2*Get_dW_dI1(3,3) + 4*Get_dW_dI2(3,3) in 3D

Implements AbstractIncompressibleMaterialLaw< DIM >.

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

continuum_mechanics/src/problem/material_laws/AbstractIsotropicIncompressibleMaterialLaw.hpp
continuum_mechanics/src/problem/material_laws/AbstractIsotropicIncompressibleMaterialLaw.cpp

AbstractIsotropicIncompressibleMaterialLaw< DIM > Class Template Reference

Public Member Functions

Protected Member Functions

Detailed Description

template<unsigned DIM> class AbstractIsotropicIncompressibleMaterialLaw< DIM >

Constructor & Destructor Documentation

Member Function Documentation

template<unsigned DIM>
class AbstractIsotropicIncompressibleMaterialLaw< DIM >