EulerAngleUpdater Class Reference

Update Euler angles of each grains after rigid body rotation This class estimates the rotation of principal axes of the grains due to applied torques and calculates the final grain orientation. More...

#include <EulerAngleUpdater.h>

Inheritance diagram for EulerAngleUpdater:

Public Member Functions
	EulerAngleUpdater (const InputParameters &parameters)
virtual void	initialize () override
virtual void	execute () override
virtual void	finalize () override
virtual const EulerAngles &	getEulerAngles (unsigned int) const override
virtual const EulerAngles &	getEulerAnglesOld (unsigned int) const
virtual unsigned int	getGrainNum () const override

Protected Attributes
const GrainTrackerInterface &	_grain_tracker
const EulerAngleProvider &	_euler
const GrainForceAndTorqueInterface &	_grain_torque
const VectorPostprocessorValue &	_grain_volumes
const Real	_mr
bool	_first_time
std::vector< EulerAngles >	_angles
std::vector< EulerAngles >	_angles_old

Detailed Description

Update Euler angles of each grains after rigid body rotation This class estimates the rotation of principal axes of the grains due to applied torques and calculates the final grain orientation.

Step1: Calculate RotationTensor based on euler angles from previous time step (R0) Step2: Obtain the torque acting on the grains at current time Step Step3: Calculate the angular velocities around global axes Step4: Calculate change in euler angles due to torque and corresponding rotation matrix(R1) Step5: Calculate final rotation matrix, R = R1 * R0, determines the final position of any rotated vector Step6: Back-calculate the euler angles from the final rotation matrix Step7: Ensure euler angles comply with Bunge definitions

Definition at line 37 of file EulerAngleUpdater.h.

Constructor & Destructor Documentation

EulerAngleUpdater()

EulerAngleUpdater::EulerAngleUpdater

(

const InputParameters &

parameters

)

Definition at line 36 of file EulerAngleUpdater.C.

  : EulerAngleProvider(params),
    _grain_tracker(getUserObject<GrainTrackerInterface>("grain_tracker_object")),
    _euler(getUserObject<EulerAngleProvider>("euler_angle_provider")),
    _grain_torque(getUserObject<GrainForceAndTorqueInterface>("grain_torques_object")),
    _grain_volumes(getVectorPostprocessorValue("grain_volumes", "feature_volumes")),
    _mr(getParam<Real>("rotation_constant")),
    _first_time(true)
{
}

Member Function Documentation

execute()

virtual void EulerAngleUpdater::execute ( )

inlineoverridevirtual

Definition at line 43 of file EulerAngleUpdater.h.

{}

finalize()

virtual void EulerAngleUpdater::finalize ( )

inlineoverridevirtual

Definition at line 44 of file EulerAngleUpdater.h.

{}

getEulerAngles()

const EulerAngles & EulerAngleUpdater::getEulerAngles ( unsigned int  i ) const

overridevirtual

Implements EulerAngleProvider.

Definition at line 168 of file EulerAngleUpdater.C.

Referenced by EulerAngleUpdaterCheck::initialize().

{
  mooseAssert(i < getGrainNum(), "Requesting Euler angles for an invalid grain id");
  return _angles[i];
}

getEulerAnglesOld()

const EulerAngles & EulerAngleUpdater::getEulerAnglesOld ( unsigned int  i ) const

virtual

Definition at line 175 of file EulerAngleUpdater.C.

Referenced by EulerAngleUpdaterCheck::initialize().

{
  mooseAssert(i < getGrainNum(), "Requesting Euler angles for an invalid grain id");
  return _angles_old[i];
}

getGrainNum()

unsigned int EulerAngleUpdater::getGrainNum ( ) const

overridevirtual

Implements EulerAngleProvider.

Definition at line 162 of file EulerAngleUpdater.C.

Referenced by getEulerAngles(), and getEulerAnglesOld().

{
  return _angles.size();
}

initialize()

void EulerAngleUpdater::initialize ( )

overridevirtual

Change in euler angles are obtained from the torque & angular velocities about the material axes. Change in phi1, Phi and phi2 are caused by rotation about z axis, x' axis & z'' axis, respectively. Components of the angular velocities across z, x' and z'' axes are obtained from the torque values. This yields change in euler angles due to grain rotation.

Final RotationMatrix = RotationMatrix due to applied torque X old RotationMatrix Updated Euler angles are obtained by back-tracking the angles from the rotation matrix For details about the componenets of the rotation matrix please refer to RotationTensor.C Phi = acos(R33); phi1 = atan2(R31,-R32); phi2 = atan2(R13,R23) for phi != 0.0 por 180.0

Definition at line 48 of file EulerAngleUpdater.C.

{
  const auto grain_num = _grain_tracker.getTotalFeatureCount();

  if (_first_time)
  {
    _angles.resize(grain_num);
    _angles_old.resize(grain_num);
    for (unsigned int i = 0; i < grain_num; ++i)
      _angles[i] = _euler.getEulerAngles(i); // Read initial euler angles
  }

  unsigned int angle_size = _angles.size();
  for (unsigned int i = angle_size; i < grain_num; ++i) // if new grains are created
    _angles.push_back(_euler.getEulerAngles(i));        // Assign initial euler angles

  for (unsigned int i = 0; i < grain_num; ++i)
  {
    if (!_first_time && !_fe_problem.converged())
      _angles[i] = _angles_old[i];

    RealGradient torque = _grain_torque.getTorqueValues()[i];

    if (i <= angle_size) // if new grains are created
      _angles_old[i] = _angles[i];
    else
      _angles_old.push_back(_angles[i]);

    RotationTensor R0(_angles_old[i]); // RotationTensor as per old euler angles
    RealVectorValue torque_rotated =
        R0 * torque; // Applied torque is rotated to allign with old grain axes
    RealVectorValue omega =
        _mr / _grain_volumes[i] * torque_rotated; // Angular velocity as per old grain axes
    RealVectorValue angle_change;
    angle_change(0) = omega(2) * _dt;
    angle_change(1) =
        (omega(0) * std::cos(angle_change(0)) + omega(1) * std::sin(angle_change(0))) * _dt;
    angle_change(2) = (omega(0) * std::sin(angle_change(0)) * std::sin(angle_change(1)) -
                       omega(1) * std::cos(angle_change(0)) * std::sin(angle_change(1)) +
                       omega(2) * std::cos(angle_change(1))) *
                      _dt;
    angle_change *= (180.0 / libMesh::pi);

    RotationTensor R1(angle_change); // Rotation matrix due to torque
    RealTensorValue R = R1 * R0;

    if (R(2, 2) != 1.0 && R(2, 2) != -1.0) // checks if cos(Phi) = 1 or -1
    {
      _angles[i].phi1 = std::atan2(R(2, 0), -R(2, 1)) * (180.0 / libMesh::pi);
      _angles[i].Phi = std::acos(R(2, 2)) * (180.0 / libMesh::pi);
      _angles[i].phi2 = std::atan2(R(0, 2), R(1, 2)) * (180.0 / libMesh::pi);
    }
    else if (R(2, 2) == 1.0) // special case for Phi = 0.0
    {
      if (R0(2, 2) == 1.0)
        // when Phi_old = 0.0; all the rotations are about z axis and angles accumulates after each
        // rotation
        _angles[i].phi1 = _angles_old[i].phi1 + _angles_old[i].phi2 + angle_change(0);
      else
        _angles[i].phi1 = angle_change(0);
      // Comply with bunge euler angle definitions, 0.0 <= phi1 <= 360.0
      if (std::abs(_angles[i].phi1) > 360.0)
      {
        int laps = _angles[i].phi1 / 360.0;
        _angles[i].phi1 -= laps * 360.0;
      }
      _angles[i].Phi = 0.0;
      _angles[i].phi2 = -_angles[i].phi1 + std::atan2(R(0, 1), R(1, 1)) * (180.0 / libMesh::pi);
    }
    else
    {
      if (R0(2, 2) == 1.0)
        _angles[i].phi1 = _angles_old[i].phi1 + _angles_old[i].phi2 + angle_change(0);
      else
        _angles[i].phi1 = angle_change(0);
      // Comply with bunge euler angle definitions, 0.0 <= phi1 <= 360.0
      if (std::abs(_angles[i].phi1) > 360.0)
      {
        int laps = _angles[i].phi1 / 360.0;
        _angles[i].phi1 -= laps * 360.0;
      }
      _angles[i].Phi = 180.0;
      _angles[i].phi2 = _angles[i].phi1 - std::atan2(-R(0, 1), -R(1, 1)) * (180.0 / libMesh::pi);
    }

    // Following checks and updates are done only to comply with bunge euler angle definitions, 0.0
    // <= phi1/phi2 <= 360.0
    if (_angles[i].phi1 < 0.0)
      _angles[i].phi1 += 360.0;
    if (_angles[i].phi2 < 0.0)
      _angles[i].phi2 += 360.0;
    if (_angles[i].Phi < 0.0)
      mooseError("Euler angle out of range.");
  }

  _first_time = false;
}

Member Data Documentation

_angles

std::vector<EulerAngles> EulerAngleUpdater::_angles

protected

Definition at line 59 of file EulerAngleUpdater.h.

Referenced by getEulerAngles(), getGrainNum(), and initialize().

_angles_old

std::vector<EulerAngles> EulerAngleUpdater::_angles_old

protected

Definition at line 60 of file EulerAngleUpdater.h.

Referenced by getEulerAnglesOld(), and initialize().

_euler

const EulerAngleProvider& EulerAngleUpdater::_euler

protected

Definition at line 52 of file EulerAngleUpdater.h.

Referenced by initialize().

_first_time

bool EulerAngleUpdater::_first_time

protected

Definition at line 57 of file EulerAngleUpdater.h.

Referenced by initialize().

_grain_torque

const GrainForceAndTorqueInterface& EulerAngleUpdater::_grain_torque

protected

Definition at line 53 of file EulerAngleUpdater.h.

Referenced by initialize().

_grain_tracker

const GrainTrackerInterface& EulerAngleUpdater::_grain_tracker

protected

Definition at line 51 of file EulerAngleUpdater.h.

Referenced by initialize().

_grain_volumes

const VectorPostprocessorValue& EulerAngleUpdater::_grain_volumes

protected

Definition at line 54 of file EulerAngleUpdater.h.

Referenced by initialize().

_mr

const Real EulerAngleUpdater::_mr

protected

Definition at line 56 of file EulerAngleUpdater.h.

Referenced by initialize().

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The documentation for this class was generated from the following files:

• phase_field/include/userobjects/EulerAngleUpdater.h
• phase_field/src/userobjects/EulerAngleUpdater.C