oomph::GeneralisedMooneyRivlin Class Reference

#include <constitutive_laws.h>

Inheritance diagram for oomph::GeneralisedMooneyRivlin:

Public Member Functions
	GeneralisedMooneyRivlin (double *nu_pt, double *c1_pt)
	GeneralisedMooneyRivlin (double *nu_pt, double *c1_pt, double *e_pt)
virtual	~GeneralisedMooneyRivlin ()
	Virtual destructor. More...
double	W (const DenseMatrix< double > &gamma)
	Return the strain energy in terms of strain tensor. More...
double	W (const Vector< double > &I)
	Return the strain energy in terms of the strain invariants. More...
void	derivatives (Vector< double > &I, Vector< double > &dWdI)
bool	requires_incompressibility_constraint ()
Public Member Functions inherited from oomph::StrainEnergyFunction
	StrainEnergyFunction ()
	Constructor takes no arguments. More...
virtual	~StrainEnergyFunction ()
	Empty virtual destructor. More...
virtual void	derivative (const DenseMatrix< double > &gamma, DenseMatrix< double > &dWdgamma)

Private Attributes
double *	Nu_pt
	Poisson's ratio. More...
double *	C1_pt
	Mooney-Rivlin parameter. More...
double *	E_pt
	Young's modulus. More...
bool	Must_delete_e

Detailed Description

///////////////////////////////////////////////////////////////// ///////////////////////////////////////////////////////////////// ///////////////////////////////////////////////////////////////// Generalisation of Mooney Rivlin constitutive law to compressible media as suggested on p. 553 of Fung, Y.C. & Tong, P. "Classical and Computational Solid Mechanics" World Scientific (2001). Input parameters are Young's modulus E, Poisson ratio nu and the Mooney-Rivlin constant C1. In the small-deformation-limit the behaviour becomes equivalent to that of linear elasticity with the same E and nu.

Note that there's a factor of 2 difference between C1 and the Mooney Rivlin C1!

Constructor & Destructor Documentation

GeneralisedMooneyRivlin() [1/2]

oomph::GeneralisedMooneyRivlin::GeneralisedMooneyRivlin ( double *  nu_pt, double *  c1_pt  )

inline

Constructor takes the pointers to the constitutive parameters: Poisson's ratio, the Mooney-Rivlin parameter. Young's modulus is set to 1, implying that it has been used to scale the stresses

      : StrainEnergyFunction(),
        Nu_pt(nu_pt),
        C1_pt(c1_pt),
        E_pt(new double(1.0)),
        Must_delete_e(true)
    {
    }

GeneralisedMooneyRivlin() [2/2]

oomph::GeneralisedMooneyRivlin::GeneralisedMooneyRivlin ( double *  nu_pt, double *  c1_pt, double *  e_pt  )

inline

Constructor takes the pointers to the constitutive parameters: Poisson's ratio, the Mooney-Rivlin parameter and Young's modulus

      : StrainEnergyFunction(),
        Nu_pt(nu_pt),
        C1_pt(c1_pt),
        E_pt(e_pt),
        Must_delete_e(false)
    {
    }

~GeneralisedMooneyRivlin()

virtual oomph::GeneralisedMooneyRivlin::~GeneralisedMooneyRivlin ( )

inlinevirtual

Virtual destructor.

    {
      if (Must_delete_e) delete E_pt;
    }

References E_pt, and Must_delete_e.

Member Function Documentation

derivatives()

void oomph::GeneralisedMooneyRivlin::derivatives ( Vector< double > &  I, Vector< double > &  dWdI  )

inlinevirtual

Return the derivatives of the strain energy function with respect to the strain invariants

Reimplemented from oomph::StrainEnergyFunction.

    {
      double G = (*E_pt) / (2.0 * (1.0 + (*Nu_pt)));
      dWdI[0] = 0.5 * (*C1_pt);
      dWdI[1] = 0.5 * (G - (*C1_pt));
      dWdI[2] = 0.5 * ((*C1_pt) - 2.0 * G +
                       2.0 * (1.0 - (*Nu_pt)) * G * (I[2] - 1.0) /
                         (2.0 * (1.0 - 2.0 * (*Nu_pt))));
    }

References G, and I.

requires_incompressibility_constraint()

bool oomph::GeneralisedMooneyRivlin::requires_incompressibility_constraint ( )

inlinevirtual

Pure virtual function in which the user 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::StrainEnergyFunction.

    {
      return false;
    }

W() [1/2]

double oomph::GeneralisedMooneyRivlin::W ( const DenseMatrix< double > &  gamma )

inlinevirtual

Return the strain energy in terms of strain tensor.

Reimplemented from oomph::StrainEnergyFunction.

    {
      return StrainEnergyFunction::W(gamma);
    }

References mathsFunc::gamma(), and oomph::StrainEnergyFunction::W().

W() [2/2]

double oomph::GeneralisedMooneyRivlin::W ( const Vector< double > &  I )

inlinevirtual

Return the strain energy in terms of the strain invariants.

Reimplemented from oomph::StrainEnergyFunction.

    {
      double G = (*E_pt) / (2.0 * (1.0 + (*Nu_pt)));
      return 0.5 * ((*C1_pt) * (I[0] - 3.0) + (G - (*C1_pt)) * (I[1] - 3.0) +
                    ((*C1_pt) - 2.0 * G) * (I[2] - 1.0) +
                    (1.0 - (*Nu_pt)) * G * (I[2] - 1.0) * (I[2] - 1.0) /
                      (2.0 * (1.0 - 2.0 * (*Nu_pt))));
    }

References C1_pt, G, I, and Nu_pt.

Member Data Documentation

C1_pt

double* oomph::GeneralisedMooneyRivlin::C1_pt

private

Mooney-Rivlin parameter.

Referenced by W().

E_pt

double* oomph::GeneralisedMooneyRivlin::E_pt

private

Young's modulus.

Referenced by ~GeneralisedMooneyRivlin().

Must_delete_e

bool oomph::GeneralisedMooneyRivlin::Must_delete_e

private

Boolean flag to indicate if storage for elastic modulus must be deleted in destructor

Referenced by ~GeneralisedMooneyRivlin().

Nu_pt

double* oomph::GeneralisedMooneyRivlin::Nu_pt

private

Poisson's ratio.

Referenced by W().

---

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

• constitutive_laws.h