Material to compute the angular orientation of order parameter interfaces. More...

#include <InterfaceOrientationMaterial.h>

Inheritance diagram for InterfaceOrientationMaterial:

Public Member Functions
	InterfaceOrientationMaterial (const InputParameters &parameters)

Protected Member Functions
virtual void	computeQpProperties ()

Private Attributes
Real	_delta

unsigned int	_j

Real	_theta0

Real	_eps_bar

MaterialProperty< Real > &	_eps

MaterialProperty< Real > &	_deps

MaterialProperty< RealGradient > &	_depsdgrad_op

MaterialProperty< RealGradient > &	_ddepsdgrad_op

const VariableValue &	_op

const VariableGradient &	_grad_op

Detailed Description

Material to compute the angular orientation of order parameter interfaces.

See R. Kobayashi, Physica D, 63, 410-423 (1993), final (non-numbered) equation on p. 412. doi:10.1016/0167-2789(93)90120-P

Definition at line 25 of file InterfaceOrientationMaterial.h.

Constructor & Destructor Documentation

◆ InterfaceOrientationMaterial()

InterfaceOrientationMaterial::InterfaceOrientationMaterial ( const InputParameters & parameters )

Definition at line 31 of file InterfaceOrientationMaterial.C.

   : Material(parameters),
     _delta(getParam<Real>("anisotropy_strength")),
     _j(getParam<unsigned int>("mode_number")),
     _theta0(getParam<Real>("reference_angle")),
     _eps_bar(getParam<Real>("eps_bar")),
     _eps(declareProperty<Real>("eps")),
     _deps(declareProperty<Real>("deps")),
     _depsdgrad_op(declareProperty<RealGradient>("depsdgrad_op")),
     _ddepsdgrad_op(declareProperty<RealGradient>("ddepsdgrad_op")),
     _op(coupledValue("op")),
     _grad_op(coupledGradient("op"))
 {
   // this currently only works in 2D simulations
   if (_mesh.dimension() != 2)
     mooseError("InterfaceOrientationMaterial requires a two-dimensional mesh.");
 }

Member Function Documentation

◆ computeQpProperties()

void InterfaceOrientationMaterial::computeQpProperties ( )

protectedvirtual

Definition at line 50 of file InterfaceOrientationMaterial.C.

 {
   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);
   _deps[_qp] = -_eps_bar * _delta * _j * std::sin(_j * (angle - _theta0 * libMesh::pi / 180.0));
   Real d2eps =
       -_eps_bar * _delta * _j * _j * 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;
 }