#include <AbstractMaterialLaw.hpp>

Inheritance diagram for AbstractMaterialLaw< DIM >:

Collaboration diagram for AbstractMaterialLaw< DIM >:

Public Member Functions
	AbstractMaterialLaw ()

virtual	~AbstractMaterialLaw ()

virtual 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)=0

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
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
c_matrix< double, DIM, DIM > *	mpChangeOfBasisMatrix

Detailed Description

template<unsigned DIM>
class AbstractMaterialLaw< DIM >

AbstractMaterialLaw

A hyper-elastic material law for finite elasticity

The law is given by a strain energy function W(E), where E is the strain, such that the (2nd Piola-Kirchhoff) stress T = dW/dE

Definition at line 55 of file AbstractMaterialLaw.hpp.

Constructor & Destructor Documentation

◆ AbstractMaterialLaw()

template<unsigned DIM>

AbstractMaterialLaw< DIM >::AbstractMaterialLaw ( )

Constuctor

Definition at line 39 of file AbstractMaterialLaw.cpp.

◆ ~AbstractMaterialLaw()

template<unsigned DIM>

virtual AbstractMaterialLaw< DIM >::~AbstractMaterialLaw ( )

inlinevirtual

Destructor

Definition at line 95 of file AbstractMaterialLaw.hpp.

Member Function Documentation

◆ Compute1stPiolaKirchoffStress()

template<unsigned DIM>

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

Compute the 1st Piola Kirchoff stress, given the deformation gradient F and the pressure. The 1st Piola Kirchoff stress given by

S^{Mi} = T^{MN} F^i_M,

where T is the 2nd PK stress, dW/dE.

Note that this stress is not symmetric and the least useful of the three stresses.

Parameters

rF	the deformation gradient
pressure	the pressure
rS	an empty matrix, which will be filled in with the stress

Note: the compute the material part of the stress (the pressure-independent part), just pass in pressure=0.0

Definition at line 83 of file AbstractMaterialLaw.cpp.

References Inverse().

◆ Compute2ndPiolaKirchoffStress()

template<unsigned DIM>

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

Compute the 2nd Piola Kirchoff stress, given the deformation tensor C and the pressure. The 2nd Piola Kirchoff stress given by

T^{MN} = dW/dE_{MN} = 2dW/dC_{MN}

Parameters

rC	the Lagrange deformation tensor (C=F^T F), not F, and not E
pressure	the pressure
rT	an empty matrix, which will be filled in with the stress

Note: to compute the material part of the stress (the pressure-independent part), just pass in pressure=0.0

Definition at line 100 of file AbstractMaterialLaw.cpp.

References Inverse().

◆ ComputeCauchyStress()

template<unsigned DIM>

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

Compute the Cauchy stress (the true stress), given the deformation gradient F and the pressure. The Cauchy stress is given by

sigma^{ij} = (1/detF) F^i_M T^{MN} F^j_N

where T is the 2nd Piola Kirchoff stress, dW/dE

Parameters

rF	the deformation gradient
pressure	the pressure
rSigma	an empty matrix, which will be filled in with the Cauchy stress

Note: the compute the material part of the stress (the pressure-independent part), just pass in pressure=0.0

Definition at line 45 of file AbstractMaterialLaw.cpp.

References Determinant(), and Inverse().

◆ ComputeStressAndStressDerivative()

template<unsigned DIM>

virtual void AbstractMaterialLaw< 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
	)

pure 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))

dTdE is a fourth-order tensor, where dTdE(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.
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.

Implemented in AbstractIsotropicCompressibleMaterialLaw< DIM >, AbstractIsotropicIncompressibleMaterialLaw< DIM >, AbstractIsotropicIncompressibleMaterialLaw< 3 >, CompressibleExponentialLaw< DIM >, and PoleZeroMaterialLaw< DIM >.

Referenced by CompressibleNonlinearElasticitySolver< DIM >::AssembleOnElement(), and IncompressibleNonlinearElasticitySolver< DIM >::AssembleOnElement().

◆ ComputeTransformedDeformationTensor()

template<unsigned DIM>

void AbstractMaterialLaw< DIM >::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
	)

protected

Transform the input (C and inv(C), where C in the deformation tensor) to the local coordinate system

Parameters

rC	deformation tensor C (input)
rInvC	inverse of C (input)
rCTransformed	P^T C P (output)
rInvCTransformed	P^T inv(C) P (output)

Definition at line 132 of file AbstractMaterialLaw.cpp.

Referenced by SchmidCostaExponentialLaw2d::ComputeStressAndStressDerivative().

◆ ResetToNoChangeOfBasisMatrix()

template<unsigned DIM>

void AbstractMaterialLaw< DIM >::ResetToNoChangeOfBasisMatrix ( )

Reset back to no change of basis matrix

Definition at line 126 of file AbstractMaterialLaw.cpp.

◆ ScaleMaterialParameters()

template<unsigned DIM>

void AbstractMaterialLaw< DIM >::ScaleMaterialParameters ( double scaleFactor )

virtual

Set a scale factor by which (dimensional) material parameters are scaled. This method can be optionally implemented in the child class; if no implementation is made an exception is thrown. A scale factor may be used/needed to improve GMRES convergence. Note that is a material law is scaled like this any dimensionally equivalent terms (eg gravity, tractions, active tensions) must also be scaled. Also, computed pressure will come out scaled.

Parameters

scaleFactor the scale factor

Reimplemented in CompressibleMooneyRivlinMaterialLaw< DIM >, MooneyRivlinMaterialLaw< DIM >, and PoleZeroMaterialLaw< DIM >.

Definition at line 113 of file AbstractMaterialLaw.cpp.

References EXCEPTION.

◆ SetChangeOfBasisMatrix()

template<unsigned DIM>

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

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

Note that no copy of this matrix is taken, so the original matrix must persist whilst this class is used. Call ResetToNoChangeOfBasisMatrix() if necessary.

The change of matrix should have the form (writing the preferred directions as fibre, sheet and normal, as in heart simulations): P = [a_f a_s a_n], where each a_i is a vector.

Parameters

rChangeOfBasisMatrix Change of basis matrix.

Definition at line 120 of file AbstractMaterialLaw.cpp.

Referenced by CompressibleNonlinearElasticitySolver< DIM >::AssembleOnElement(), and IncompressibleNonlinearElasticitySolver< DIM >::AssembleOnElement().

◆ TransformStressAndStressDerivative()

template<unsigned DIM>

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

protected

Transform the output (T and dTdE) back to the original coordinate system

Parameters

rT	stress being computed
rDTdE	the stress derivative to be transformed (assuming the final parameter is true)
transformDTdE	a boolean flag saying whether the stress derivative is to be transformed or not

Definition at line 153 of file AbstractMaterialLaw.cpp.

Referenced by SchmidCostaExponentialLaw2d::ComputeStressAndStressDerivative().

Member Data Documentation

◆ mpChangeOfBasisMatrix

template<unsigned DIM>

c_matrix<double,DIM,DIM>* AbstractMaterialLaw< DIM >::mpChangeOfBasisMatrix

protected

Some material laws are based on a particular local set of preferred directions, eg anisotropic cardiac laws, which use the fibre sheet and normal directions. This matrix can defines the orientation and should set before T and dTdE are computed.

The change of matrix should have the form P = [a_f a_s a_n], where each a_i is a vector.

Definition at line 65 of file AbstractMaterialLaw.hpp.

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

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

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ AbstractMaterialLaw()

◆ ~AbstractMaterialLaw()

Member Function Documentation

◆ Compute1stPiolaKirchoffStress()

◆ Compute2ndPiolaKirchoffStress()

◆ ComputeCauchyStress()

◆ ComputeStressAndStressDerivative()

◆ ComputeTransformedDeformationTensor()

◆ ResetToNoChangeOfBasisMatrix()

◆ ScaleMaterialParameters()

◆ SetChangeOfBasisMatrix()

◆ TransformStressAndStressDerivative()

Member Data Documentation

◆ mpChangeOfBasisMatrix