GRINS::IncompressiblePlaneStressHyperelasticity< StrainEnergy > Class Template Reference

#include <incompressible_plane_stress_hyperelasticity.h>

Inheritance diagram for GRINS::IncompressiblePlaneStressHyperelasticity< StrainEnergy >:

Collaboration diagram for GRINS::IncompressiblePlaneStressHyperelasticity< StrainEnergy >:

Public Member Functions
	IncompressiblePlaneStressHyperelasticity (const GetPot &input)
virtual	~IncompressiblePlaneStressHyperelasticity ()
void	compute_stress (unsigned int dim, const libMesh::TensorValue< libMesh::Real > &g_contra, const libMesh::TensorValue< libMesh::Real > &g_cov, const libMesh::TensorValue< libMesh::Real > &G_contra, const libMesh::TensorValue< libMesh::Real > &G_cov, libMesh::TensorValue< libMesh::Real > &stress)
void	compute_stress_and_elasticity (unsigned int dim, const libMesh::TensorValue< libMesh::Real > &g_contra, const libMesh::TensorValue< libMesh::Real > &g_cov, const libMesh::TensorValue< libMesh::Real > &G_contra, const libMesh::TensorValue< libMesh::Real > &G_cov, libMesh::TensorValue< libMesh::Real > &stress, ElasticityTensor &C)
libMesh::Real	compute_33_stress (const libMesh::TensorValue< libMesh::Real > &g_contra, const libMesh::TensorValue< libMesh::Real > &g_cov, const libMesh::TensorValue< libMesh::Real > &G_contra, const libMesh::TensorValue< libMesh::Real > &G_cov)
	This is primarily a helper function for the plane stress cases. More...

Private Member Functions
void	compute_stress_imp (unsigned int dim, const libMesh::TensorValue< libMesh::Real > &a_contra, const libMesh::TensorValue< libMesh::Real > &a_cov, const libMesh::TensorValue< libMesh::Real > &A_contra, const libMesh::TensorValue< libMesh::Real > &A_cov, libMesh::TensorValue< libMesh::Real > &stress)
void	compute_stress_and_elasticity_imp (unsigned int dim, const libMesh::TensorValue< libMesh::Real > &a_contra, const libMesh::TensorValue< libMesh::Real > &a_cov, const libMesh::TensorValue< libMesh::Real > &A_contra, const libMesh::TensorValue< libMesh::Real > &A_cov, libMesh::TensorValue< libMesh::Real > &stress, ElasticityTensor &C)
void	compute_I1_I2 (const libMesh::TensorValue< libMesh::Real > &a_contra, const libMesh::TensorValue< libMesh::Real > &a_cov, const libMesh::TensorValue< libMesh::Real > &A_contra, const libMesh::TensorValue< libMesh::Real > &A_cov, libMesh::Real lambda_sq, libMesh::Real A_over_a, libMesh::Real &I1, libMesh::Real &I2) const
void	compute_stress_terms (libMesh::Real lambda_sq, libMesh::Real A_over_a, libMesh::Real I1, libMesh::Real I2, libMesh::Real &a_term, libMesh::Real &A_term) const
void	compute_stress_deriv_terms (libMesh::Real lambda_sq, libMesh::Real A_over_a, libMesh::Real I1, libMesh::Real I2, const libMesh::TensorValue< libMesh::Real > &a_contra, const libMesh::TensorValue< libMesh::Real > &A_contra, libMesh::TensorValue< libMesh::Real > &daterm_dstrain, libMesh::TensorValue< libMesh::Real > &dAterm_dstrain) const
void	compute_Acontra_deriv (const libMesh::TensorValue< libMesh::Real > &A_contra, ElasticityTensor &dAcontra_dstrain) const
libMesh::Real	compute_33_stress_imp (const libMesh::TensorValue< libMesh::Real > &g_contra, const libMesh::TensorValue< libMesh::Real > &g_cov, const libMesh::TensorValue< libMesh::Real > &G_contra, const libMesh::TensorValue< libMesh::Real > &G_cov)

Private Attributes
StrainEnergy	_W

Friends
class	StressStrainLaw< IncompressiblePlaneStressHyperelasticity< StrainEnergy > >

Detailed Description

template<typename StrainEnergy>
class GRINS::IncompressiblePlaneStressHyperelasticity< StrainEnergy >

Definition at line 45 of file incompressible_plane_stress_hyperelasticity.h.

Constructor & Destructor Documentation

template<typename StrainEnergy >

GRINS::IncompressiblePlaneStressHyperelasticity< StrainEnergy >::IncompressiblePlaneStressHyperelasticity

(

const GetPot &

input

)

Definition at line 37 of file incompressible_plane_stress_hyperelasticity.C.

    : _W(input)
  {
    return;
  }

template<typename StrainEnergy >

GRINS::IncompressiblePlaneStressHyperelasticity< StrainEnergy >::~IncompressiblePlaneStressHyperelasticity ( )

virtual

Definition at line 44 of file incompressible_plane_stress_hyperelasticity.C.

  {
    return;
  }

Member Function Documentation

libMesh::Real GRINS::StressStrainLaw< IncompressiblePlaneStressHyperelasticity< StrainEnergy > >::compute_33_stress ( const libMesh::TensorValue< libMesh::Real > &  g_contra, const libMesh::TensorValue< libMesh::Real > &  g_cov, const libMesh::TensorValue< libMesh::Real > &  G_contra, const libMesh::TensorValue< libMesh::Real > &  G_cov  )

inherited

This is primarily a helper function for the plane stress cases.

template<typename StrainEnergy >

libMesh::Real GRINS::IncompressiblePlaneStressHyperelasticity< StrainEnergy >::compute_33_stress_imp ( const libMesh::TensorValue< libMesh::Real > &  g_contra, const libMesh::TensorValue< libMesh::Real > &  g_cov, const libMesh::TensorValue< libMesh::Real > &  G_contra, const libMesh::TensorValue< libMesh::Real > &  G_cov  )

private

Definition at line 239 of file incompressible_plane_stress_hyperelasticity.C.

  {
    std::cerr << "Error: compute_33_stress shouldn't be called for incompressible materials." << std::endl;
    libmesh_error();
    return 0.0;
  }

template<typename StrainEnergy >

void GRINS::IncompressiblePlaneStressHyperelasticity< StrainEnergy >::compute_Acontra_deriv ( const libMesh::TensorValue< libMesh::Real > &  A_contra, ElasticityTensor &  dAcontra_dstrain  ) const

private

Definition at line 217 of file incompressible_plane_stress_hyperelasticity.C.

  {
    for( unsigned int alpha = 0; alpha < 2; alpha++ )
      {
        for( unsigned int beta = 0; beta < 2; beta++ )
          {
            for( unsigned int lambda = 0; lambda < 2; lambda++ )
              {
                for( unsigned int mu = 0; mu < 2; mu++ )
                  {
                    dAcontra_dstrain(alpha,beta,lambda,mu) = -( A_contra(alpha,lambda)*A_contra(beta,mu)
                                                                + A_contra(alpha,mu)*A_contra(beta,lambda) );
                  }
              }
          }
      }

    return;
  }

template<typename StrainEnergy >

void GRINS::IncompressiblePlaneStressHyperelasticity< StrainEnergy >::compute_I1_I2 ( const libMesh::TensorValue< libMesh::Real > &  a_contra, const libMesh::TensorValue< libMesh::Real > &  a_cov, const libMesh::TensorValue< libMesh::Real > &  A_contra, const libMesh::TensorValue< libMesh::Real > &  A_cov, libMesh::Real  lambda_sq, libMesh::Real  A_over_a, libMesh::Real &  I1, libMesh::Real &  I2  ) const

private

Definition at line 131 of file incompressible_plane_stress_hyperelasticity.C.

  {
    I1 = 0.0;
    I2 = 0.0;
    for( unsigned int alpha = 0; alpha < 2; alpha++ )
      {
        for( unsigned int beta = 0; beta < 2; beta++ )
          {
            I1 += a_contra(alpha,beta)*A_cov(alpha,beta);
            I2 += a_cov(alpha,beta)*A_contra(alpha,beta);
          }
      }

    I1 += lambda_sq;
    I2 += A_over_a;

    return;
  }

void GRINS::StressStrainLaw< IncompressiblePlaneStressHyperelasticity< StrainEnergy > >::compute_stress ( unsigned int  dim, const libMesh::TensorValue< libMesh::Real > &  g_contra, const libMesh::TensorValue< libMesh::Real > &  g_cov, const libMesh::TensorValue< libMesh::Real > &  G_contra, const libMesh::TensorValue< libMesh::Real > &  G_cov, libMesh::TensorValue< libMesh::Real > &  stress  )

inherited

void GRINS::StressStrainLaw< IncompressiblePlaneStressHyperelasticity< StrainEnergy > >::compute_stress_and_elasticity ( unsigned int  dim, const libMesh::TensorValue< libMesh::Real > &  g_contra, const libMesh::TensorValue< libMesh::Real > &  g_cov, const libMesh::TensorValue< libMesh::Real > &  G_contra, const libMesh::TensorValue< libMesh::Real > &  G_cov, libMesh::TensorValue< libMesh::Real > &  stress, ElasticityTensor &  C  )

inherited

template<typename StrainEnergy >

void GRINS::IncompressiblePlaneStressHyperelasticity< StrainEnergy >::compute_stress_and_elasticity_imp ( unsigned int  dim, const libMesh::TensorValue< libMesh::Real > &  a_contra, const libMesh::TensorValue< libMesh::Real > &  a_cov, const libMesh::TensorValue< libMesh::Real > &  A_contra, const libMesh::TensorValue< libMesh::Real > &  A_cov, libMesh::TensorValue< libMesh::Real > &  stress, ElasticityTensor &  C  )

private

Definition at line 82 of file incompressible_plane_stress_hyperelasticity.C.

  {
    // We're treating a_* and A_* as 2x2, but we're cheating to pick up lambda^2
    libMesh::Real lambda_sq = A_cov(2,2);

    libMesh::Real A_over_a = 1.0/lambda_sq; // We're incompressible

    libMesh::Real I1, I2;
    this->compute_I1_I2(a_contra,a_cov,A_contra,A_cov,lambda_sq,A_over_a,I1,I2);

    libMesh::Real a_term, A_term;
    this->compute_stress_terms( lambda_sq, A_over_a, I1, I2, a_term, A_term );

    libMesh::TensorValue<libMesh::Real> daterm_dstrain, dAterm_dstrain;
    this->compute_stress_deriv_terms( lambda_sq, A_over_a, I1, I2, a_contra, A_contra, daterm_dstrain, dAterm_dstrain );

    ElasticityTensor dAcontra_dstrain;
    this->compute_Acontra_deriv( A_contra, dAcontra_dstrain );

    // Now compute stress
    stress.zero();
    for( unsigned int alpha = 0; alpha < 2; alpha++ )
      {
        for( unsigned int beta = 0; beta < 2; beta++ )
          {
            stress(alpha,beta) = a_contra(alpha,beta)*a_term + A_contra(alpha,beta)*A_term;

            for( unsigned int lambda = 0; lambda < 2; lambda++ )
              {
                for( unsigned int mu = 0; mu < 2; mu++ )
                  {
                    C(alpha,beta,lambda,mu) = a_contra(alpha,beta)*daterm_dstrain(lambda,mu)
                                            + dAcontra_dstrain(alpha,beta,lambda,mu)*A_term
                                            + A_contra(alpha,beta)*dAterm_dstrain(lambda,mu);
                  }
              }
          }
      }

    return;
  }

template<typename StrainEnergy >

void GRINS::IncompressiblePlaneStressHyperelasticity< StrainEnergy >::compute_stress_deriv_terms ( libMesh::Real  lambda_sq, libMesh::Real  A_over_a, libMesh::Real  I1, libMesh::Real  I2, const libMesh::TensorValue< libMesh::Real > &  a_contra, const libMesh::TensorValue< libMesh::Real > &  A_contra, libMesh::TensorValue< libMesh::Real > &  daterm_dstrain, libMesh::TensorValue< libMesh::Real > &  dAterm_dstrain  ) const

private

Definition at line 174 of file incompressible_plane_stress_hyperelasticity.C.

  {
    daterm_dstrain.zero();
    dAterm_dstrain.zero();

    libMesh::Real dWdI1 = _W.dI1(I1,I2,1.0); // We're incompressible
    libMesh::Real dWdI2 = _W.dI2(I1,I2,1.0);

    // A = det(A_cov) = 1/det(A_contra)
    //libMesh::Real A = 1.0/( A_contra(0,0)*A_contra(1,1) - A_contra(0,1)*A_contra(1,0) );

    for( unsigned int alpha = 0; alpha < 2; alpha++ )
      {
        for( unsigned int beta = 0; beta < 2; beta++ )
          {
            // a_term = 2.0*(dWdI1 + dWdI2*lambda^2);
            // => da_dstrain = 2.0*dWdI2*dlambda^2_dstrain
            // dlambda_sq_dstrain = -2*lambda^2 A^{alpha,beta}
            const libMesh::Real dlamsq_dstrain = -2.0*lambda_sq*A_contra(alpha,beta);

            daterm_dstrain(alpha,beta) = 2.0*dWdI2*dlamsq_dstrain;

            // A_term = 2.0*dWdI2*A_over_a + p;
            // A = det(A_cov) ==> dA_dstrain = 2*A*A_contra(alpha,beta)
            // p = -2.0*lambda_sq*( dWdI1 + dWdI2*(I1-lambda_sq) );
            const libMesh::Real dI1_dstrain = 2.0*a_contra(alpha,beta) + dlamsq_dstrain;

            const libMesh::Real dp_dstrain = -2.0*dlamsq_dstrain*( dWdI1 + dWdI2*(I1-lambda_sq) )
                                             -2.0*lambda_sq*dWdI2*(dI1_dstrain - dlamsq_dstrain);

            dAterm_dstrain(alpha,beta) = 2.0*dWdI2*A_over_a*(2.0*A_contra(alpha,beta)) + dp_dstrain;
          }
      }

    return;
  }

template<typename StrainEnergy >

void GRINS::IncompressiblePlaneStressHyperelasticity< StrainEnergy >::compute_stress_imp ( unsigned int  dim, const libMesh::TensorValue< libMesh::Real > &  a_contra, const libMesh::TensorValue< libMesh::Real > &  a_cov, const libMesh::TensorValue< libMesh::Real > &  A_contra, const libMesh::TensorValue< libMesh::Real > &  A_cov, libMesh::TensorValue< libMesh::Real > &  stress  )

private

Definition at line 50 of file incompressible_plane_stress_hyperelasticity.C.

  {
    // We're treating a_* and A_* as 2x2, but we're cheating to pick up lambda^2
    libMesh::Real lambda_sq = A_cov(2,2);

    libMesh::Real A_over_a = 1.0/lambda_sq; // We're incompressible

    libMesh::Real I1, I2;
    this->compute_I1_I2(a_contra,a_cov,A_contra,A_cov,lambda_sq,A_over_a,I1,I2);

    libMesh::Real a_term, A_term;
    this->compute_stress_terms( lambda_sq, A_over_a, I1, I2, a_term, A_term );

    // Now compute stress
    stress.zero();
    for( unsigned int alpha = 0; alpha < 2; alpha++ )
      {
        for( unsigned int beta = 0; beta < 2; beta++ )
          {
            stress(alpha,beta) = a_contra(alpha,beta)*a_term + A_contra(alpha,beta)*A_term;
          }
      }

    return;
  }

template<typename StrainEnergy >

void GRINS::IncompressiblePlaneStressHyperelasticity< StrainEnergy >::compute_stress_terms ( libMesh::Real  lambda_sq, libMesh::Real  A_over_a, libMesh::Real  I1, libMesh::Real  I2, libMesh::Real &  a_term, libMesh::Real &  A_term  ) const

private

Definition at line 156 of file incompressible_plane_stress_hyperelasticity.C.

  {
    libMesh::Real dWdI1 = _W.dI1(I1,I2,1.0); // We're incompressible
    libMesh::Real dWdI2 = _W.dI2(I1,I2,1.0);

    // Notation used in Green/Adkins
    // Comes from enforcing plane stress
    libMesh::Real p = -2.0*lambda_sq*( dWdI1 + dWdI2*(I1-lambda_sq) );

    a_term = 2.0*(dWdI1 + dWdI2*lambda_sq);
    A_term = 2.0*dWdI2*A_over_a + p;

    return;
  }

Friends And Related Function Documentation

template<typename StrainEnergy >

friend class StressStrainLaw< IncompressiblePlaneStressHyperelasticity< StrainEnergy > >

friend

Definition at line 52 of file incompressible_plane_stress_hyperelasticity.h.

Member Data Documentation

template<typename StrainEnergy >

StrainEnergy GRINS::IncompressiblePlaneStressHyperelasticity< StrainEnergy >::_W

private

Definition at line 97 of file incompressible_plane_stress_hyperelasticity.h.

---

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

• src/properties/include/grins/incompressible_plane_stress_hyperelasticity.h
• src/properties/src/incompressible_plane_stress_hyperelasticity.C