#include <constitutive_laws.h>
Public Member Functions  
GeneralisedHookean (double *nu_pt, double *e_pt)  
GeneralisedHookean (double *nu_pt)  
virtual  ~GeneralisedHookean () 
Virtual destructor. More...  
void  calculate_second_piola_kirchhoff_stress (const DenseMatrix< double > &g, const DenseMatrix< double > &G, DenseMatrix< double > &sigma) 
Calculate the contravariant 2nd Piola Kirchhoff stress tensor. Arguments are the covariant undeformed and deformed metric tensor and the matrix in which to return the stress tensor. More...  
void  calculate_second_piola_kirchhoff_stress (const DenseMatrix< double > &g, const DenseMatrix< double > &G, DenseMatrix< double > &sigma_dev, DenseMatrix< double > &G_contra, double &Gdet) 
Calculate the deviatoric part of the contravariant 2nd Piola Kirchhoff stress tensor . Also return the contravariant deformed metric tensor and the determinant of the deformed metric tensor. This form is appropriate for trulyincompressible materials for which where the "pressure" is determined by . More...  
void  calculate_second_piola_kirchhoff_stress (const DenseMatrix< double > &g, const DenseMatrix< double > &G, DenseMatrix< double > &sigma_dev, DenseMatrix< double > &Gcontra, double &gen_dil, double &inv_kappa) 
Calculate the deviatoric part of the contravariant 2nd Piola Kirchoff stress tensor. Also return the contravariant deformed metric tensor, the generalised dilatation, and the inverse of the bulk modulus . This form is appropriate for nearincompressible materials for which where the "pressure" is determined from . More...  
bool  requires_incompressibility_constraint () 
Pure virtual function in which the writer must declare if the constitutive equation requires an incompressible formulation in which the volume constraint is enforced explicitly. Used as a sanity check in PARANOID mode. False. More...  
Public Member Functions inherited from oomph::ConstitutiveLaw  
ConstitutiveLaw ()  
Empty constructor. More...  
virtual  ~ConstitutiveLaw () 
Empty virtual destructor. More...  
virtual void  calculate_d_second_piola_kirchhoff_stress_dG (const DenseMatrix< double > &g, const DenseMatrix< double > &G, const DenseMatrix< double > &sigma, RankFourTensor< double > &d_sigma_dG, const bool &symmetrize_tensor=true) 
Calculate the derivatives of the contravariant 2nd Piola Kirchhoff stress tensor with respect to the deformed metric tensor. Arguments are the covariant undeformed and deformed metric tensor, the current value of the stress tensor and the rank four tensor in which to return the derivatives of the stress tensor The default implementation uses finite differences, but can be overloaded for constitutive laws in which an analytic formulation is possible. If the boolean flag symmetrize_tensor is false, only the "upper triangular" entries of the tensor will be filled in. This is a useful efficiency when using the derivatives in Jacobian calculations. More...  
virtual void  calculate_d_second_piola_kirchhoff_stress_dG (const DenseMatrix< double > &g, const DenseMatrix< double > &G, const DenseMatrix< double > &sigma, const double &detG, const double &interpolated_solid_p, RankFourTensor< double > &d_sigma_dG, DenseMatrix< double > &d_detG_dG, const bool &symmetrize_tensor=true) 
Calculate the derivatives of the contravariant 2nd Piola Kirchhoff stress tensor . with respect to the deformed metric tensor. Also return the derivatives of the determinant of the deformed metric tensor with respect to the deformed metric tensor. This form is appropriate for trulyincompressible materials. The default implementation uses finite differences for the derivatives that depend on the constitutive law, but not for the derivatives of the determinant, which are generic. More...  
virtual void  calculate_d_second_piola_kirchhoff_stress_dG (const DenseMatrix< double > &g, const DenseMatrix< double > &G, const DenseMatrix< double > &sigma, const double &gen_dil, const double &inv_kappa, const double &interpolated_solid_p, RankFourTensor< double > &d_sigma_dG, DenseMatrix< double > &d_gen_dil_dG, const bool &symmetrize_tensor=true) 
Calculate the derivatives of the contravariant 2nd Piola Kirchoff stress tensor with respect to the deformed metric tensor. Also return the derivatives of the generalised dilatation, with respect to the deformed metric tensor. This form is appropriate for nearincompressible materials. The default implementation uses finite differences. If the boolean flag symmetrize_tensor is false, only the "upper triangular" entries of the tensor will be filled in. This is a useful efficiency when using the derivatives in Jacobian calculations. More...  
Private Attributes  
double *  Nu_pt 
Poisson ratio. More...  
double *  E_pt 
Young's modulus. More...  
bool  Must_delete_e 
Boolean flag to indicate if storage for elastic modulus must be deleted in destructor. More...  
Additional Inherited Members  
Protected Member Functions inherited from oomph::ConstitutiveLaw  
bool  is_matrix_square (const DenseMatrix< double > &M) 
Test whether a matrix is square. More...  
bool  are_matrices_of_equal_dimensions (const DenseMatrix< double > &M1, const DenseMatrix< double > &M2) 
Test whether two matrices are of equal dimensions. More...  
void  error_checking_in_input (const DenseMatrix< double > &g, const DenseMatrix< double > &G, DenseMatrix< double > &sigma) 
Check for errors in the input, i.e. check that the dimensions of the arrays are all consistent. More...  
double  calculate_contravariant (const DenseMatrix< double > &Gcov, DenseMatrix< double > &Gcontra) 
Calculate a contravariant tensor from a covariant tensor, and return the determinant of the covariant tensor. More...  
void  calculate_d_contravariant_dG (const DenseMatrix< double > &Gcov, RankFourTensor< double > &dGcontra_dG, DenseMatrix< double > &d_detG_dG) 
Calculate the derivatives of the contravariant tensor and the derivatives of the determinant of the covariant tensor with respect to the components of the covariant tensor. More...  
Class for a "nonrational" extension of classical linear elasticity to large displacements:
where
For small strains this approaches the version appropriate for linear elasticity, obtained by replacing with .
We provide three versions of calculate_second_piola_kirchhoff_stress()
:
where the pressure needs to be determined independently via the incompressibility constraint. In this case, the stress returned by
calculate_second_piola_kirchhoff_stress()
contains only the deviatoric part of the 2nd Piola Kirchhoff stress, The function also returns the contravariant metric tensor (since it is needed to form the complete stress tensor), and the determinant of the deformed covariant metric tensor (since it is needed in the equation that enforces the incompressibility).
and the small "generalised dilatation"
[ represents the actual dilatation in the small strain limit; for large deformations it doesn't have any sensible interpretation (or does it?). It is simply the term that needs to go to zero as .] In this case, the stress returned by
calculate_second_piola_kirchhoff_stress()
contains only the deviatoric part of the 2nd Piola Kirchhoff stress, The function also returns the contravariant metric tensor (since it is needed to form the complete stress tensor), the inverse of the bulk modulus, and the generalised dilatation (since they are needed in the equation that determines the pressure).
Definition at line 714 of file constitutive_laws.h.

inline 
The constructor takes the pointers to values of material parameters: Poisson's ratio and Young's modulus.
Definition at line 721 of file constitutive_laws.h.

inline 
The constructor takes the pointers to value of Poisson's ratio . Young's modulus is set to E=1.0, implying that all stresses have been nondimensionalised on on it.
Definition at line 729 of file constitutive_laws.h.

inlinevirtual 
Virtual destructor.
Definition at line 735 of file constitutive_laws.h.
References E_pt, and Must_delete_e.

virtual 
Calculate the contravariant 2nd Piola Kirchhoff stress tensor. Arguments are the covariant undeformed and deformed metric tensor and the matrix in which to return the stress tensor.
Calculate the contravariant 2nd Piola Kirchhoff stress tensor. Arguments are the covariant undeformed (stressfree) and deformed metric tensors, g and G, and the matrix in which to return the stress tensor.
Implements oomph::ConstitutiveLaw.
Definition at line 673 of file constitutive_laws.cc.
References oomph::ConstitutiveLaw::calculate_contravariant(), oomph::ConstitutiveLaw::error_checking_in_input(), i, and oomph::DenseMatrix< T >::nrow().
Referenced by calculate_second_piola_kirchhoff_stress().

virtual 
Calculate the deviatoric part of the contravariant 2nd Piola Kirchhoff stress tensor . Also return the contravariant deformed metric tensor and the determinant of the deformed metric tensor. This form is appropriate for trulyincompressible materials for which where the "pressure" is determined by .
Calculate the deviatoric part of the contravariant 2nd Piola Kirchhoff stress tensor . Also return the contravariant deformed metric tensor and the determinant of the deformed metric tensor. This form is appropriate for trulyincompressible materials for which where the "pressure" is determined by .
Reimplemented from oomph::ConstitutiveLaw.
Definition at line 801 of file constitutive_laws.cc.
References oomph::ConstitutiveLaw::calculate_contravariant(), oomph::ConstitutiveLaw::error_checking_in_input(), i, and oomph::DenseMatrix< T >::nrow().

virtual 
Calculate the deviatoric part of the contravariant 2nd Piola Kirchoff stress tensor. Also return the contravariant deformed metric tensor, the generalised dilatation, and the inverse of the bulk modulus . This form is appropriate for nearincompressible materials for which where the "pressure" is determined from .
Calculate the deviatoric part of the contravariant 2nd Piola Kirchoff stress tensor. Also return the contravariant deformed metric tensor, the generalised dilatation, and the inverse of the bulk modulus . This form is appropriate for nearincompressible materials for which where the "pressure" is determined from .
Reimplemented from oomph::ConstitutiveLaw.
Definition at line 755 of file constitutive_laws.cc.
References calculate_second_piola_kirchhoff_stress(), E_pt, i, oomph::DenseMatrix< T >::nrow(), and Nu_pt.

inlinevirtual 
Pure virtual function in which the writer must declare if the constitutive equation requires an incompressible formulation in which the volume constraint is enforced explicitly. Used as a sanity check in PARANOID mode. False.
Implements oomph::ConstitutiveLaw.
Definition at line 783 of file constitutive_laws.h.

private 
Young's modulus.
Definition at line 791 of file constitutive_laws.h.
Referenced by calculate_second_piola_kirchhoff_stress(), and ~GeneralisedHookean().

private 
Boolean flag to indicate if storage for elastic modulus must be deleted in destructor.
Definition at line 795 of file constitutive_laws.h.
Referenced by ~GeneralisedHookean().

private 
Poisson ratio.
Definition at line 788 of file constitutive_laws.h.
Referenced by calculate_second_piola_kirchhoff_stress().