src/InclusionMicrostructure/PolyhedronInclusion.cpp

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/* This file is part of MoDELib, the Mechanics Of Defects Evolution Library.
 *
 *
 * MoDELib is distributed without any warranty under the
 * GNU General Public License (GPL) v2 <http://www.gnu.org/licenses/>.
 */
 
#ifndef model_PolyhedronInclusion_cpp_
#define model_PolyhedronInclusion_cpp_
 
 
#include <InclusionMicrostructure/PolyhedronInclusion.h>
#include <numbers>
 
namespace model
{
 
 
//    template <int dim>
//    void PolyhedronInclusion<dim>::addSlipSystems(const std::vector<std::shared_ptr<SlipSystem>>& slipSystems)
//    {
//
//        for(const auto& slipSystem : slipSystems)
//        {
//            if(gammaSurfaceMap.find(slipSystem->gammaSurface.get())==gammaSurfaceMap.end())
//            {// current slipSystem gammaSurface not found
//
//                //                    GammaSurface temp();
//                //
//                //                    gammaSurfaceMap.emaplace(slipSystem->gammaSurface.get(),temp);
//            }
//        }
//
//    }
 
//    template <int dim>
//    double PolyhedronInclusion<dim>::misfitEnergy(const Eigen::Matrix<double,3,1>& b, const GammaSurface* const matrixGammaSurface) const
//    {
//        const auto iter(gammaSurfaceMap.find(matrixGammaSurface));
//        return iter==gammaSurfaceMap.end()? 0.0 : iter->second(b);
//    }
 
 
 
 
    template <int dim>
    PolyhedronInclusion<dim>::PolyhedronInclusion(const std::map<size_t,PolyhedronInclusionNodeIO<dim>>& nodesMap,
                                                  const std::map<size_t,std::vector<size_t>>& faceIDs,
                                            const MatrixDim& _eT,
                                            const double& _nu,
                                            const double& _mu,
                                            const double& _mobilityReduction,
                                            const int& _phaseID,
                                            const std::shared_ptr<SecondPhase<dim>>& sph) :
    /* init */ EshelbyInclusionBase<dim>(_eT,_nu,_mu,_mobilityReduction,_phaseID,sph)
    /* init */,delta(MatrixDim::Identity())
    /* init */,nodes(nodesMap)
    /* init */,faces(getFaces(nodesMap,faceIDs))
    {
//        std::cout<<"Creating PolyhedronInclusion "<<this->sID<<" (type "<<this->phaseID<<"):\n eT="<<this->eT<<std::endl;
        
        for(const auto& face : faces)
        {
            VectorDim C(VectorDim::Zero()); // face center
            for(const auto& nodePair : face.second)
            {
//                const auto nodeIter(nodes.find(nodeID));
                C+=nodePair.second;
//                if(nodeIter!=nodes.end())
//                {
//                    C+=nodeIter->second.P;
//                }
//                else
//                {
//                    throw std::runtime_error("PolyhedronInclusion: nodeID not found in nodes.");
//                }
            }
            C/=face.second.size();
            
            VectorDim nA(VectorDim::Zero()); // normal
//            const VectorDim P0(nodes.find(face.second.front())->second.P);
            const VectorDim P0(face.second.front().second);
            for(size_t k=0;k<face.second.size();++k)
            {
                const size_t k1(k<face.second.size()-1? k+1 : 0);
//                const VectorDim Pk(nodes.find(face.second[k])->second.P);
//                const VectorDim Pk1(nodes.find(face.second[k1])->second.P);
                const VectorDim Pk(face.second[k].second);
                const VectorDim Pk1(face.second[k1].second);
                nA+= 0.5*(Pk-P0).cross(Pk1-Pk);
            }
 
            Plane<3> plane(C,nA);
            for(const auto& nodePair : face.second)
            {
//                const auto nodeIter(nodes.find(nodeID));
//                if(nodeIter!=nodes.end())
//                {
                    if(!plane.contains(nodePair.second))
                    {
                        throw std::runtime_error("PolyhedronInclusion: face plane does not include face vertex.");
                    }
//                }
            }
            this->emplace(face.first,plane);
        }
    }
 
    template <int dim>
    const std::map<size_t,Plane<dim>>& PolyhedronInclusion<dim>::planes() const
    {
        return *this;
    }
 
    template <int dim>
    bool PolyhedronInclusion<dim>::contains(const VectorDim& x) const
    {
        bool contained(true);
        for(const auto& plane : this->planes())
        {
            contained=(contained && plane.second.isAbove(x));
        }
        return contained;
    }
 
template <int dim>
std::map<size_t,std::vector<std::pair<size_t,typename PolyhedronInclusion<dim>::VectorDim>>> PolyhedronInclusion<dim>::getFaces(const std::map<size_t,PolyhedronInclusionNodeIO<dim>>& nodesMap,
                                                                                                                                const std::map<size_t,std::vector<size_t>>& faceIDs)
{
    std::map<size_t,std::vector<std::pair<size_t,VectorDim>>> temp;
    for(const auto& fID : faceIDs)
    {
        std::vector<std::pair<size_t,VectorDim>> tempV;
        for(const auto& nID : fID.second)
        {
            const auto nodeIter(nodesMap.find(nID));
            if(nodeIter!=nodesMap.end())
            {
                tempV.emplace_back(nID,nodeIter->second.P);
            }
            else
            {
                throw std::runtime_error("PolyhedronInclusion node not found.");
            }
        }
        temp.emplace(fID.first,tempV);
    }
    return temp;
}
 
template <int dim>
double PolyhedronInclusion<dim>::Phi_u_II_a(double a, double b, double le)
{
    if (a != 0 && b != 0 && le != 0) {
        return -a / abs(a) * atan(le / b) + asin(a * le * abs(b) / (b * sqrt((a * a + b * b) * (b * b + le * le))));
    }
    else if (a == 0) {
        return 0.0;
    }
    else if (a != 0) {
 
        return 0.0;
    }
 
    // a, b, le equals zero
    return 0.0;
}
 
template <int dim>
double PolyhedronInclusion<dim>::Phi_u_II_b(double a, double b, double le)
{
    double dis = sqrt(a * a + b * b + le * le);
    if (a != 0 && b != 0 && le != 0) {
        return (1.0 / (b * b + le * le)) * (
            -le * dis + le * abs(a) + (b * b + le * le) * atanh(le / dis));
    }
    else if (a == 0) {
        if (b != 0) {    // le may equal zero, all includes
            return -le / dis + atanh(le / dis);
        }
        else { // b ==0, le != 0
            return 0.0;
        }
    }
    else if (a != 0) {
        if (b != 0 && le == 0) {
            return 0.0;
        }
        else if (b == 0 && le == 0) {
            return 0.0;
        }
        else if (b == 0 && le != 0) {
            return (-dis + abs(a)) / le + atanh(le / dis);
        }
    }
    
    // a, b, le equals zero
    return 0.0;
}
 
template <int dim>
double PolyhedronInclusion<dim>::Phi_u_II_le(double a, double b, double le)
{
    if (a != 0 && b != 0 && le != 0) {
        return b * (a * a + b * b + le * le - sqrt(a * a + b * b + le * le) * abs(a)) / ((b * b + le * le) * sqrt(a * a + b * b + le * le));
    }
    else if (a == 0) {
        if (b != 0 || le != 0) {
            return b / sqrt(b * b + le * le);
        }
        else {
            return 0.0;
        }
    }
    else if (a != 0) {
        if (b != 0 && le == 0) {
            return (sqrt(a * a + b * b) - abs(a)) / b;
        }
        else if (b == 0 && le != 0) {
            return 0.0;
        }
        else if (b == 0 && le == 0) {
            return 0.0;
        }
    }
    
    return 0.0;
}
 
//template <int dim>
//double PolyhedronInclusion<dim>::PHI_ij(int i, int j, double a, double b, double lm, double lp, const VectorDim& Svnorm, const VectorDim& Vnorm, const VectorDim& Vdir)
//{
//    return -(Svnorm[i]) * (-(Phi_u_II_a(a, b, lp) - Phi_u_II_a(a, b, lm)) * Svnorm[j]
//                           - (Phi_u_II_b(a, b, lp) - Phi_u_II_b(a, b, lm)) * Vnorm[j]
//                           - (Phi_u_II_le(a, b, lp)) * Vdir[j] + (Phi_u_II_le(a, b, lm)) * Vdir[j]);
//}
 
//template <int dim>
//double PolyhedronInclusion<dim>::PHI_ij(int i, int j, const VectorDim& x) const
//{
//    double result=0.0;
//    for(const auto& face : faces)
//    {
//        const auto& P0(face.second[0].second);
//        const auto& P1(face.second[1].second);
//        const auto& P2(face.second[2].second);
//        const VectorDim Svnorm((P1-P0).cross(P2-P1).normalized());
//        const double a(Svnorm.dot(P0-x));
//        for(size_t e=0;e<face.second.size();++e)
//        {
//            const size_t e1(e<face.second.size()-1? e+1 : 0);
//            const VectorDim& vm(face.second[e].second);
//            const VectorDim& vp(face.second[e1].second);
//            const VectorDim Vdir((vp-vm).normalized());
//            const VectorDim Vnorm(Vdir.cross(Svnorm));
//            const double b((vp-x).dot(Vnorm));
//            const double lm((vm-x).dot(Vdir));
//            const double lp((vp-x).dot(Vdir));
//            result+=PHI_ij(i,j,a,b,lm,lp,Svnorm,Vnorm,Vdir);
//        }
//    }
//    return result;
//}
 
template <int dim>
double PolyhedronInclusion<dim>::Psi_I1_a_a_a(double a, double b, double le)
{
    double dis = sqrt(a * a + b * b + le * le);
    if (a < 0 && b != 0 && le != 0) {
        return a * b * le / ((a * a + b * b) * dis) + 2.0 * atan(le / b) + 2.0 * atan(a * le / (b * dis));
    }
    else if (a > 0 && b != 0 && le != 0) {
        return a * b * le / ((a * a + b * b) * dis) - 2.0 * atan(le / b) + 2.0 * atan(a * le / (b * dis));
    }
        
    return 0.0;
}
 
template <int dim>
double PolyhedronInclusion<dim>::Psi_I1_a_a_b(double a, double b, double le)
{
    double dis = sqrt(a * a + b * b + le * le);
    if (a < 0 && b != 0 && le != 0) {
        return -le * (2.0 * a * a + b * b + a * b * b / dis) / ((a * a + b * b) * (dis - a)) + atanh(le / dis);
    }
    else if (a > 0 && b != 0 && le != 0) {
        return 2.0 * a * le / (b * b + le * le) + (le / dis) * (-2.0 + b * b / (a * a + b * b) - 2.0 * a * a / (b * b + le * le)) + atanh(le / dis);
    }
    else if (a == 0) {
        if (b != 0) {
            return -le / dis + atanh(le / dis);
        }
        else {   // include b = 0, le != 0, this is infinite
            return 0.0;
        }
    }
    else if (a != 0) {
        if (b != 0 && le == 0) {
            return 0.0;
        }
        else if (b == 0 && le != 0) {
            return 2.0 * (abs(a) - dis) / le + atanh(le / dis);
        }
        else if (b == 0 && le == 0) {
            return 0.0;
        }
    }
    
    return 0.0;
}
 
template <int dim>
double PolyhedronInclusion<dim>::Psi_I1_a_a_le(double a, double b, double le)
{
    double dis = sqrt(a * a + b * b + le * le);
    if (a != 0 && b != 0 && le != 0) {
        return (b / (b * b + le * le)) * (-2.0 * abs(a) + dis + (a * a) / dis);
    }
    else if (a == 0) {
        if (b != 0) {
            return b / dis;
        }
        else {
            return 0.0;
        }
    }
    else if (a != 0) {
        if (b != 0 && le == 0) {
            return ((2.0 * a * a + b * b) / dis - 2.0 * abs(a)) / b;
        }
        else if (b == 0 && le != 0) {
            return 0.0;
        }
        else if (b == 0 && le == 0) {
            return 0.0;
        }
    }
    
    return 0.0;
}
 
template <int dim>
double PolyhedronInclusion<dim>::Psi_I1_a_b_b(double a, double b, double le)
{
    double dis = sqrt(a * a + b * b + le * le);
    if (a != 0 && b != 0 && le != 0) {
        return (a * b * le / ((a * a + b * b) * pow(b * b + le * le, 2.0) * dis)) * (
            2.0 * pow(a, 4.0) - le * le * (b * b + le * le) + a * a * (3.0 * b * b + le * le) - 2.0 * (a * a + b * b) * dis * abs(a)
            );
    }
    
    return 0.0;
 
}
 
template <int dim>
double PolyhedronInclusion<dim>::Psi_I1_a_b_le(double a, double b, double le)
{
    double dis = sqrt(a * a + b * b + le * le);
    if (a != 0 && b != 0 && le != 0) {
        return (a / (pow(b * b + le * le, 2.0) * dis)) * (
            -pow(a * b, 2.0) + (a * a + b * b) * le * le + pow(le, 4.0) + (b * b - le * le) * dis * abs(a)
            );
    }
    else if (a == 0) {
        return 0.0;
    }
    else if (a != 0) {
        if (b != 0 && le == 0) {
            return a * (-a * a / dis + abs(a)) / (b * b);
        }
        else if (b == 0 && le != 0) {
            return a * (dis - abs(a)) / (le * le);
        }
        else if (b == 0 && le == 0) {
            return 0.5 * a / abs(a);
        }
    }
    
    return 0.0;
}
 
template <int dim>
double PolyhedronInclusion<dim>::Psi_I1_a_le_le(double a, double b, double le)
{
    double dis = sqrt(a * a + b * b + le * le);
    if (a != 0 && b != 0 && le != 0) {
        return -a * b * le * (
            a * a + dis * dis - 2.0 * dis * abs(a)
            ) / (pow(b * b + le * le, 2.0) * dis);
    }
 
    return 0.0;
}
 
template <int dim>
double PolyhedronInclusion<dim>::Psi_I1_b_b_b(double a, double b, double le)
{
    double dis = sqrt(a * a + b * b + le * le);
    if (a != 0 && b != 0 && le != 0) {
        return (1.0 / (3.0 * (a * a + b * b) * pow(b * b + le * le, 3.0) * dis)) * (
            2.0 * pow(a, 6.0) * le * (-3.0 * b * b + le * le) - b * b * le * pow(b * b + le * le, 2.0) * (3.0 * b * b + 4.0 * le * le)
            - a * a * le * (b * b + le * le) * (3.0 * pow(b, 4.0) + pow(le, 4.0)) + pow(a, 4.0) * (-9.0 * pow(b, 4.0) * le + pow(le, 5.0))
            )
            - 2.0 * le * (-3.0 * b * b + le * le) * pow(abs(a), 3.0) / (3.0 * pow(b * b + le * le, 3.0))
            + atanh(le / dis);
    }
    else if (a == 0) {
        if (b != 0) {
            return -le * (3.0 * b * b + 4.0 * le * le) / (3.0 * dis * dis * dis) + atanh(le / dis);
        }
        else { // infinite
            return 0.0;
        }
    }
    else if (a != 0) {
        if (b != 0 && le == 0) {
            return 0.0;
        }
        else if (b == 0 && le != 0) {
            return (1.0 / (3.0 * pow(le, 3.0) * dis)) * (2.0 * pow(a, 4.0) + a * a * le * le - pow(le, 4.0)) - 2.0 * pow(abs(a), 3.0) / (3.0 * le * le * le) + atanh(le / dis);
        }
        else if (b == 0 && le == 0) {
            return 0.0;
        }
    }
    
    return 0.0;
}
 
template <int dim>
double PolyhedronInclusion<dim>::Psi_I1_b_b_le(double a, double b, double le)
{
    double dis = sqrt(a * a + b * b + le * le);
    if (a != 0 && b != 0 && le != 0) {
        return (b / (3.0 * pow(b * b + le * le, 3.0) * dis)) * (
            2.0 * pow(a, 4.0) * (b * b - 3.0 * le * le) + a * a * (b * b - 3.0 * le * le) * (b * b + le * le)
            + pow(b * b + le * le, 2.0) * (2.0 * b * b + 3.0 * le * le) - 2.0 * (b * b - 3.0 * le * le) * dis * pow(abs(a), 3.0)
            );
    }
    else if (a == 0) {
        if (b != 0) {
            return b * (2.0 * b * b + 3.0 * le * le) / (3.0 * dis * dis * dis);
        }
        else {
            return 0.0;
        }
    }
    else if (a != 0) {
        if (b != 0 && le == 0) {
            return (2.0 * pow(a, 4.0) + pow(a * b, 2.0) + 2.0 * pow(b, 4.0) - 2.0 * dis * pow(abs(a), 3.0)) / (3.0 * pow(b, 3.0) * dis);
        }
        else if (b == 0 && le != 0) {
            return 0.0;
        }
        else if (b == 0 && le == 0) {
            return 0.0;
        }
    }
    
    return 0.0;
}
 
template <int dim>
double PolyhedronInclusion<dim>::Psi_I1_b_le_le(double a, double b, double le)
{
    double dis = sqrt(a * a + b * b + le * le);
    if (a != 0 && b != 0 && le != 0) {
         return (le / (3.0 * pow(b * b + le * le, 3.0) * dis)) * (
            pow(a, 4.0) * (6.0 * b * b - 2.0 * le * le) + a * a * (3.0 * b * b - le * le) * (b * b + le * le)
            + le * le * pow(b * b + le * le, 2.0) + 2.0 * (-3.0 * b * b + le * le) * dis * pow(abs(a), 3.0)
            );
    }
    else if (a == 0) {
        if (b != 0) {
            return pow(le, 3.0) / (3.0 * dis * dis * dis);
        }
        else if (le != 0) {
            return 0.0; // le / (3.0 * abs(le));
        }
        else {
            return 0.0;
        }
    }
    else if (a != 0) {
        if (b != 0 && le == 0) {
            return 0.0;
        }
        else if (b == 0 && le != 0) {
            return (-2.0 * pow(a, 4.0) - pow(a * le, 2.0) + pow(le, 4.0) + 2.0 * dis * pow(abs(a), 3.0)) / (3.0 * dis * pow(le, 3.0));
        }
        else if (b == 0 && le == 0) {
            return 0.0;
        }
    }
    
    return 0.0;
}
 
template <int dim>
double PolyhedronInclusion<dim>::Psi_I1_le_le_le(double a, double b, double le)
{
    double dis = sqrt(a * a + b * b + le * le);
    if (a != 0 && b != 0 && le != 0) {
        return (b / (3.0 * pow(b * b + le * le, 3.0) * dis)) * (
            -2.0 * pow(a, 4.0) * (b * b - 3.0 * le * le) - a * a * (b * b - 3.0 * le * le) * (b * b + le * le)
            + b * b * pow(b * b + le * le, 2.0) + 2.0 * (b * b - 3.0 * le * le) * dis * pow(abs(a), 3.0)
            );
    }
    else if (a == 0) {
        if (b != 0) {
            return pow(b, 3.0) / (3.0 * dis * dis * dis);
        }
        else {
            return 0.0;
        }
    }
    else if (a != 0) {
        if (b != 0 && le == 0) {
            return (-2.0 * pow(a, 4.0) - pow(a * b, 2.0) + pow(b, 4.0) + 2.0 * dis * pow(abs(a), 3.0)) / (3.0 * dis * pow(b, 3.0));
        }
        else if (b == 0 && le != 0) {
            return 0.0;
        }
        else if (b == 0 && le == 0) {
            return 0.0;
        }
    }
    
    return 0.0;
}
 
 
//template <int dim>
//double PolyhedronInclusion<dim>::PSI_ijkl(int i, int j, int k, int l, double a, double b, double lm, double lp, const VectorDim& Svnorm, const VectorDim& Vnorm, const VectorDim& Vdir)
//{
//    return (-(Psi_I1_a_a_a(a, b, lp) - Psi_I1_a_a_a(a, b, lm)) * Svnorm[i] * Svnorm[j] * Svnorm[k] - (Psi_I1_b_b_b(a, b, lp) - Psi_I1_b_b_b(a, b, lm)) * Vnorm[i] * Vnorm[j] * Vnorm[k]
//       - (Psi_I1_le_le_le(a, b, lp) - Psi_I1_le_le_le(a, b, lm)) * Vdir[i] * Vdir[j] * Vdir[k] - (Psi_I1_a_a_b(a, b, lp) - Psi_I1_a_a_b(a, b, lm)) * (Svnorm[i] * Svnorm[j] * Vnorm[k] + Svnorm[i] * Vnorm[j] * Svnorm[k] + Vnorm[i] * Svnorm[j] * Svnorm[k])
//       - (Psi_I1_a_a_le(a, b, lp) - Psi_I1_a_a_le(a, b, lm)) * (Svnorm[i] * Svnorm[j] * Vdir[k] + Svnorm[i] * Vdir[j] * Svnorm[k] + Vdir[i] * Svnorm[j] * Svnorm[k]) - (Psi_I1_a_b_b(a, b, lp) - Psi_I1_a_b_b(a, b, lm)) * (Svnorm[i] * Vnorm[j] * Vnorm[k] + Svnorm[j] * Vnorm[i] * Vnorm[k] + Svnorm[k] * Vnorm[j] * Vnorm[i])
//       - (Psi_I1_b_b_le(a, b, lp) - Psi_I1_b_b_le(a, b, lm)) * (Vdir[i] * Vnorm[j] * Vnorm[k] + Vdir[j] * Vnorm[i] * Vnorm[k] + Vdir[k] * Vnorm[i] * Vnorm[j]) - (Psi_I1_a_le_le(a, b, lp) - Psi_I1_a_le_le(a, b, lm)) * (Svnorm[i] * Vdir[j] * Vdir[k] + Svnorm[j] * Vdir[i] * Vdir[k] + Svnorm[k] * Vdir[i] * Vdir[j])
//       - (Psi_I1_b_le_le(a, b, lp) - Psi_I1_b_le_le(a, b, lm)) * (Vnorm[i] * Vdir[j] * Vdir[k] + Vnorm[j] * Vdir[i] * Vdir[k] + Vnorm[k] * Vdir[i] * Vdir[j])
//       - (Psi_I1_a_b_le(a, b, lp) - Psi_I1_a_b_le(a, b, lm)) * (Svnorm[i] * Vnorm[j] * Vdir[k] + Svnorm[i] * Vnorm[k] * Vdir[j] + Svnorm[j] * Vnorm[i] * Vdir[k] + Svnorm[k] * Vnorm[i] * Vdir[j] + Svnorm[j] * Vnorm[k] * Vdir[i] + Svnorm[k] * Vnorm[j] * Vdir[i])) * (-Svnorm[l]);
//}
 
 
//template <int dim>
//double PolyhedronInclusion<dim>::PSI_ijkl(int i, int j, int k, int l, const VectorDim& x) const
//{
//    double result=0.0;
//    for(const auto& face : faces)
//    {
//        const auto& P0(face.second[0].second);
//        const auto& P1(face.second[1].second);
//        const auto& P2(face.second[2].second);
//        const VectorDim Svnorm((P1-P0).cross(P2-P1).normalized());
//        const double a(Svnorm.dot(P0-x));
//        for(size_t e=0;e<face.second.size();++e)
//        {
//            const size_t e1(e<face.second.size()-1? e+1 : 0);
//            const VectorDim& vm(face.second[e].second);
//            const VectorDim& vp(face.second[e1].second);
//            const VectorDim Vdir((vp-vm).normalized());
//            const VectorDim Vnorm(Vdir.cross(Svnorm));
//            const double b((vp-x).dot(Vnorm));
//            const double lm((vm-x).dot(Vdir));
//            const double lp((vp-x).dot(Vdir));
//            result+=PSI_ijkl(i,j,k,l,a,b,lm,lp,Svnorm,Vnorm,Vdir);
//        }
//    }
//    return result;
//}
 
//    template <int dim>
//    double PolyhedronInclusion<dim>::eshelbyTensorComponent(const int&i,const int&j,const int&k,const int&l,const VectorDim& x) const
//    {
//        auto delta_xy = [] (const int x, const int y) -> int {return x==y;};
//
//        return  0.125/(std::numbers::pi*(1.0-this->nu))*(PSI_ijkl(i,j,k,l,x)
//                                                         -2.0*this->nu*delta_xy(k,l)*PHI_ij(i,j,x)
//                                                         -(1.0-this->nu)*(PHI_ij(i,l,x)*delta_xy(j,k)
//                                                                          +PHI_ij(j,k,x)*delta_xy(i,l)
//                                                                          +PHI_ij(j,l,x)*delta_xy(i,k)
//                                                                          +PHI_ij(i,k,x)*delta_xy(j,l)));
//    }
 
template <int dim>
double PolyhedronInclusion<dim>::eshelbyTensorComponent(const int&i,const int&j,const int&k,const int&l,const MatrixDim& PHI,const MatrixDim& delta, const Psi_I1& psi,const VectorDim& Svnorm,const VectorDim& Vnorm,const VectorDim& Vdir) const
{
        
    const double psi_val= (-psi.I1_a_a_a * Svnorm[i] * Svnorm[j] * Svnorm[k] - psi.I1_b_b_b * Vnorm[i] * Vnorm[j] * Vnorm[k]
       - psi.I1_le_le_le * Vdir[i] * Vdir[j] * Vdir[k] - psi.I1_a_a_b * (Svnorm[i] * Svnorm[j] * Vnorm[k] + Svnorm[i] * Vnorm[j] * Svnorm[k] + Vnorm[i] * Svnorm[j] * Svnorm[k])
       - psi.I1_a_a_le * (Svnorm[i] * Svnorm[j] * Vdir[k] + Svnorm[i] * Vdir[j] * Svnorm[k] + Vdir[i] * Svnorm[j] * Svnorm[k]) - psi.I1_a_b_b * (Svnorm[i] * Vnorm[j] * Vnorm[k] + Svnorm[j] * Vnorm[i] * Vnorm[k] + Svnorm[k] * Vnorm[j] * Vnorm[i])
       - psi.I1_b_b_le * (Vdir[i] * Vnorm[j] * Vnorm[k] + Vdir[j] * Vnorm[i] * Vnorm[k] + Vdir[k] * Vnorm[i] * Vnorm[j]) - psi.I1_a_le_le * (Svnorm[i] * Vdir[j] * Vdir[k] + Svnorm[j] * Vdir[i] * Vdir[k] + Svnorm[k] * Vdir[i] * Vdir[j])
       - psi.I1_b_le_le * (Vnorm[i] * Vdir[j] * Vdir[k] + Vnorm[j] * Vdir[i] * Vdir[k] + Vnorm[k] * Vdir[i] * Vdir[j])
       - psi.I1_a_b_le * (Svnorm[i] * Vnorm[j] * Vdir[k] + Svnorm[i] * Vnorm[k] * Vdir[j] + Svnorm[j] * Vnorm[i] * Vdir[k] + Svnorm[k] * Vnorm[i] * Vdir[j] + Svnorm[j] * Vnorm[k] * Vdir[i] + Svnorm[k] * Vnorm[j] * Vdir[i])) * (-Svnorm[l]);
 
    
    return  0.125/(std::numbers::pi*(1.0-this->nu))*(psi_val
                                                     -2.0*this->nu*delta(k,l)*PHI(i,j)
                                                     -(1.0-this->nu)*(PHI(i,l)*delta(j,k)
                                                                      +PHI(j,k)*delta(i,l)
                                                                      +PHI(j,l)*delta(i,k)
                                                                      +PHI(i,k)*delta(j,l)));
}
 
    template <int dim>
    typename PolyhedronInclusion<dim>::MatrixVoigtSize PolyhedronInclusion<dim>::eshelbyTensorVoigt(const VectorDim& x) const
    {
        Eigen::Matrix<double,voigtSize,voigtSize> temp(Eigen::Matrix<double,voigtSize,voigtSize>::Zero());
        Psi_I1 psi;
 
        for(const auto& face : faces)
        {
            const auto& P0(face.second[0].second);
            const auto& P1(face.second[1].second);
            const auto& P2(face.second[2].second);
            const VectorDim Svnorm((P1-P0).cross(P2-P1).normalized());
            const double a(Svnorm.dot(P0-x));
            for(size_t e=0;e<face.second.size();++e)
            {
                const size_t e1(e<face.second.size()-1? e+1 : 0);
                const VectorDim& vm(face.second[e].second);
                const VectorDim& vp(face.second[e1].second);
                const VectorDim Vdir((vp-vm).normalized());
                const VectorDim Vnorm(Vdir.cross(Svnorm));
                const double b((vp-x).dot(Vnorm));
                const double lm((vm-x).dot(Vdir));
                const double lp((vp-x).dot(Vdir));
                
                psi.I1_a_a_a=Psi_I1_a_a_a(a, b, lp) - Psi_I1_a_a_a(a, b, lm);
                psi.I1_b_b_b=Psi_I1_b_b_b(a, b, lp) - Psi_I1_b_b_b(a, b, lm);
                psi.I1_le_le_le=Psi_I1_le_le_le(a, b, lp) - Psi_I1_le_le_le(a, b, lm);
                psi.I1_a_a_b=Psi_I1_a_a_b(a, b, lp) - Psi_I1_a_a_b(a, b, lm);
                psi.I1_a_a_le=Psi_I1_a_a_le(a, b, lp) - Psi_I1_a_a_le(a, b, lm);
                psi.I1_a_b_b=Psi_I1_a_b_b(a, b, lp) - Psi_I1_a_b_b(a, b, lm);
                psi.I1_b_b_le=Psi_I1_b_b_le(a, b, lp) - Psi_I1_b_b_le(a, b, lm);
                psi.I1_a_le_le=Psi_I1_a_le_le(a, b, lp) - Psi_I1_a_le_le(a, b, lm);
                psi.I1_b_le_le=Psi_I1_b_le_le(a, b, lp) - Psi_I1_b_le_le(a, b, lm);
                psi.I1_a_b_le=Psi_I1_a_b_le(a, b, lp) - Psi_I1_a_b_le(a, b, lm);
                
                const VectorDim PHI_j(-(Phi_u_II_a(a, b, lp) - Phi_u_II_a(a, b, lm))*Svnorm
                                      -(Phi_u_II_b(a, b, lp) - Phi_u_II_b(a, b, lm))*Vnorm
                                      -(Phi_u_II_le(a, b, lp))*Vdir + (Phi_u_II_le(a, b, lm))*Vdir);
                const MatrixDim PHI(-Svnorm*PHI_j.transpose());
                
                
                for(int iV=0;iV<voigtTraits.voigtSize;++iV)
                {
                    const size_t i(voigtTraits.tensorIndex(iV,0));
                    const size_t j(voigtTraits.tensorIndex(iV,1));
 
                    for(int jV=0;jV<voigtTraits.voigtSize;++jV)
                    {
                        const size_t k(voigtTraits.tensorIndex(jV,0));
                        const size_t l(voigtTraits.tensorIndex(jV,1));
                        temp(iV,jV)+=eshelbyTensorComponent(i,j,k,l,PHI,delta,psi,Svnorm,Vnorm,Vdir);
                    }
                }
                
            }
        }
        
        // 11 22 33 12 23 13 -> 00 11 22 01 12 02
        
        
        // 0000, 0011, 0022, 0001, 0012, 0002
        // 1100, 1111, 1122, 1101, 1112, 1102
        
        
//        temp(voigtTraits.voigtIndex(0,0),voigtTraits.voigtIndex(0,0))=eshelbyTensorComponent(0,0,0,0,x);
//        temp(voigtTraits.voigtIndex(0,0),voigtTraits.voigtIndex(1,1))=eshelbyTensorComponent(0,0,1,1,x);
//        temp(voigtTraits.voigtIndex(0,0),voigtTraits.voigtIndex(2,2))=eshelbyTensorComponent(0,0,2,2,x);
//        temp(voigtTraits.voigtIndex(0,0),voigtTraits.voigtIndex(0,1))=eshelbyTensorComponent(0,0,0,1,x);
//        temp(voigtTraits.voigtIndex(0,0),voigtTraits.voigtIndex(1,2))=eshelbyTensorComponent(0,0,1,2,x);
//        temp(voigtTraits.voigtIndex(0,0),voigtTraits.voigtIndex(2,0))=eshelbyTensorComponent(0,0,2,0,x);
//
//        temp(voigtTraits.voigtIndex(1,1),voigtTraits.voigtIndex(0,0))=eshelbyTensorComponent(1,1,0,0,x);
//        temp(voigtTraits.voigtIndex(1,1),voigtTraits.voigtIndex(1,1))=eshelbyTensorComponent(1,1,1,1,x);
//        temp(voigtTraits.voigtIndex(1,1),voigtTraits.voigtIndex(2,2))=eshelbyTensorComponent(1,1,2,2,x);
//        temp(voigtTraits.voigtIndex(1,1),voigtTraits.voigtIndex(1,2))=eshelbyTensorComponent(1,1,1,2,x);
//        temp(voigtTraits.voigtIndex(1,1),voigtTraits.voigtIndex(2,0))=eshelbyTensorComponent(1,1,2,0,x);
//        temp(voigtTraits.voigtIndex(1,1),voigtTraits.voigtIndex(0,1))=eshelbyTensorComponent(1,1,0,1,x);
//
//        temp(voigtTraits.voigtIndex(2,2),voigtTraits.voigtIndex(0,0))=eshelbyTensorComponent(2,2,0,0,x);
//        temp(voigtTraits.voigtIndex(2,2),voigtTraits.voigtIndex(1,1))=eshelbyTensorComponent(2,2,1,1,x);
//        temp(voigtTraits.voigtIndex(2,2),voigtTraits.voigtIndex(2,2))=eshelbyTensorComponent(2,2,2,2,x);
//        temp(voigtTraits.voigtIndex(2,2),voigtTraits.voigtIndex(1,2))=eshelbyTensorComponent(2,2,1,2,x);
//        temp(voigtTraits.voigtIndex(2,2),voigtTraits.voigtIndex(2,0))=eshelbyTensorComponent(2,2,2,0,x);
//        temp(voigtTraits.voigtIndex(2,2),voigtTraits.voigtIndex(0,1))=eshelbyTensorComponent(2,2,0,1,x);
//
//        temp(voigtTraits.voigtIndex(0,1),voigtTraits.voigtIndex(0,1))=2.0*eshelbyTensorComponent(0,1,0,1,x);
//        temp(voigtTraits.voigtIndex(0,1),voigtTraits.voigtIndex(0,0))=2.0*eshelbyTensorComponent(0,1,0,0,x);
//        temp(voigtTraits.voigtIndex(0,1),voigtTraits.voigtIndex(1,1))=2.0*eshelbyTensorComponent(0,1,1,1,x);
//        temp(voigtTraits.voigtIndex(0,1),voigtTraits.voigtIndex(2,2))=2.0*eshelbyTensorComponent(0,1,2,2,x);
//        temp(voigtTraits.voigtIndex(0,1),voigtTraits.voigtIndex(1,2))=2.0*eshelbyTensorComponent(0,1,1,2,x);
//        temp(voigtTraits.voigtIndex(0,1),voigtTraits.voigtIndex(2,0))=2.0*eshelbyTensorComponent(0,1,2,0,x);
//
//        temp(voigtTraits.voigtIndex(2,0),voigtTraits.voigtIndex(2,0))=2.0*eshelbyTensorComponent(2,0,2,0,x);
//        temp(voigtTraits.voigtIndex(2,0),voigtTraits.voigtIndex(0,0))=2.0*eshelbyTensorComponent(2,0,0,0,x);
//        temp(voigtTraits.voigtIndex(2,0),voigtTraits.voigtIndex(1,1))=2.0*eshelbyTensorComponent(2,0,1,1,x);
//        temp(voigtTraits.voigtIndex(2,0),voigtTraits.voigtIndex(2,2))=2.0*eshelbyTensorComponent(2,0,2,2,x);
//        temp(voigtTraits.voigtIndex(2,0),voigtTraits.voigtIndex(1,2))=2.0*eshelbyTensorComponent(2,0,1,2,x);
//        temp(voigtTraits.voigtIndex(2,0),voigtTraits.voigtIndex(0,1))=2.0*eshelbyTensorComponent(2,0,0,1,x);
//
//        temp(voigtTraits.voigtIndex(1,2),voigtTraits.voigtIndex(1,2))=2.0*eshelbyTensorComponent(1,2,1,2,x);
//        temp(voigtTraits.voigtIndex(1,2),voigtTraits.voigtIndex(0,0))=2.0*eshelbyTensorComponent(1,2,0,0,x);
//        temp(voigtTraits.voigtIndex(1,2),voigtTraits.voigtIndex(1,1))=2.0*eshelbyTensorComponent(1,2,1,1,x);
//        temp(voigtTraits.voigtIndex(1,2),voigtTraits.voigtIndex(2,2))=2.0*eshelbyTensorComponent(1,2,2,2,x);
//        temp(voigtTraits.voigtIndex(1,2),voigtTraits.voigtIndex(2,0))=2.0*eshelbyTensorComponent(1,2,2,0,x);
//        temp(voigtTraits.voigtIndex(1,2),voigtTraits.voigtIndex(0,1))=2.0*eshelbyTensorComponent(1,2,0,1,x);
        
        
        return temp;
    }
 
 
    template <int dim>
    typename PolyhedronInclusion<dim>::MatrixDim PolyhedronInclusion<dim>::strain(const VectorDim& x) const
    {
        return this->eTNorm>FLT_EPSILON? voigtTraits.v2m(eshelbyTensorVoigt(x)*voigtTraits.m2v(this->eT,true),true) : MatrixDim::Zero();
    }
 
    template <int dim>
    typename PolyhedronInclusion<dim>::MatrixDim PolyhedronInclusion<dim>::elasticStrain(const VectorDim& x) const
    {
        if(contains(x))
        {
            return strain(x)-this->eT;
        }
        else
        {
            return strain(x);
        }
    }
 
    template <int dim>
    typename PolyhedronInclusion<dim>::MatrixDim PolyhedronInclusion<dim>::stress(const VectorDim& x) const
    {
        const MatrixDim elStrain(elasticStrain(x));
        return this->lambda*elStrain.trace()*MatrixDim::Identity()+2.0*this->mu*elStrain;
    }
 
    template <int dim>
    const SymmetricVoigtTraits<dim> PolyhedronInclusion<dim>::voigtTraits=SymmetricVoigtTraits<dim>((typename SymmetricVoigtTraits<dim>::VoigtSizeMatrixType()<<0,0,1,1,2,2,1,2,0,2,0,1).finished());
    //const typename PolyhedronInclusion<dim>::VoigtSizeMatrixType PolyhedronInclusion<dim>::voigtOrder=(PolyhedronInclusion<dim>::VoigtSizeMatrixType()<<0,0,0,1,0,2,1,1,1,2,2,2).finished();
 
    template class PolyhedronInclusion<3>;
 
}
#endif