AbstractIsotropicIncompressibleMaterialLaw< DIM > Class Template Reference

#include <AbstractIsotropicIncompressibleMaterialLaw.hpp>

Inheritance diagram for AbstractIsotropicIncompressibleMaterialLaw< 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 ()
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 ()

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
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)

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

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 55 of file AbstractIsotropicIncompressibleMaterialLaw.hpp.

Constructor & Destructor Documentation

~AbstractIsotropicIncompressibleMaterialLaw()

template<unsigned DIM>

AbstractIsotropicIncompressibleMaterialLaw< DIM >::~AbstractIsotropicIncompressibleMaterialLaw ( )

virtual

Destructor.

Definition at line 39 of file AbstractIsotropicIncompressibleMaterialLaw.cpp.

Member Function Documentation

ComputeStressAndStressDerivative()

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  )

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 44 of file AbstractIsotropicIncompressibleMaterialLaw.cpp.

References SecondInvariant(), and Trace().

Get_d2W_dI1()

template<unsigned DIM>

virtual double AbstractIsotropicIncompressibleMaterialLaw< DIM >::Get_d2W_dI1 ( double  I1, double  I2  )

protectedpure virtual

Returns

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.

Get_d2W_dI1I2()

template<unsigned DIM>

virtual double AbstractIsotropicIncompressibleMaterialLaw< DIM >::Get_d2W_dI1I2 ( double  I1, double  I2  )

protectedpure virtual

Returns

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.

Get_d2W_dI2()

template<unsigned DIM>

virtual double AbstractIsotropicIncompressibleMaterialLaw< DIM >::Get_d2W_dI2 ( double  I1, double  I2  )

protectedpure virtual

Returns

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.

Get_dW_dI1()

template<unsigned DIM>

virtual double AbstractIsotropicIncompressibleMaterialLaw< DIM >::Get_dW_dI1 ( double  I1, double  I2  )

protectedpure virtual

Returns

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.

Get_dW_dI2()

template<unsigned DIM>

virtual double AbstractIsotropicIncompressibleMaterialLaw< DIM >::Get_dW_dI2 ( double  I1, double  I2  )

protectedpure virtual

Returns

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.

GetZeroStrainPressure()

template<unsigned DIM>

double AbstractIsotropicIncompressibleMaterialLaw< DIM >::GetZeroStrainPressure ( )

virtual

Returns

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 and 2*Get_dW_dI1(2,0) in 2D.

Implements AbstractIncompressibleMaterialLaw< DIM >.

Definition at line 137 of file AbstractIsotropicIncompressibleMaterialLaw.cpp.

---

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