assembly.C File Reference

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Functions
Real	kronecker_delta (unsigned int i, unsigned int j)
Real	elasticity_tensor (unsigned int i, unsigned int j, unsigned int k, unsigned int l)

Function Documentation

elasticity_tensor()

Real elasticity_tensor	(	unsigned int	i,
		unsigned int	j,
		unsigned int	k,
		unsigned int	l
	)

Definition at line 40 of file assembly.C.

{
  // Define the Poisson ratio and Young's modulus
  const Real nu = 0.3;
  const Real E  = 1.;
 
  // Define the Lame constants (lambda_1 and lambda_2) based on nu and E
  const Real lambda_1 = E * nu / ((1. + nu) * (1. - 2.*nu));
  const Real lambda_2 = 0.5 * E / (1. + nu);
 
  return lambda_1 * kronecker_delta(i, j) * kronecker_delta(k, l)
    + lambda_2 * (kronecker_delta(i, k) * kronecker_delta(j, l) + kronecker_delta(i, l) * kronecker_delta(j, k));
}

References kronecker_delta(), and libMesh::Real.

Referenced by LinearElasticity::assemble(), LinearElasticity::compute_stresses(), compute_stresses(), LargeDeformationElasticity::compute_stresses(), ElasticitySystem::element_time_derivative(), AssemblyA0::interior_assembly(), AssemblyA1::interior_assembly(), AssemblyA2::interior_assembly(), LargeDeformationElasticity::jacobian(), and LargeDeformationElasticity::residual().

kronecker_delta()

Real kronecker_delta ( unsigned int  i, unsigned int  j  )

inline

Definition at line 34 of file assembly.C.

{
  return i == j ? 1. : 0.;
}

Referenced by elasticity_tensor(), ElasticitySystem::elasticity_tensor(), LargeDeformationElasticity::elasticity_tensor(), and LinearElasticity::elasticity_tensor().