Real
StressDivergenceTensors::computeQpJacobian()
{
if (_use_finite_deform_jacobian)
return ElasticityTensorTools::elasticJacobian(_finite_deform_Jacobian_mult[_qp],
_component,
_component,
_grad_test[_i][_qp],
_grad_phi_undisplaced[_j][_qp]);
Real sum_C3x3 = _Jacobian_mult[_qp].sum3x3();
RealGradient sum_C3x1 = _Jacobian_mult[_qp].sum3x1();
Real jacobian = 0.0;
// B^T_i * C * B_j
jacobian += ElasticityTensorTools::elasticJacobian(
_Jacobian_mult[_qp], _component, _component, _grad_test[_i][_qp], _grad_phi[_j][_qp]);
if (_volumetric_locking_correction)
{
// jacobian = Bbar^T_i * C * Bbar_j where Bbar = B + Bvol
// jacobian = B^T_i * C * B_j + Bvol^T_i * C * Bvol_j + Bvol^T_i * C * B_j + B^T_i * C * Bvol_j
// Bvol^T_i * C * Bvol_j
jacobian += sum_C3x3 * (_avg_grad_test[_i][_component] - _grad_test[_i][_qp](_component)) *
(_avg_grad_phi[_j][_component] - _grad_phi[_j][_qp](_component)) / 9.0;
// B^T_i * C * Bvol_j
jacobian += sum_C3x1(_component) * _grad_test[_i][_qp](_component) *
(_avg_grad_phi[_j][_component] - _grad_phi[_j][_qp](_component)) / 3.0;
// Bvol^T_i * C * B_j
RankTwoTensor phi;
if (_component == 0)
{
phi(0, 0) = _grad_phi[_j][_qp](0);
phi(0, 1) = phi(1, 0) = _grad_phi[_j][_qp](1);
phi(0, 2) = phi(2, 0) = _grad_phi[_j][_qp](2);
}
else if (_component == 1)
{
phi(1, 1) = _grad_phi[_j][_qp](1);
phi(0, 1) = phi(1, 0) = _grad_phi[_j][_qp](0);
phi(1, 2) = phi(2, 1) = _grad_phi[_j][_qp](2);
}
else if (_component == 2)
{
phi(2, 2) = _grad_phi[_j][_qp](2);
phi(0, 2) = phi(2, 0) = _grad_phi[_j][_qp](0);
phi(1, 2) = phi(2, 1) = _grad_phi[_j][_qp](1);
}
jacobian += (_Jacobian_mult[_qp] * phi).trace() *
(_avg_grad_test[_i][_component] - _grad_test[_i][_qp](_component)) / 3.0;
}
return jacobian;
}
Real
StressDivergence::computeQpJacobian()
{
Real sum_C3x3 = _Jacobian_mult[_qp].sum_3x3();
RealGradient sum_C3x1 = _Jacobian_mult[_qp].sum_3x1();
Real jacobian = 0.0;
// B^T_i * C * B_j
jacobian += _Jacobian_mult[_qp].stiffness(
_component, _component, _grad_test[_i][_qp], _grad_phi[_j][_qp]); // B^T_i * C *B_j
if (_volumetric_locking_correction)
{
// jacobian = Bbar^T_i * C * Bbar_j where Bbar = B + Bvol
// jacobian = B^T_i * C * B_j + Bvol^T_i * C * Bvol_j + Bvol^T_i * C * B_j + B^T_i * C * Bvol_j
// Bvol^T_i * C * Bvol_j
jacobian += sum_C3x3 * (_avg_grad_test[_i][_component] - _grad_test[_i][_qp](_component)) *
(_avg_grad_phi[_j][_component] - _grad_phi[_j][_qp](_component)) / 9.0;
// B^T_i * C * Bvol_j
jacobian += sum_C3x1(_component) * _grad_test[_i][_qp](_component) *
(_avg_grad_phi[_j][_component] - _grad_phi[_j][_qp](_component)) / 3.0;
// Bvol^T_i * C * B_j
SymmTensor phi;
if (_component == 0)
{
phi.xx() = _grad_phi[_j][_qp](0);
phi.xy() = _grad_phi[_j][_qp](1);
phi.xz() = _grad_phi[_j][_qp](2);
}
else if (_component == 1)
{
phi.yy() = _grad_phi[_j][_qp](1);
phi.xy() = _grad_phi[_j][_qp](0);
phi.yz() = _grad_phi[_j][_qp](2);
}
else if (_component == 2)
{
phi.zz() = _grad_phi[_j][_qp](2);
phi.xz() = _grad_phi[_j][_qp](0);
phi.yz() = _grad_phi[_j][_qp](1);
}
SymmTensor tmp(_Jacobian_mult[_qp] * phi);
jacobian += (tmp.xx() + tmp.yy() + tmp.zz()) *
(_avg_grad_test[_i][_component] - _grad_test[_i][_qp](_component)) / 3.0;
}
if (_dt > 0)
return jacobian * (1 + _alpha + _zeta / _dt);
else
return jacobian;
}
Real
StressDivergence::computeQpOffDiagJacobian(unsigned int jvar)
{
unsigned int coupled_component = 0;
bool active = false;
if (_xdisp_coupled && jvar == _xdisp_var)
{
coupled_component = 0;
active = true;
}
else if (_ydisp_coupled && jvar == _ydisp_var)
{
coupled_component = 1;
active = true;
}
else if (_zdisp_coupled && jvar == _zdisp_var)
{
coupled_component = 2;
active = true;
}
if (active)
{
Real sum_C3x3 = _Jacobian_mult[_qp].sum_3x3();
RealGradient sum_C3x1 = _Jacobian_mult[_qp].sum_3x1();
Real jacobian = 0.0;
jacobian += _Jacobian_mult[_qp].stiffness(
_component, coupled_component, _grad_test[_i][_qp], _grad_phi[_j][_qp]); // B^T_i * C *B_j
if (_volumetric_locking_correction)
{
// jacobian = Bbar^T_i * C * Bbar_j where Bbar = B + Bvol
// jacobian = B^T_i * C * B_j + Bvol^T_i * C * Bvol_j + Bvol^T_i * C * B_j + B^T_i * C *
// Bvol_j
// Bvol^T_i * C * Bvol_j
jacobian += sum_C3x3 * (_avg_grad_test[_i][_component] - _grad_test[_i][_qp](_component)) *
(_avg_grad_phi[_j][coupled_component] - _grad_phi[_j][_qp](coupled_component)) /
9.0;
// B^T_i * C * Bvol_j
jacobian += sum_C3x1(_component) * _grad_test[_i][_qp](_component) *
(_avg_grad_phi[_j][coupled_component] - _grad_phi[_j][_qp](coupled_component)) /
3.0;
// Bvol^T_i * C * B_i
SymmTensor phi;
if (coupled_component == 0)
{
phi.xx() = _grad_phi[_j][_qp](0);
phi.xy() = _grad_phi[_j][_qp](1);
phi.xz() = _grad_phi[_j][_qp](2);
}
else if (coupled_component == 1)
{
phi.yy() = _grad_phi[_j][_qp](1);
phi.xy() = _grad_phi[_j][_qp](0);
phi.yz() = _grad_phi[_j][_qp](2);
}
else if (coupled_component == 2)
{
phi.zz() = _grad_phi[_j][_qp](2);
phi.xz() = _grad_phi[_j][_qp](0);
phi.yz() = _grad_phi[_j][_qp](1);
}
SymmTensor tmp(_Jacobian_mult[_qp] * phi);
jacobian += (tmp.xx() + tmp.yy() + tmp.zz()) *
(_avg_grad_test[_i][_component] - _grad_test[_i][_qp](_component)) / 3.0;
}
if (_dt > 0)
return jacobian * (1 + _alpha + _zeta / _dt);
else
return jacobian;
}
if (_temp_coupled && jvar == _temp_var)
return _d_stress_dT[_qp].rowDot(_component, _grad_test[_i][_qp]) * _phi[_j][_qp];
return 0;
}