cl_Material_Lead.hpp

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/*
 * BELFEM -- The Berkeley Lab Finite Element Framework
 * Copyright (c) 2026, The Regents of the University of California, through
 * Lawrence Berkeley National Laboratory (subject to receipt of any required
 * approvals from the U.S. Dept. of Energy).  All rights reserved.
 *
 * Developers: Christian Messe, Gregory Giard
 * 
 * See the top-level LICENSE file for the complete license and disclaimer.
 */
 
#ifndef BELFEM_CL_MATERIAL_LEAD_HPP
#define BELFEM_CL_MATERIAL_LEAD_HPP
 
#include "cl_Material_Metal.hpp"
#include "cl_Bezier.hpp"
#include "fn_polyval.hpp"
namespace belfem
{
    namespace material
    {
        class Lead : public Metal
        {
            // debye temperature
            Cell< Vector< real > > mDebyePolys ;
            Vector< real > mTDebyeSwitch ;
 
            Bezier * mThermalExpansion = nullptr ;
            Vector< real > mThermalExpansionCryo ;
            Bezier * mDebyeTemperature = nullptr ;
 
            Cell< Vector< real > > mKohlerLongPolys ;
            Cell< Vector< real > > mKohlerTransPolys ;
            Vector< real > mBSKohlerLongSwitch ;
            Vector< real > mBSKohlerTransSwitch ;
        public:
            Lead( const real RRR = BELFEM_QUIET_NAN,
                  const bool aBuildTables = true );
 
            ~Lead() override;
 
        protected:
 
            real
            alpha_custom( const real T ) const override ;
 
            real
            debye_custom(const real T) const override;
 
            real
            kohler( const real B, const real S, const real beta ) const override ;
        private:
 
            void
            set_constants();
 
            void
            create_alpha();
 
            void
            create_cp();
 
            void
            create_debye();
 
            void
            create_kohler();
        };
 
        inline real
        Lead::kohler( const real B, const real S, const real beta ) const
        {
            if ( B < BELFEM_EPSILON ) return 0.0 ;
 
            real BS = B * S ;
 
            real Along ;
 
            if ( BS < mBSKohlerLongSwitch( 0 ) )
            {
                Along = polyval( mKohlerLongPolys(0), BS );
            }
            else if ( BS < mBSKohlerLongSwitch( 1 ) )
            {
                Along = std::exp( polyval( mKohlerLongPolys(1), std::log(BS) ) );
            }
            else
            {
                Along = polyval( mKohlerLongPolys(2), BS );
            }
 
            real Atrans ;
            if ( BS < mBSKohlerTransSwitch( 0 ) )
            {
                Atrans = polyval( mKohlerTransPolys(0), BS );
            }
            else
            {
                Atrans = std::exp( polyval( mKohlerTransPolys(1), std::log(BS) ) );
            }
 
            real c = std::cos( beta );
            real c2 = c*c ;
            real s2 = 1.0 - c2 ;
 
            // Pippard's angular interpolation formula
            return Along * c2 + Atrans * s2 ;
        }
 
    }
}
#endif //BELFEM_CL_MATERIAL_LEAD_HPP