Real
StressDivergenceRZTensors::calculateJacobian(unsigned int ivar, unsigned int jvar)
{
RealGradient test, test_z, phi, phi_z;
if (ivar == 0) //Case grad_test for x, requires contributions from stress_xx, stress_xy, and stress_zz
{
test(0) = _grad_test[_i][_qp](0);
test(1) = _grad_test[_i][_qp](1);
test_z(2) = _test[_i][_qp] / _q_point[_qp](0);
}
else // Case grad_test for y
{
test(0) = _grad_test[_i][_qp](0);
test(1) = _grad_test[_i][_qp](1);
}
if (jvar == 0)
{
phi(0) = _grad_phi[_j][_qp](0);
phi(1) = _grad_phi[_j][_qp](1);
phi_z(2) = _phi[_j][_qp] / _q_point[_qp](0);
}
else
{
phi(0) = _grad_phi[_j][_qp](0);
phi(1) = _grad_phi[_j][_qp](1);
}
if (ivar == 0 && jvar == 0) // Case when both phi and test are functions of x and z; requires four terms
{
const Real first_sum = ElasticityTensorTools::elasticJacobian(_Jacobian_mult[_qp], ivar, jvar, test, phi); //test_x and phi_x
const Real second_sum = ElasticityTensorTools::elasticJacobian(_Jacobian_mult[_qp], 2, 2, test_z, phi_z); //test_z and phi_z
const Real mixed_sum1 = ElasticityTensorTools::elasticJacobian(_Jacobian_mult[_qp], ivar, 2, test, phi_z); //test_x and phi_z
const Real mixed_sum2 = ElasticityTensorTools::elasticJacobian(_Jacobian_mult[_qp], 2, jvar, test_z, phi); //test_z and phi_x
return first_sum + second_sum + mixed_sum1 + mixed_sum2;
}
else if (ivar == 0 && jvar == 1)
{
const Real first_sum = ElasticityTensorTools::elasticJacobian(_Jacobian_mult[_qp], ivar, jvar, test, phi); //test_x and phi_y
const Real mixed_sum2 = ElasticityTensorTools::elasticJacobian(_Jacobian_mult[_qp], 2, jvar, test_z, phi); //test_z and phi_y
return first_sum + mixed_sum2;
}
else if (ivar == 1 && jvar == 0)
{
const Real second_sum = ElasticityTensorTools::elasticJacobian(_Jacobian_mult[_qp], ivar, jvar, test, phi); //test_y and phi_x
const Real mixed_sum1 = ElasticityTensorTools::elasticJacobian(_Jacobian_mult[_qp], ivar, 2, test, phi_z); //test_y and phi_z
return second_sum + mixed_sum1;
}
else if (ivar == 1 && jvar == 1)
return ElasticityTensorTools::elasticJacobian(_Jacobian_mult[_qp], ivar, jvar, test, phi); //test_y and phi_y
else
mooseError("Invalid component in Jacobian Calculation");
}
Real
StressDivergenceRZTensors::calculateJacobian(unsigned int ivar, unsigned int jvar)
{
// B^T_i * C * B_j
RealGradient test, test_z, phi, phi_z;
Real first_term = 0.0;
if (ivar == 0) // Case grad_test for x, requires contributions from stress_xx, stress_xy, and
// stress_zz
{
test(0) = _grad_test[_i][_qp](0);
test(1) = _grad_test[_i][_qp](1);
test_z(2) = _test[_i][_qp] / _q_point[_qp](0);
}
else // Case grad_test for y
{
test(0) = _grad_test[_i][_qp](0);
test(1) = _grad_test[_i][_qp](1);
}
if (jvar == 0)
{
phi(0) = _grad_phi[_j][_qp](0);
phi(1) = _grad_phi[_j][_qp](1);
phi_z(2) = _phi[_j][_qp] / _q_point[_qp](0);
}
else
{
phi(0) = _grad_phi[_j][_qp](0);
phi(1) = _grad_phi[_j][_qp](1);
}
if (ivar == 0 &&
jvar == 0) // Case when both phi and test are functions of x and z; requires four terms
{
const Real first_sum = ElasticityTensorTools::elasticJacobian(
_Jacobian_mult[_qp], ivar, jvar, test, phi); // test_x and phi_x
const Real second_sum = ElasticityTensorTools::elasticJacobian(
_Jacobian_mult[_qp], 2, 2, test_z, phi_z); // test_z and phi_z
const Real mixed_sum1 = ElasticityTensorTools::elasticJacobian(
_Jacobian_mult[_qp], ivar, 2, test, phi_z); // test_x and phi_z
const Real mixed_sum2 = ElasticityTensorTools::elasticJacobian(
_Jacobian_mult[_qp], 2, jvar, test_z, phi); // test_z and phi_x
first_term = first_sum + second_sum + mixed_sum1 + mixed_sum2;
}
else if (ivar == 0 && jvar == 1)
{
const Real first_sum = ElasticityTensorTools::elasticJacobian(
_Jacobian_mult[_qp], ivar, jvar, test, phi); // test_x and phi_y
const Real mixed_sum2 = ElasticityTensorTools::elasticJacobian(
_Jacobian_mult[_qp], 2, jvar, test_z, phi); // test_z and phi_y
first_term = first_sum + mixed_sum2;
}
else if (ivar == 1 && jvar == 0)
{
const Real second_sum = ElasticityTensorTools::elasticJacobian(
_Jacobian_mult[_qp], ivar, jvar, test, phi); // test_y and phi_x
const Real mixed_sum1 = ElasticityTensorTools::elasticJacobian(
_Jacobian_mult[_qp], ivar, 2, test, phi_z); // test_y and phi_z
first_term = second_sum + mixed_sum1;
}
else if (ivar == 1 && jvar == 1)
first_term = ElasticityTensorTools::elasticJacobian(
_Jacobian_mult[_qp], ivar, jvar, test, phi); // test_y and phi_y
else
mooseError("Invalid component in Jacobian Calculation");
Real val = 0.0;
// volumetric locking correction
// K = Bbar^T_i * C * Bbar^T_j where Bbar = B + Bvol
// K = B^T_i * C * B_j + Bvol^T_i * C * Bvol_j + B^T_i * C * Bvol_j + Bvol^T_i * C * B_j
if (_volumetric_locking_correction)
{
RealGradient new_test(2, 0.0);
RealGradient new_phi(2, 0.0);
new_test(0) = _grad_test[_i][_qp](0) + _test[_i][_qp] / _q_point[_qp](0);
new_test(1) = _grad_test[_i][_qp](1);
new_phi(0) = _grad_phi[_j][_qp](0) + _phi[_j][_qp] / _q_point[_qp](0);
new_phi(1) = _grad_phi[_j][_qp](1);
// Bvol^T_i * C * Bvol_j
val += _Jacobian_mult[_qp].sum3x3() * (_avg_grad_test[_i][ivar] - new_test(ivar)) *
(_avg_grad_phi[_j][jvar] - new_phi(jvar)) / 3.0;
// B^T_i * C * Bvol_j
RealGradient sum_3x1 = _Jacobian_mult[_qp].sum3x1();
if (ivar == 0 && jvar == 0)
val += (sum_3x1(0) * test(0) + sum_3x1(2) * test_z(2)) * (_avg_grad_phi[_j][0] - new_phi(0));
else if (ivar == 0 && jvar == 1)
val += (sum_3x1(0) * test(0) + sum_3x1(2) * test_z(2)) * (_avg_grad_phi[_j][1] - new_phi(1));
else if (ivar == 1 && jvar == 0)
val += sum_3x1(1) * test(1) * (_avg_grad_phi[_j][0] - new_phi(0));
else
val += sum_3x1(1) * test(1) * (_avg_grad_phi[_j][1] - new_phi(1));
// Bvol^T_i * C * B_j
// val = trace (C * B_j) *(avg_grad_test[_i][ivar] - new_test(ivar))
if (jvar == 0)
for (unsigned int i = 0; i < 3; ++i)
val +=
(_Jacobian_mult[_qp](i, i, 0, 0) * phi(0) + _Jacobian_mult[_qp](i, i, 0, 1) * phi(1) +
_Jacobian_mult[_qp](i, i, 2, 2) * phi_z(2)) *
(_avg_grad_test[_i][ivar] - new_test(ivar));
else if (jvar == 1)
for (unsigned int i = 0; i < 3; ++i)
val +=
(_Jacobian_mult[_qp](i, i, 0, 1) * phi(0) + _Jacobian_mult[_qp](i, i, 1, 1) * phi(1)) *
(_avg_grad_test[_i][ivar] - new_test(ivar));
}
return val / 3.0 + first_term;
}