HaighWestergaard.h

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/* ---------------------------------------------------------------------
 *                                       _
 *  _ __ ___   __ _ _ __ _ __ ___   ___ | |_
 * | '_ ` _ \ / _` | '__| '_ ` _ \ / _ \| __|
 * | | | | | | (_| | |  | | | | | | (_) | |_
 * |_| |_| |_|\__,_|_|  |_| |_| |_|\___/ \__|
 *
 * Unit of Strength of Materials and Structural Analysis
 * University of Innsbruck,
 * 2020 - today
 *
 * festigkeitslehre@uibk.ac.at
 *
 * Matthias Neuner matthias.neuner@uibk.ac.at
 * Magdalena Schreter magdalena.schreter@uibk.ac.at
 * Alexander Dummer alexander.dummer@uibk.ac.at
 *
 * This file is part of the MAteRialMOdellingToolbox (marmot).
 *
 * This library is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 *
 * The full text of the license can be found in the file LICENSE.md at
 * the top level directory of marmot.
 * ---------------------------------------------------------------------
 */
 
#pragma once
#include "Marmot/MarmotMath.h"
#include "Marmot/MarmotTypedefs.h"
#include "Marmot/MarmotVoigt.h"
 
namespace Marmot {
  namespace ContinuumMechanics::HaighWestergaard {
 
    template < typename T = double >
    struct HaighWestergaardCoordinates {
 
      T xi;
      T rho;
      T theta;
    };
 
    template < typename T = double >
    HaighWestergaardCoordinates< T > haighWestergaard( const Eigen::Matrix< T, 6, 1 >& stress )
    {
      using namespace Constants;
      using namespace Marmot::ContinuumMechanics::VoigtNotation::Invariants;
      HaighWestergaardCoordinates< T > hw;
      const auto                       J2_ = J2( stress );
      hw.xi                                = I1( stress ) / sqrt3;
      hw.rho                               = sqrt( 2. * J2_ );
 
      if ( Marmot::Math::makeReal( hw.rho ) != 0 ) {
        const T J3_ = J3( stress );
        const T x   = 3. * ( sqrt3 / 2. ) * J3_ / ( pow( J2_, 3. / 2 ) );
        if ( Marmot::Math::makeReal( x ) <= -1 )
          hw.theta = 1. / 3 * Pi;
        else if ( Marmot::Math::makeReal( x ) >= 1 )
          hw.theta = 0.;
        else if ( x != x )
          hw.theta = 1. / 3 * Marmot::Constants::Pi;
        else
          hw.theta = 1. / 3 * acos( x );
      }
      else
        hw.theta = 0.;
 
      return hw;
    }
    HaighWestergaardCoordinates< double > haighWestergaardFromStrain( const Marmot::Vector6d& strain );
 
  } // namespace ContinuumMechanics::HaighWestergaard
} // namespace Marmot