void
Compute2DFiniteStrain::computeProperties()
{
// Method from Rashid, 1993
RankTwoTensor ave_Fhat;
Real ave_dfgrd_det = 0.0;
for (_qp = 0; _qp < _qrule->n_points(); ++_qp)
{
// Deformation gradient calculation for 2D problems
// Note: x_disp is the radial displacement, y_disp is the axial displacement
RankTwoTensor A((*_grad_disp[0])[_qp], (*_grad_disp[1])[_qp], (*_grad_disp[2])[_qp]); //Deformation gradient
RankTwoTensor Fbar((*_grad_disp_old[0])[_qp], (*_grad_disp_old[1])[_qp], (*_grad_disp_old[2])[_qp]); //Old Deformation gradient
// Compute the displacement gradient (2,2) value for plane strain, generalized plane strain, or axisymmetric problems
A(2,2) = computeGradDispZZ();
Fbar(2,2) = computeGradDispZZold();
// Gauss point deformation gradient
_deformation_gradient[_qp] = A;
_deformation_gradient[_qp].addIa(1.0);
A -= Fbar; //very nearly A = gradU - gradUold, adapted to cylindrical coords
Fbar.addIa(1.0); //Fbar = ( I + gradUold)
//Incremental deformation gradient _Fhat = I + A Fbar^-1
_Fhat[_qp] = A * Fbar.inverse();
_Fhat[_qp].addIa(1.0);
// Calculate average _Fhat for volumetric locking correction
ave_Fhat += _Fhat[_qp] * _JxW[_qp] * _coord[_qp];
// Average deformation gradient
ave_dfgrd_det += _deformation_gradient[_qp].det() * _JxW[_qp] * _coord[_qp];
}
// needed for volumetric locking correction
ave_Fhat /= _current_elem_volume;
// average deformation gradient
ave_dfgrd_det /=_current_elem_volume;
for (_qp = 0; _qp < _qrule->n_points(); ++_qp)
{
// Finalize volumetric locking correction
_Fhat[_qp] *= std::cbrt(ave_Fhat.det() / _Fhat[_qp].det());
computeQpStrain();
// Volumetric locking correction
_deformation_gradient[_qp] *= std::cbrt(ave_dfgrd_det / _deformation_gradient[_qp].det());
}
}
void
Compute2DIncrementalStrain::computeTotalStrainIncrement(RankTwoTensor & total_strain_increment)
{
// Deformation gradient calculation for 2D problems
// Note: x_disp is the radial displacement, y_disp is the axial displacement
RankTwoTensor A((*_grad_disp[0])[_qp], (*_grad_disp[1])[_qp], (*_grad_disp[2])[_qp]); //Deformation gradient
RankTwoTensor Fbar((*_grad_disp_old[0])[_qp], (*_grad_disp_old[1])[_qp], (*_grad_disp_old[2])[_qp]); //Old Deformation gradient
// Compute the displacement gradient (2,2) value for plane strain, generalized plane strain, or axisymmetric problems
A(2,2) = computeGradDispZZ();
Fbar(2,2) = computeGradDispZZOld();
_deformation_gradient[_qp] = A;
_deformation_gradient[_qp].addIa(1.0);
A -= Fbar; //very nearly A = gradU - gradUold, adapted to cylindrical coords
total_strain_increment = 0.5 * (A + A.transpose());
}
