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

#include <InterfaceOrientationMultiphaseMaterial.h>

Inheritance diagram for InterfaceOrientationMultiphaseMaterial:

Public Member Functions
	InterfaceOrientationMultiphaseMaterial (const InputParameters &parameters)

Protected Member Functions
virtual void	computeQpProperties ()

Private Attributes
MaterialPropertyName	_kappa_name

MaterialPropertyName	_dkappadgrad_etaa_name

MaterialPropertyName	_d2kappadgrad_etaa_name

Real	_delta

unsigned int	_j

Real	_theta0

Real	_kappa_bar

MaterialProperty< Real > &	_kappa

MaterialProperty< RealGradient > &	_dkappadgrad_etaa

MaterialProperty< RealTensorValue > &	_d2kappadgrad_etaa

const VariableValue &	_etaa

const VariableGradient &	_grad_etaa

const VariableValue &	_etab

const VariableGradient &	_grad_etab

Detailed Description

Material to compute the angular orientation of order parameter interfaces.

Definition at line 23 of file InterfaceOrientationMultiphaseMaterial.h.

Constructor & Destructor Documentation

◆ InterfaceOrientationMultiphaseMaterial()

InterfaceOrientationMultiphaseMaterial::InterfaceOrientationMultiphaseMaterial ( const InputParameters & parameters )

Definition at line 42 of file InterfaceOrientationMultiphaseMaterial.C.

   : Material(parameters),
     _kappa_name(getParam<MaterialPropertyName>("kappa_name")),
     _dkappadgrad_etaa_name(getParam<MaterialPropertyName>("dkappadgrad_etaa_name")),
     _d2kappadgrad_etaa_name(getParam<MaterialPropertyName>("d2kappadgrad_etaa_name")),
     _delta(getParam<Real>("anisotropy_strength")),
     _j(getParam<unsigned int>("mode_number")),
     _theta0(getParam<Real>("reference_angle")),
     _kappa_bar(getParam<Real>("kappa_bar")),
     _kappa(declareProperty<Real>(_kappa_name)),
     _dkappadgrad_etaa(declareProperty<RealGradient>(_dkappadgrad_etaa_name)),
     _d2kappadgrad_etaa(declareProperty<RealTensorValue>(_d2kappadgrad_etaa_name)),
     _etaa(coupledValue("etaa")),
     _grad_etaa(coupledGradient("etaa")),
     _etab(coupledValue("etab")),
     _grad_etab(coupledGradient("etab"))
 {
   // this currently only works in 2D simulations
   if (_mesh.dimension() != 2)
     mooseError("InterfaceOrientationMultiphaseMaterial requires a two-dimensional mesh.");
 }

Member Function Documentation

◆ computeQpProperties()

void InterfaceOrientationMultiphaseMaterial::computeQpProperties ( )

protectedvirtual

Definition at line 66 of file InterfaceOrientationMultiphaseMaterial.C.

 {
   const Real tol = 1e-9;
   const Real cutoff = 1.0 - tol;
  
   // Normal direction of the interface
   Real n = 0.0;
   const RealGradient nd = _grad_etaa[_qp] - _grad_etab[_qp];
   const Real nx = nd(0);
   const Real ny = nd(1);
   const Real n2x = nd(0) * nd(0);
   const Real n2y = nd(1) * nd(1);
   const Real nsq = nd.norm_sq();
   const Real n2sq = nsq * nsq;
   if (nsq > tol)
     n = nx / std::sqrt(nsq);
  
   if (n > cutoff)
     n = cutoff;
  
   if (n < -cutoff)
     n = -cutoff;
  
   // Calculate the orientation angle
   const Real angle = std::acos(n) * MathUtils::sign(ny);
  
   // Compute derivatives of the angle wrt n
   const Real dangledn = -MathUtils::sign(ny) / std::sqrt(1.0 - n * n);
   const Real d2angledn2 = -MathUtils::sign(ny) * n / (1.0 - n * n) / std::sqrt(1.0 - n * n);
  
   // Compute derivative of n wrt grad_eta
   RealGradient dndgrad_etaa;
   if (nsq > tol)
   {
     dndgrad_etaa(0) = ny * ny;
     dndgrad_etaa(1) = -nx * ny;
     dndgrad_etaa /= nsq * std::sqrt(nsq);
   }
  
   // Compute the square of dndgrad_etaa
   RealTensorValue dndgrad_etaa_sq;
   if (nsq > tol)
   {
     dndgrad_etaa_sq(0, 0) = n2y * n2y;
     dndgrad_etaa_sq(0, 1) = -nx * ny * n2y;
     dndgrad_etaa_sq(1, 0) = -nx * ny * n2y;
     dndgrad_etaa_sq(1, 1) = n2x * n2y;
     dndgrad_etaa_sq /= n2sq * nsq;
   }
  
   // Compute the second derivative of n wrt grad_eta
   RealTensorValue d2ndgrad_etaa2;
   if (nsq > tol)
   {
     d2ndgrad_etaa2(0, 0) = -3.0 * nx * n2y;
     d2ndgrad_etaa2(0, 1) = -ny * n2y + 2.0 * ny * n2x;
     d2ndgrad_etaa2(1, 0) = -ny * n2y + 2.0 * ny * n2x;
     d2ndgrad_etaa2(1, 1) = -nx * n2x + 2.0 * nx * n2y;
     d2ndgrad_etaa2 /= n2sq * std::sqrt(nsq);
   }
  
   // Calculate interfacial coefficient kappa and its derivatives wrt the angle
   Real anglediff = _j * (angle - _theta0 * libMesh::pi / 180.0);
   _kappa[_qp] =
       _kappa_bar * (1.0 + _delta * std::cos(anglediff)) * (1.0 + _delta * std::cos(anglediff));
   Real dkappadangle =
       -2.0 * _kappa_bar * _delta * _j * (1.0 + _delta * std::cos(anglediff)) * std::sin(anglediff);
   Real d2kappadangle =
       2.0 * _kappa_bar * _delta * _delta * _j * _j * std::sin(anglediff) * std::sin(anglediff) -
       2.0 * _kappa_bar * _delta * _j * _j * (1.0 + _delta * std::cos(anglediff)) *
           std::cos(anglediff);
  
   // Compute derivatives of kappa wrt grad_eta
   _dkappadgrad_etaa[_qp] = dkappadangle * dangledn * dndgrad_etaa;
   _d2kappadgrad_etaa[_qp] = d2kappadangle * dangledn * dangledn * dndgrad_etaa_sq +
                             dkappadangle * d2angledn2 * dndgrad_etaa_sq +
                             dkappadangle * dangledn * d2ndgrad_etaa2;
 }