void
InterfaceOrientationMaterial::computeQpProperties()
{
Real cutoff = 0.99999;
// cosine of the gradient orientation angle
Real n;
if (_grad_op[_qp].norm() == 0)
n = 0;
else
n = _grad_op[_qp](0) / _grad_op[_qp].norm();
if (n > cutoff)
n = cutoff;
if (n < -cutoff)
n = -cutoff;
const Real angle = std::acos(n);
// Compute derivative of angle wrt n
const Real dangledn = - 1.0 / std::sqrt(1.0 - n * n);
// Compute derivative of n with respect to grad_op
RealGradient dndgrad_op;
if (_grad_op[_qp].norm_sq() == 0)
dndgrad_op = 0;
else
{
dndgrad_op(0) = _grad_op[_qp](1) * _grad_op[_qp](1);
dndgrad_op(1) = - _grad_op[_qp](0) * _grad_op[_qp](1);
dndgrad_op /= (_grad_op[_qp].norm_sq() * _grad_op[_qp].norm());
}
// Calculate interfacial parameter epsilon and its derivatives
_eps[_qp]= _eps_bar * (_delta * std::cos(_j * (angle - _theta0 * libMesh::pi/180.0)) + 1.0);
_deps[_qp]= - _eps_bar * _delta * _delta * std::sin(_j * (angle - _theta0 * libMesh::pi/180.0));
Real d2eps = - _eps_bar * _delta * _delta * _delta * std::cos(_j * (angle - _theta0 * libMesh::pi/180.0));
// Compute derivatives of epsilon and its derivative wrt grad_op
_depsdgrad_op[_qp] = _deps[_qp] * dangledn * dndgrad_op;
_ddepsdgrad_op[_qp] = d2eps * dangledn * dndgrad_op;
}
void
WidmanstattenMaterial::computeQpProperties()
{
const Real tol = 1e-9;
const Real cutoff = 1.0 - tol;
// cosine of the gradient orientation angle
Real n = 0.0;
const Real nsq = _grad_op[_qp].norm_sq();
if (nsq > tol)
n = _grad_op[_qp](0) / std::sqrt(nsq);
if (n > cutoff)
n = cutoff;
if (n < -cutoff)
n = -cutoff;
const Real angle = std::acos(n) * MathUtils::sign(_grad_op[_qp](1));
// Compute derivative of angle wrt n
const Real dangledn = - MathUtils::sign(_grad_op[_qp](1)) / std::sqrt(1.0 - n * n);
// Compute derivative of n with respect to grad_op
RealGradient dndgrad_op;
if (nsq > tol)
{
dndgrad_op(0) = _grad_op[_qp](1) * _grad_op[_qp](1);
dndgrad_op(1) = - _grad_op[_qp](0) * _grad_op[_qp](1);
dndgrad_op /= (_grad_op[_qp].norm_sq() * _grad_op[_qp].norm());
}
// Calculate interfacial parameter epsilon and its derivatives
_eps[_qp]= _eps_bar * (_delta * std::cos(_j * (angle - _theta0 * libMesh::pi/180.0)) + 1.0) * (1 / (1 + _delta));
_deps[_qp]= - _eps_bar * (_delta * _j * std::sin(_j * (angle - _theta0 * libMesh::pi/180.0)) * (1 / (1 + _delta)));
Real d2eps = - _eps_bar * (_delta * _j * _j * std::cos(_j * (angle - _theta0 * libMesh::pi/180.0)) * (1 / (1 + _delta)));
// Compute derivatives of epsilon and its derivative wrt grad_op
_depsdgrad_op[_qp] = _deps[_qp] * dangledn * dndgrad_op;
_ddepsdgrad_op[_qp] = d2eps * dangledn * dndgrad_op;
}
