AbstractMaterialLaw< DIM > Class Template Reference

#include <AbstractMaterialLaw.hpp>

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List of all members.

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 48 of file AbstractMaterialLaw.hpp.

Constructor & Destructor Documentation

template<unsigned DIM>
AbstractMaterialLaw< DIM >::AbstractMaterialLaw (  )  [inline]

Constuctor

Definition at line 32 of file AbstractMaterialLaw.cpp.

template<unsigned DIM>
virtual AbstractMaterialLaw< DIM >::~AbstractMaterialLaw (  )  [inline, virtual]

Destructor

Definition at line 88 of file AbstractMaterialLaw.hpp.

Member Function Documentation

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 
) [inline, 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 127 of file AbstractMaterialLaw.cpp.

References AbstractMaterialLaw< DIM >::mpChangeOfBasisMatrix.

Referenced by SchmidCostaExponentialLaw2d::ComputeStressAndStressDerivative(), PoleZeroMaterialLaw< DIM >::ComputeStressAndStressDerivative(), and CompressibleExponentialLaw< DIM >::ComputeStressAndStressDerivative().

template<unsigned DIM>
void AbstractMaterialLaw< DIM >::TransformStressAndStressDerivative ( c_matrix< double, DIM, DIM > &  rT,
FourthOrderTensor< DIM, DIM, DIM, DIM > &  rDTdE,
bool  transformDTdE 
) [inline, 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 149 of file AbstractMaterialLaw.cpp.

References AbstractMaterialLaw< DIM >::mpChangeOfBasisMatrix.

Referenced by SchmidCostaExponentialLaw2d::ComputeStressAndStressDerivative(), PoleZeroMaterialLaw< DIM >::ComputeStressAndStressDerivative(), and CompressibleExponentialLaw< DIM >::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 >, CompressibleExponentialLaw< DIM >, PoleZeroMaterialLaw< DIM >, and AbstractIsotropicIncompressibleMaterialLaw< 3 >.

Referenced by AbstractMaterialLaw< DIM >::Compute1stPiolaKirchoffStress(), AbstractMaterialLaw< DIM >::Compute2ndPiolaKirchoffStress(), AbstractMaterialLaw< DIM >::ComputeCauchyStress(), AbstractNonlinearElasticitySolver< DIM >::ComputeStressAndStressDerivative(), and AbstractCardiacMechanicsSolver< ELASTICITY_SOLVER, DIM >::ComputeStressAndStressDerivative().

template<unsigned DIM>
void AbstractMaterialLaw< DIM >::ComputeCauchyStress ( c_matrix< double, DIM, DIM > &  rF,
double  pressure,
c_matrix< double, DIM, DIM > &  rSigma 
) [inline]

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 40 of file AbstractMaterialLaw.cpp.

References AbstractMaterialLaw< DIM >::ComputeStressAndStressDerivative(), Determinant(), and Inverse().

template<unsigned DIM>
void AbstractMaterialLaw< DIM >::Compute1stPiolaKirchoffStress ( c_matrix< double, DIM, DIM > &  rF,
double  pressure,
c_matrix< double, DIM, DIM > &  rS 
) [inline]

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 76 of file AbstractMaterialLaw.cpp.

References AbstractMaterialLaw< DIM >::ComputeStressAndStressDerivative(), and Inverse().

template<unsigned DIM>
void AbstractMaterialLaw< DIM >::Compute2ndPiolaKirchoffStress ( c_matrix< double, DIM, DIM > &  rC,
double  pressure,
c_matrix< double, DIM, DIM > &  rT 
) [inline]

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 93 of file AbstractMaterialLaw.cpp.

References AbstractMaterialLaw< DIM >::ComputeStressAndStressDerivative(), and Inverse().

template<unsigned DIM>
void AbstractMaterialLaw< DIM >::ScaleMaterialParameters ( double  scaleFactor  )  [inline, 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 105 of file AbstractMaterialLaw.cpp.

References EXCEPTION.

template<unsigned DIM>
void AbstractMaterialLaw< DIM >::SetChangeOfBasisMatrix ( c_matrix< double, DIM, DIM > &  rChangeOfBasisMatrix  )  [inline]

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 114 of file AbstractMaterialLaw.cpp.

References AbstractMaterialLaw< DIM >::mpChangeOfBasisMatrix.

Referenced by AbstractCardiacMechanicsSolver< ELASTICITY_SOLVER, DIM >::ComputeStressAndStressDerivative().

template<unsigned DIM>
void AbstractMaterialLaw< DIM >::ResetToNoChangeOfBasisMatrix (  )  [inline]

Reset back to no change of basis matrix

Definition at line 120 of file AbstractMaterialLaw.cpp.

References AbstractMaterialLaw< DIM >::mpChangeOfBasisMatrix.

Member Data Documentation

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 58 of file AbstractMaterialLaw.hpp.

Referenced by AbstractMaterialLaw< DIM >::ComputeTransformedDeformationTensor(), AbstractMaterialLaw< DIM >::ResetToNoChangeOfBasisMatrix(), AbstractMaterialLaw< DIM >::SetChangeOfBasisMatrix(), and AbstractMaterialLaw< DIM >::TransformStressAndStressDerivative().

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