GenericElastic.cpp

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#include "GenericElastic.hpp"
 
#include <polyfem/assembler/MooneyRivlinElasticity.hpp>
#include <polyfem/assembler/MooneyRivlin3ParamElasticity.hpp>
#include <polyfem/assembler/IsochoricNeoHookean.hpp>
#include <polyfem/assembler/OgdenElasticity.hpp>
#include <polyfem/assembler/NeoHookeanElasticityAutodiff.hpp>
#include <polyfem/assembler/VolumePenalty.hpp>
#include <polyfem/assembler/AMIPSEnergy.hpp>
 
#include <polyfem/assembler/HGOFiber.hpp>
#include <polyfem/assembler/ActiveFiber.hpp>
#include <polyfem/assembler/HGODispersion.hpp>
 
#include <polyfem/utils/Logger.hpp>
 
namespace polyfem::assembler
{
 
    template <typename Derived>
    template <int dim>
    Eigen::Matrix<double, dim * dim, dim> GenericElastic<Derived>::compute_B_block(const Eigen::Matrix<double, 1, dim> &g) const
    {
        Eigen::Matrix<double, dim * dim, dim> B(size() * size(), size());
        B.setZero();
 
        for (int i = 0; i < dim; ++i)     // displacement component
            for (int j = 0; j < dim; ++j) // gradient direction
                B(i * dim + j, i) = g(j);
 
        return B;
    }
 
    template <typename Derived>
    GenericElastic<Derived>::GenericElastic()
    {
    }
 
    template <typename Derived>
    void GenericElastic<Derived>::assign_stress_tensor(
        const OutputData &data,
        const int all_size,
        const ElasticityTensorType &type,
        Eigen::MatrixXd &all,
        const std::function<Eigen::MatrixXd(const Eigen::MatrixXd &)> &fun) const
    {
        Eigen::MatrixXd deformation_grad(size(), size());
        Eigen::MatrixXd stress_tensor(size(), size());
 
        typedef DScalar1<double, Eigen::Matrix<double, Eigen::Dynamic, 1, 0, 9, 1>> Diff;
 
        const auto &displacement = data.fun;
        const auto &local_pts = data.local_pts;
        const auto &bs = data.bs;
        const auto &gbs = data.gbs;
        const auto el_id = data.el_id;
 
        assert(displacement.cols() == 1);
 
        all.resize(local_pts.rows(), all_size);
        DiffScalarBase::setVariableCount(deformation_grad.size());
 
        Eigen::Matrix<Diff, Eigen::Dynamic, Eigen::Dynamic, 0, 3, 3> def_grad(size(), size());
 
        ElementAssemblyValues vals;
        vals.compute(el_id, size() == 3, local_pts, bs, gbs);
 
        for (long p = 0; p < local_pts.rows(); ++p)
        {
            compute_diplacement_grad(size(), bs, vals, local_pts, p, displacement, deformation_grad);
 
            // Id + grad d
            for (int d = 0; d < size(); ++d)
                deformation_grad(d, d) += 1;
 
            if (type == ElasticityTensorType::F)
            {
                all.row(p) = fun(deformation_grad);
                continue;
            }
 
            for (int d1 = 0; d1 < size(); ++d1)
            {
                for (int d2 = 0; d2 < size(); ++d2)
                    def_grad(d1, d2) = Diff(d1 * size() + d2, deformation_grad(d1, d2));
            }
 
            const auto val = derived().elastic_energy(local_pts.row(p), data.t, vals.element_id, def_grad);
 
            for (int d1 = 0; d1 < size(); ++d1)
            {
                for (int d2 = 0; d2 < size(); ++d2)
                    stress_tensor(d1, d2) = val.getGradient()(d1 * size() + d2);
            }
 
            stress_tensor = 1.0 / deformation_grad.determinant() * stress_tensor * deformation_grad.transpose();
 
            if (type == ElasticityTensorType::PK1)
                stress_tensor = pk1_from_cauchy(stress_tensor, deformation_grad);
            else if (type == ElasticityTensorType::PK2)
                stress_tensor = pk2_from_cauchy(stress_tensor, deformation_grad);
 
            all.row(p) = fun(stress_tensor);
        }
    }
 
    template <typename Derived>
    double GenericElastic<Derived>::compute_energy(const NonLinearAssemblerData &data) const
    {
        return compute_energy_aux<double>(data);
    }
 
    template <typename Derived>
    Eigen::VectorXd GenericElastic<Derived>::assemble_gradient(const NonLinearAssemblerData &data) const
    {
        if (autodiff_type_ == AutodiffType::FULL)
            return assemble_gradient_full_ad(data);
        else if (autodiff_type_ == AutodiffType::STRESS)
        {
#ifndef NDEBUG
            auto grad = assemble_gradient_stress_ad(data);
            auto grad_full = assemble_gradient_full_ad(data);
            assert((std::isnan(grad.norm()) && std::isnan(grad_full.norm())) || (grad - grad_full).norm() < 1e-6);
#endif
            return assemble_gradient_stress_ad(data);
        }
        else
        {
#ifndef NDEBUG
            auto grad = assemble_gradient_stress_noad(data);
            auto grad_full = assemble_gradient_stress_ad(data);
            assert((std::isnan(grad.norm()) && std::isnan(grad_full.norm())) || (grad - grad_full).norm() < 1e-6);
#endif
            return assemble_gradient_stress_noad(data);
        }
    }
 
    template <typename Derived>
    Eigen::VectorXd GenericElastic<Derived>::assemble_gradient_full_ad(const NonLinearAssemblerData &data) const
    {
        const int n_bases = data.vals.basis_values.size();
        return polyfem::gradient_from_energy(
            size(), n_bases, data,
            [&](const NonLinearAssemblerData &data) { return compute_energy_aux<DScalar1<double, Eigen::Matrix<double, 6, 1>>>(data); },
            [&](const NonLinearAssemblerData &data) { return compute_energy_aux<DScalar1<double, Eigen::Matrix<double, 8, 1>>>(data); },
            [&](const NonLinearAssemblerData &data) { return compute_energy_aux<DScalar1<double, Eigen::Matrix<double, 12, 1>>>(data); },
            [&](const NonLinearAssemblerData &data) { return compute_energy_aux<DScalar1<double, Eigen::Matrix<double, 18, 1>>>(data); },
            [&](const NonLinearAssemblerData &data) { return compute_energy_aux<DScalar1<double, Eigen::Matrix<double, 24, 1>>>(data); },
            [&](const NonLinearAssemblerData &data) { return compute_energy_aux<DScalar1<double, Eigen::Matrix<double, 30, 1>>>(data); },
            [&](const NonLinearAssemblerData &data) { return compute_energy_aux<DScalar1<double, Eigen::Matrix<double, 60, 1>>>(data); },
            [&](const NonLinearAssemblerData &data) { return compute_energy_aux<DScalar1<double, Eigen::Matrix<double, 81, 1>>>(data); },
            [&](const NonLinearAssemblerData &data) { return compute_energy_aux<DScalar1<double, Eigen::Matrix<double, Eigen::Dynamic, 1, 0, SMALL_N, 1>>>(data); },
            [&](const NonLinearAssemblerData &data) { return compute_energy_aux<DScalar1<double, Eigen::Matrix<double, Eigen::Dynamic, 1, 0, BIG_N, 1>>>(data); },
            [&](const NonLinearAssemblerData &data) { return compute_energy_aux<DScalar1<double, Eigen::VectorXd>>(data); });
    }
 
    template <typename Derived>
    Eigen::VectorXd GenericElastic<Derived>::assemble_gradient_stress_ad(const NonLinearAssemblerData &data) const
    {
        Eigen::Matrix<double, Eigen::Dynamic, 1> gradient;
 
        if (size() == 2)
        {
            switch (data.vals.basis_values.size())
            {
            case 3:
            {
                gradient.resize(6);
                compute_gradient_from_stress<3, 2>(data, gradient);
                break;
            }
            case 6:
            {
                gradient.resize(12);
                compute_gradient_from_stress<6, 2>(data, gradient);
                break;
            }
            case 10:
            {
                gradient.resize(20);
                compute_gradient_from_stress<10, 2>(data, gradient);
                break;
            }
            default:
            {
                gradient.resize(data.vals.basis_values.size() * 2);
                compute_gradient_from_stress<Eigen::Dynamic, 2>(data, gradient);
                break;
            }
            }
        }
        else // if (size() == 3)
        {
            assert(size() == 3);
            switch (data.vals.basis_values.size())
            {
            case 4:
            {
                gradient.resize(12);
                compute_gradient_from_stress<4, 3>(data, gradient);
                break;
            }
            case 10:
            {
                gradient.resize(30);
                compute_gradient_from_stress<10, 3>(data, gradient);
                break;
            }
            case 20:
            {
                gradient.resize(60);
                compute_gradient_from_stress<20, 3>(data, gradient);
                break;
            }
            default:
            {
                gradient.resize(data.vals.basis_values.size() * 3);
                compute_gradient_from_stress<Eigen::Dynamic, 3>(data, gradient);
                break;
            }
            }
        }
 
        return gradient;
    }
 
    template <typename Derived>
    Eigen::VectorXd GenericElastic<Derived>::assemble_gradient_stress_noad(const NonLinearAssemblerData &data) const
    {
        Eigen::Matrix<double, Eigen::Dynamic, 1> gradient;
 
        if (size() == 2)
        {
            switch (data.vals.basis_values.size())
            {
            case 3:
            {
                gradient.resize(6);
                compute_gradient_from_stress_noad<3, 2>(data, gradient);
                break;
            }
            case 6:
            {
                gradient.resize(12);
                compute_gradient_from_stress_noad<6, 2>(data, gradient);
                break;
            }
            case 10:
            {
                gradient.resize(20);
                compute_gradient_from_stress_noad<10, 2>(data, gradient);
                break;
            }
            default:
            {
                gradient.resize(data.vals.basis_values.size() * 2);
                compute_gradient_from_stress_noad<Eigen::Dynamic, 2>(data, gradient);
                break;
            }
            }
        }
        else // if (size() == 3)
        {
            assert(size() == 3);
            switch (data.vals.basis_values.size())
            {
            case 4:
            {
                gradient.resize(12);
                compute_gradient_from_stress_noad<4, 3>(data, gradient);
                break;
            }
            case 10:
            {
                gradient.resize(30);
                compute_gradient_from_stress_noad<10, 3>(data, gradient);
                break;
            }
            case 20:
            {
                gradient.resize(60);
                compute_gradient_from_stress_noad<20, 3>(data, gradient);
                break;
            }
            default:
            {
                gradient.resize(data.vals.basis_values.size() * 3);
                compute_gradient_from_stress_noad<Eigen::Dynamic, 3>(data, gradient);
                break;
            }
            }
        }
 
        return gradient;
    }
 
    template <typename Derived>
    Eigen::MatrixXd GenericElastic<Derived>::assemble_hessian(const NonLinearAssemblerData &data) const
    {
        if (autodiff_type_ == AutodiffType::FULL)
            return assemble_hessian_full_ad(data);
        else if (autodiff_type_ == AutodiffType::STRESS)
        {
#ifndef NDEBUG
            auto hessian = assemble_hessian_stress_ad(data);
            auto hessian_full = assemble_hessian_full_ad(data);
            assert((std::isnan(hessian.norm()) && std::isnan(hessian_full.norm())) || (hessian - hessian_full).norm() < 1e-5);
#endif
            return assemble_hessian_stress_ad(data);
        }
        else
        {
#ifndef NDEBUG
            auto hessian = assemble_hessian_stress_noad(data);
            auto hessian_full = assemble_hessian_stress_ad(data);
            assert((std::isnan(hessian.norm()) && std::isnan(hessian_full.norm())) || (hessian - hessian_full).norm() < 1e-5);
#endif
            return assemble_hessian_stress_noad(data);
        }
    }
 
    template <typename Derived>
    Eigen::MatrixXd GenericElastic<Derived>::assemble_hessian_full_ad(const NonLinearAssemblerData &data) const
    {
        const int n_bases = data.vals.basis_values.size();
        return polyfem::hessian_from_energy(
            size(), n_bases, data,
            [&](const NonLinearAssemblerData &data) { return compute_energy_aux<DScalar2<double, Eigen::Matrix<double, 6, 1>, Eigen::Matrix<double, 6, 6>>>(data); },
            [&](const NonLinearAssemblerData &data) { return compute_energy_aux<DScalar2<double, Eigen::Matrix<double, 8, 1>, Eigen::Matrix<double, 8, 8>>>(data); },
            [&](const NonLinearAssemblerData &data) { return compute_energy_aux<DScalar2<double, Eigen::Matrix<double, 12, 1>, Eigen::Matrix<double, 12, 12>>>(data); },
            [&](const NonLinearAssemblerData &data) { return compute_energy_aux<DScalar2<double, Eigen::Matrix<double, 18, 1>, Eigen::Matrix<double, 18, 18>>>(data); },
            [&](const NonLinearAssemblerData &data) { return compute_energy_aux<DScalar2<double, Eigen::Matrix<double, 24, 1>, Eigen::Matrix<double, 24, 24>>>(data); },
            [&](const NonLinearAssemblerData &data) { return compute_energy_aux<DScalar2<double, Eigen::Matrix<double, 30, 1>, Eigen::Matrix<double, 30, 30>>>(data); },
            [&](const NonLinearAssemblerData &data) { return compute_energy_aux<DScalar2<double, Eigen::Matrix<double, 60, 1>, Eigen::Matrix<double, 60, 60>>>(data); },
            [&](const NonLinearAssemblerData &data) { return compute_energy_aux<DScalar2<double, Eigen::Matrix<double, 81, 1>, Eigen::Matrix<double, 81, 81>>>(data); },
            [&](const NonLinearAssemblerData &data) { return compute_energy_aux<DScalar2<double, Eigen::Matrix<double, Eigen::Dynamic, 1, 0, SMALL_N, 1>, Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic, 0, SMALL_N, SMALL_N>>>(data); },
            [&](const NonLinearAssemblerData &data) { return compute_energy_aux<DScalar2<double, Eigen::VectorXd, Eigen::MatrixXd>>(data); });
    }
 
    template <typename Derived>
    Eigen::MatrixXd GenericElastic<Derived>::assemble_hessian_stress_ad(const NonLinearAssemblerData &data) const
    {
        Eigen::MatrixXd hessian;
 
        if (size() == 2)
        {
            switch (data.vals.basis_values.size())
            {
            case 3:
            {
                hessian.resize(6, 6);
                hessian.setZero();
                compute_hessian_from_stress<3, 2>(data, hessian);
                break;
            }
            case 6:
            {
                hessian.resize(12, 12);
                hessian.setZero();
                compute_hessian_from_stress<6, 2>(data, hessian);
                break;
            }
            case 10:
            {
                hessian.resize(20, 20);
                hessian.setZero();
                compute_hessian_from_stress<10, 2>(data, hessian);
                break;
            }
            default:
            {
                hessian.resize(data.vals.basis_values.size() * 2, data.vals.basis_values.size() * 2);
                hessian.setZero();
                compute_hessian_from_stress<Eigen::Dynamic, 2>(data, hessian);
                break;
            }
            }
        }
        else // if (size() == 3)
        {
            assert(size() == 3);
            switch (data.vals.basis_values.size())
            {
            case 4:
            {
                hessian.resize(12, 12);
                hessian.setZero();
                compute_hessian_from_stress<4, 3>(data, hessian);
                break;
            }
            case 10:
            {
                hessian.resize(30, 30);
                hessian.setZero();
                compute_hessian_from_stress<10, 3>(data, hessian);
                break;
            }
            case 20:
            {
                hessian.resize(60, 60);
                hessian.setZero();
                compute_hessian_from_stress<20, 3>(data, hessian);
                break;
            }
            default:
            {
                hessian.resize(data.vals.basis_values.size() * 3, data.vals.basis_values.size() * 3);
                hessian.setZero();
                compute_hessian_from_stress<Eigen::Dynamic, 3>(data, hessian);
                break;
            }
            }
        }
 
        return hessian;
    }
 
    template <typename Derived>
    Eigen::MatrixXd GenericElastic<Derived>::assemble_hessian_stress_noad(const NonLinearAssemblerData &data) const
    {
        Eigen::MatrixXd hessian;
 
        if (size() == 2)
        {
            switch (data.vals.basis_values.size())
            {
            case 3:
            {
                hessian.resize(6, 6);
                hessian.setZero();
                compute_hessian_from_stress_noad<3, 2>(data, hessian);
                break;
            }
            case 6:
            {
                hessian.resize(12, 12);
                hessian.setZero();
                compute_hessian_from_stress_noad<6, 2>(data, hessian);
                break;
            }
            case 10:
            {
                hessian.resize(20, 20);
                hessian.setZero();
                compute_hessian_from_stress_noad<10, 2>(data, hessian);
                break;
            }
            default:
            {
                hessian.resize(data.vals.basis_values.size() * 2, data.vals.basis_values.size() * 2);
                hessian.setZero();
                compute_hessian_from_stress_noad<Eigen::Dynamic, 2>(data, hessian);
                break;
            }
            }
        }
        else // if (size() == 3)
        {
            assert(size() == 3);
            switch (data.vals.basis_values.size())
            {
            case 4:
            {
                hessian.resize(12, 12);
                hessian.setZero();
                compute_hessian_from_stress_noad<4, 3>(data, hessian);
                break;
            }
            case 10:
            {
                hessian.resize(30, 30);
                hessian.setZero();
                compute_hessian_from_stress_noad<10, 3>(data, hessian);
                break;
            }
            case 20:
            {
                hessian.resize(60, 60);
                hessian.setZero();
                compute_hessian_from_stress_noad<20, 3>(data, hessian);
                break;
            }
            default:
            {
                hessian.resize(data.vals.basis_values.size() * 3, data.vals.basis_values.size() * 3);
                hessian.setZero();
                compute_hessian_from_stress_noad<Eigen::Dynamic, 3>(data, hessian);
                break;
            }
            }
        }
 
        return hessian;
    }
 
    template <typename Derived>
    void GenericElastic<Derived>::compute_stress_grad_multiply_mat(
        const OptAssemblerData &data,
        const Eigen::MatrixXd &mat,
        Eigen::MatrixXd &stress,
        Eigen::MatrixXd &result) const
    {
        typedef DScalar2<double, Eigen::Matrix<double, Eigen::Dynamic, 1, 0, 9, 1>, Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic, 0, 9, 9>> Diff;
 
        const double t = data.t;
        const int el_id = data.el_id;
        const Eigen::MatrixXd &local_pts = data.local_pts;
        const Eigen::MatrixXd &global_pts = data.global_pts;
        const Eigen::MatrixXd &grad_u_i = data.grad_u_i;
 
        DiffScalarBase::setVariableCount(size() * size());
        Eigen::Matrix<Diff, Eigen::Dynamic, Eigen::Dynamic, 0, 3, 3> def_grad(size(), size());
 
        Eigen::MatrixXd F = grad_u_i;
        for (int d = 0; d < size(); ++d)
            F(d, d) += 1.;
 
        assert(local_pts.rows() == 1);
        for (int i = 0; i < size(); ++i)
            for (int j = 0; j < size(); ++j)
                def_grad(i, j) = Diff(i + j * size(), F(i, j));
 
        auto energy = derived().elastic_energy(global_pts, t, el_id, def_grad);
 
        // Grad is ∂W(F)/∂F_ij
        Eigen::MatrixXd grad = energy.getGradient().reshaped(size(), size());
        // Hessian is ∂W(F)/(∂F_ij*∂F_kl)
        Eigen::MatrixXd hess = energy.getHessian();
 
        // Stress is S_ij = ∂W(F)/∂F_ij
        stress = grad;
        // Compute ∂S_ij/∂F_kl * M_kl, same as M_ij * ∂S_ij/∂F_kl since the hessian is symmetric
        result = (hess * mat.reshaped(size() * size(), 1)).reshaped(size(), size());
    }
 
    template <typename Derived>
    void GenericElastic<Derived>::compute_stress_grad_multiply_stress(
        const OptAssemblerData &data,
        Eigen::MatrixXd &stress,
        Eigen::MatrixXd &result) const
    {
        typedef DScalar2<double, Eigen::Matrix<double, Eigen::Dynamic, 1, 0, 9, 1>, Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic, 0, 9, 9>> Diff;
 
        const double t = data.t;
        const int el_id = data.el_id;
        const Eigen::MatrixXd &local_pts = data.local_pts;
        const Eigen::MatrixXd &global_pts = data.global_pts;
        const Eigen::MatrixXd &grad_u_i = data.grad_u_i;
 
        DiffScalarBase::setVariableCount(size() * size());
        Eigen::Matrix<Diff, Eigen::Dynamic, Eigen::Dynamic, 0, 3, 3> def_grad(size(), size());
 
        Eigen::MatrixXd F = grad_u_i;
        for (int d = 0; d < size(); ++d)
            F(d, d) += 1.;
 
        assert(local_pts.rows() == 1);
        for (int i = 0; i < size(); ++i)
            for (int j = 0; j < size(); ++j)
                def_grad(i, j) = Diff(i + j * size(), F(i, j));
 
        auto energy = derived().elastic_energy(global_pts, t, el_id, def_grad);
 
        // Grad is ∂W(F)/∂F_ij
        Eigen::MatrixXd grad = energy.getGradient().reshaped(size(), size());
        // Hessian is ∂W(F)/(∂F_ij*∂F_kl)
        Eigen::MatrixXd hess = energy.getHessian();
 
        // Stress is S_ij = ∂W(F)/∂F_ij
        stress = grad;
        // Compute ∂S_ij/∂F_kl * S_kl, same as S_ij * ∂S_ij/∂F_kl since the hessian is symmetric
        result = (hess * stress.reshaped(size() * size(), 1)).reshaped(size(), size());
    }
 
    template <typename Derived>
    void GenericElastic<Derived>::compute_stress_grad_multiply_vect(
        const OptAssemblerData &data,
        const Eigen::MatrixXd &vect,
        Eigen::MatrixXd &stress,
        Eigen::MatrixXd &result) const
    {
        typedef DScalar2<double, Eigen::Matrix<double, Eigen::Dynamic, 1, 0, 9, 1>, Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic, 0, 9, 9>> Diff;
 
        const double t = data.t;
        const int el_id = data.el_id;
        const Eigen::MatrixXd &local_pts = data.local_pts;
        const Eigen::MatrixXd &global_pts = data.global_pts;
        const Eigen::MatrixXd &grad_u_i = data.grad_u_i;
 
        DiffScalarBase::setVariableCount(size() * size());
        Eigen::Matrix<Diff, Eigen::Dynamic, Eigen::Dynamic, 0, 3, 3> def_grad(size(), size());
 
        Eigen::MatrixXd F = grad_u_i;
        for (int d = 0; d < size(); ++d)
            F(d, d) += 1.;
 
        assert(local_pts.rows() == 1);
        for (int i = 0; i < size(); ++i)
            for (int j = 0; j < size(); ++j)
                def_grad(i, j) = Diff(i + j * size(), F(i, j));
 
        auto energy = derived().elastic_energy(global_pts, t, el_id, def_grad);
 
        // Grad is ∂W(F)/∂F_ij
        Eigen::MatrixXd grad = energy.getGradient().reshaped(size(), size());
        // Hessian is ∂W(F)/(∂F_ij*∂F_kl)
        Eigen::MatrixXd hess = energy.getHessian();
 
        // Stress is S_ij = ∂W(F)/∂F_ij
        stress = grad;
        result.resize(hess.rows(), vect.size());
        for (int i = 0; i < hess.rows(); ++i)
            if (vect.rows() == 1)
                // Compute ∂S_ij/∂F_kl * v_k, same as ∂S_ij/∂F_kl * v_i since the hessian is symmetric
                result.row(i) = vect * hess.row(i).reshaped(size(), size());
            else
                // Compute ∂S_ij/∂F_kl * v_l, same as ∂S_ij/∂F_kl * v_j since the hessian is symmetric
                result.row(i) = (hess.row(i).reshaped(size(), size()) * vect).transpose();
    }
 
    template class GenericElastic<MooneyRivlinElasticity>;
    template class GenericElastic<MooneyRivlin3ParamElasticity>;
    template class GenericElastic<UnconstrainedOgdenElasticity>;
    template class GenericElastic<IncompressibleOgdenElasticity>;
    template class GenericElastic<NeoHookeanAutodiff>;
    template class GenericElastic<IsochoricNeoHookean>;
    template class GenericElastic<VolumePenalty>;
    template class GenericElastic<AMIPSEnergy>;
 
    template class GenericElastic<HGOFiber>;
    template class GenericElastic<ActiveFiber>;
    template class GenericElastic<HGODispersion>;
 
} // namespace polyfem::assembler