MatParams.cpp

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#include "MatParams.hpp"
 
#include <polyfem/utils/JSONUtils.hpp>
#include <polyfem/utils/Logger.hpp>
#include <iostream>
 
namespace polyfem::assembler
{
    namespace
    {
        double convert_to_lambda(const bool is_volume, const double E, const double nu)
        {
            if (is_volume)
                return (E * nu) / ((1.0 + nu) * (1.0 - 2.0 * nu));
 
            return (nu * E) / (1.0 - nu * nu);
        }
 
        double convert_to_mu(const double E, const double nu)
        {
            return E / (2.0 * (1.0 + nu));
        }
    } // namespace
 
    GenericMatParam::GenericMatParam(const std::string &param_name)
        : param_name_(param_name)
    {
    }
 
    void GenericMatParam::add_multimaterial(const int index, const json &params, const std::string &unit_type)
    {
        for (int i = param_.size(); i <= index; ++i)
        {
            param_.emplace_back();
            param_.back().set_unit_type(unit_type);
        }
 
        if (params.count(param_name_))
        {
            param_[index].init(params[param_name_]);
        }
    }
 
    double GenericMatParam::operator()(const RowVectorNd &p, double t, int index) const
    {
        const double x = p(0);
        const double y = p(1);
        const double z = p.size() == 3 ? p(2) : 0;
 
        return (*this)(x, y, z, t, index);
    }
 
    double GenericMatParam::operator()(double x, double y, double z, double t, int index) const
    {
        assert(param_.size() == 1 || index < param_.size());
 
        const auto &tmp_param = param_.size() == 1 ? param_[0] : param_[index];
 
        return tmp_param(x, y, z, t, index);
    }
 
    GenericMatParams::GenericMatParams(const std::string &param_name)
        : param_name_(param_name)
    {
    }
 
    void GenericMatParams::add_multimaterial(const int index, const json &params, const std::string &unit_type)
    {
        if (!params.contains(param_name_))
            return;
 
        std::vector<json> params_array = utils::json_as_array(params[param_name_]);
        assert(params_array.size() == params_.size() || params_.empty());
 
        if (params_.empty())
            for (int i = 0; i < params_array.size(); ++i)
                params_.emplace_back(param_name_ + "_" + std::to_string(i));
 
        for (int i = 0; i < params_.size(); ++i)
        {
            for (int j = params_.at(i).param_.size(); j <= index; ++j)
            {
                params_.at(i).param_.emplace_back();
                params_.at(i).param_.back().set_unit_type(unit_type);
            }
 
            params_.at(i).param_[index].init(params_array[i]);
        }
    }
 
    void ElasticityTensor::resize(const int size)
    {
        if (size == 2)
            stiffness_tensor_.resize(3, 3);
        else
            stiffness_tensor_.resize(6, 6);
 
        stiffness_tensor_.setZero();
 
        size_ = size;
    }
 
    double ElasticityTensor::operator()(int i, int j) const
    {
        if (j < i)
        {
            std::swap(i, j);
        }
 
        assert(j >= i);
        return stiffness_tensor_(i, j);
    }
 
    double &ElasticityTensor::operator()(int i, int j)
    {
        if (j < i)
        {
            std::swap(i, j);
        }
 
        assert(j >= i);
        return stiffness_tensor_(i, j);
    }
 
    void ElasticityTensor::set_from_entries(const std::vector<double> &entries, const std::string &stress_units)
    {
        if (size_ == 2)
        {
            if (entries.size() == 4)
            {
                set_orthotropic(
                    entries[0],
                    entries[1],
                    entries[2],
                    entries[3], stress_units);
 
                return;
            }
 
            assert(entries.size() >= 6);
 
            (*this)(0, 0) = entries[0];
            (*this)(0, 1) = entries[1];
            (*this)(0, 2) = entries[2];
 
            (*this)(1, 1) = entries[3];
            (*this)(1, 2) = entries[4];
 
            (*this)(2, 2) = entries[5];
        }
        else
        {
            if (entries.size() == 5)
            {
                set_transversely_isotropic(
                    entries[0],
                    entries[1],
                    entries[2],
                    entries[3],
                    entries[4],
                    stress_units);
 
                return;
            }
            else if (entries.size() == 9)
            {
                set_orthotropic(
                    entries[0],
                    entries[1],
                    entries[2],
                    entries[3],
                    entries[4],
                    entries[5],
                    entries[6],
                    entries[7],
                    entries[8], stress_units);
 
                return;
            }
            assert(entries.size() >= 21);
 
            (*this)(0, 0) = entries[0];
            (*this)(0, 1) = entries[1];
            (*this)(0, 2) = entries[2];
            (*this)(0, 3) = entries[3];
            (*this)(0, 4) = entries[4];
            (*this)(0, 5) = entries[5];
 
            (*this)(1, 1) = entries[6];
            (*this)(1, 2) = entries[7];
            (*this)(1, 3) = entries[8];
            (*this)(1, 4) = entries[9];
            (*this)(1, 5) = entries[10];
 
            (*this)(2, 2) = entries[11];
            (*this)(2, 3) = entries[12];
            (*this)(2, 4) = entries[13];
            (*this)(2, 5) = entries[14];
 
            (*this)(3, 3) = entries[15];
            (*this)(3, 4) = entries[16];
            (*this)(3, 5) = entries[17];
 
            (*this)(4, 4) = entries[18];
            (*this)(4, 5) = entries[19];
 
            (*this)(5, 5) = entries[20];
        }
    }
 
    void ElasticityTensor::set_from_lambda_mu(const double lambda, const double mu, const std::string &stress_units)
    {
        if (size_ == 2)
        {
            (*this)(0, 0) = 2 * mu + lambda;
            (*this)(0, 1) = lambda;
            (*this)(0, 2) = 0;
 
            (*this)(1, 1) = 2 * mu + lambda;
            (*this)(1, 2) = 0;
 
            (*this)(2, 2) = mu;
        }
        else
        {
            (*this)(0, 0) = 2 * mu + lambda;
            (*this)(0, 1) = lambda;
            (*this)(0, 2) = lambda;
            (*this)(0, 3) = 0;
            (*this)(0, 4) = 0;
            (*this)(0, 5) = 0;
 
            (*this)(1, 1) = 2 * mu + lambda;
            (*this)(1, 2) = lambda;
            (*this)(1, 3) = 0;
            (*this)(1, 4) = 0;
            (*this)(1, 5) = 0;
 
            (*this)(2, 2) = 2 * mu + lambda;
            (*this)(2, 3) = 0;
            (*this)(2, 4) = 0;
            (*this)(2, 5) = 0;
 
            (*this)(3, 3) = mu;
            (*this)(3, 4) = 0;
            (*this)(3, 5) = 0;
 
            (*this)(4, 4) = mu;
            (*this)(4, 5) = 0;
 
            (*this)(5, 5) = mu;
        }
    }
 
    void ElasticityTensor::set_from_young_poisson(const double young, const double nu, const std::string &stress_units)
    {
        if (size_ == 2)
        {
            stiffness_tensor_ << 1.0, nu, 0.0,
                nu, 1.0, 0.0,
                0.0, 0.0, (1.0 - nu) / 2.0;
            stiffness_tensor_ *= young / (1.0 - nu * nu);
        }
        else
        {
            assert(size_ == 3);
            const double v = nu;
            stiffness_tensor_ << 1. - v, v, v, 0, 0, 0,
                v, 1. - v, v, 0, 0, 0,
                v, v, 1. - v, 0, 0, 0,
                0, 0, 0, (1. - 2. * v) / 2., 0, 0,
                0, 0, 0, 0, (1. - 2. * v) / 2., 0,
                0, 0, 0, 0, 0, (1. - 2. * v) / 2.;
            stiffness_tensor_ *= young / ((1. + v) * (1. - 2. * v));
        }
    }
 
    void ElasticityTensor::set_orthotropic(
        double Ex, double Ey, double Ez,
        double nuXY, double nuXZ, double nuYZ,
        double muYZ, double muZX, double muXY, const std::string &stress_units)
    {
        assert(size_ == 3);
 
        // from https://www.efunda.com/formulae/solid_mechanics/mat_mechanics/hooke_orthotropic.cfm
        double nuYX = nuXY * Ey / Ex;
        double nuZX = nuXZ * Ez / Ex;
        double nuZY = nuYZ * Ez / Ey;
 
        Eigen::MatrixXd compliance;
        compliance.setZero(6, 6);
        compliance << 1 / Ex, -nuYX / Ey, -nuZX / Ez, 0, 0, 0,
            -nuXY / Ex, 1 / Ey, -nuZY / Ez, 0, 0, 0,
            -nuXZ / Ex, -nuYZ / Ey, 1 / Ez, 0, 0, 0,
            0, 0, 0, 1 / (2 * muYZ), 0, 0,
            0, 0, 0, 0, 1 / (2 * muZX), 0,
            0, 0, 0, 0, 0, 1 / (2 * muXY);
        stiffness_tensor_ = compliance.inverse();
    }
 
    void ElasticityTensor::set_orthotropic(double Ex, double Ey, double nuXY, double muXY, const std::string &stress_units)
    {
        assert(size_ == 2);
 
        // from https://www.efunda.com/formulae/solid_mechanics/mat_mechanics/hooke_orthotropic.cfm
        double nuYX = nuXY * Ey / Ex;
 
        Eigen::MatrixXd compliance;
        compliance.setZero(3, 3);
        compliance << 1.0 / Ex, -nuYX / Ey, 0.0,
            -nuXY / Ex, 1.0 / Ey, 0.0,
            0.0, 0.0, 1.0 / (2 * muXY);
        stiffness_tensor_ = compliance.inverse();
    }
 
    void ElasticityTensor::set_transversely_isotropic(
        double Et, double Ea,
        double nu_t, double nu_a,
        double Ga, const std::string &stress_units)
    {
        assert(size_ == 3);
 
        // from https://osupdocs.forestry.oregonstate.edu/index.php/Transversely_Isotropic_Material
        Eigen::MatrixXd compliance;
        compliance.setZero(6, 6);
        compliance << 1 / Et, -nu_t / Et, -nu_a / Ea, 0, 0, 0,
            -nu_t / Et, 1 / Et, -nu_a / Ea, 0, 0, 0,
            -nu_a / Ea, -nu_a / Ea, 1 / Ea, 0, 0, 0,
            0, 0, 0, 1 / Ga, 0, 0,
            0, 0, 0, 0, 1 / Ga, 0,
            0, 0, 0, 0, 0, (2 * (1 + nu_t)) / Et;
        stiffness_tensor_ = compliance.inverse();
    }
 
    template <int DIM>
    double ElasticityTensor::compute_stress(const std::array<double, DIM> &strain, const int j) const
    {
        double res = 0;
 
        for (int k = 0; k < DIM; ++k)
            res += (*this)(j, k) * strain[k];
 
        return res;
    }
 
    void ElasticityTensor::rotate_stiffness(const Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic, 0, 6, 6> &rotation_mtx_voigt)
    {
        reference_stiffness_tensor_ = stiffness_tensor_;
        stiffness_tensor_ = rotation_mtx_voigt * stiffness_tensor_ * rotation_mtx_voigt.transpose();
    }
 
    void ElasticityTensor::unrotate_stiffness()
    {
        stiffness_tensor_ = reference_stiffness_tensor_;
    }
 
    LameParameters::LameParameters()
    {
        lambda_or_E_.emplace_back();
        lambda_or_E_.back().init(1.0);
 
        mu_or_nu_.emplace_back();
        mu_or_nu_.back().init(1.0);
        size_ = -1;
        is_lambda_mu_ = true;
    }
 
    void LameParameters::lambda_mu(double px, double py, double pz, double x, double y, double z, double t, int el_id, double &lambda, double &mu) const
    {
        assert(lambda_or_E_.size() == 1 || el_id < lambda_or_E_.size());
        assert(mu_or_nu_.size() == 1 || el_id < mu_or_nu_.size());
        assert(size_ == 2 || size_ == 3);
 
        const auto &tmp1 = lambda_or_E_.size() == 1 ? lambda_or_E_[0] : lambda_or_E_[el_id];
        const auto &tmp2 = mu_or_nu_.size() == 1 ? mu_or_nu_[0] : mu_or_nu_[el_id];
 
        double llambda = tmp1(x, y, z, t, el_id);
        double mmu = tmp2(x, y, z, t, el_id);
 
        if (!is_lambda_mu_)
        {
            lambda = convert_to_lambda(size_ == 3, llambda, mmu);
            mu = convert_to_mu(llambda, mmu);
        }
        else
        {
            lambda = llambda;
            mu = mmu;
        }
 
        if (lambda_mat_.size() > el_id && mu_mat_.size() > el_id)
        {
            lambda = lambda_mat_(el_id);
            mu = mu_mat_(el_id);
        }
 
        assert(!std::isnan(lambda));
        assert(!std::isnan(mu));
        assert(!std::isinf(lambda));
        assert(!std::isinf(mu));
    }
 
    void LameParameters::add_multimaterial(const int index, const json &params, const bool is_volume, const std::string &stress_unit)
    {
        const int size = is_volume ? 3 : 2;
        assert(size_ == -1 || size == size_);
        size_ = size;
 
        for (int i = lambda_or_E_.size(); i <= index; ++i)
        {
            lambda_or_E_.emplace_back();
            lambda_or_E_.back().set_unit_type(stress_unit);
            mu_or_nu_.emplace_back();
            mu_or_nu_.back().set_unit_type("");
        }
 
        if (params.count("young"))
        {
            set_e_nu(index, params["young"], params["nu"], stress_unit);
        }
        else if (params.count("E"))
        {
            set_e_nu(index, params["E"], params["nu"], stress_unit);
        }
        else if (params.count("lambda"))
        {
            lambda_or_E_[index].init(params["lambda"]);
            mu_or_nu_[index].init(params["mu"]);
 
            lambda_or_E_[index].set_unit_type(stress_unit);
            mu_or_nu_[index].set_unit_type(stress_unit);
            is_lambda_mu_ = true;
        }
    }
 
    void LameParameters::set_e_nu(const int index, const json &E, const json &nu, const std::string &stress_unit)
    {
        // TODO: conversion is always called
        is_lambda_mu_ = false;
        lambda_or_E_[index].init(E);
        mu_or_nu_[index].init(nu);
 
        lambda_or_E_[index].set_unit_type(stress_unit);
        // nu has no unit
        mu_or_nu_[index].set_unit_type("");
    }
 
    Density::Density()
    {
        rho_.emplace_back();
        rho_.back().init(1.0);
    }
 
    double Density::operator()(double px, double py, double pz, double x, double y, double z, double t, int el_id) const
    {
        assert(rho_.size() == 1 || el_id < rho_.size());
 
        const auto &tmp = rho_.size() == 1 ? rho_[0] : rho_[el_id];
        const double res = tmp(x, y, z, t, el_id);
        assert(!std::isnan(res));
        assert(!std::isinf(res));
        return res;
    }
 
    void Density::add_multimaterial(const int index, const json &params, const std::string &density_unit)
    {
        for (int i = rho_.size(); i <= index; ++i)
        {
            rho_.emplace_back();
        }
 
        if (params.count("rho"))
        {
            rho_[index].init(params["rho"]);
        }
        else if (params.count("density"))
        {
            rho_[index].init(params["density"]);
        }
 
        rho_[index].set_unit_type(density_unit);
    }
 
    FiberDirection::FiberDirection()
    {
    }
 
    void FiberDirection::resize(const int size)
    {
        assert(size == 2 || size == 3);
        size_ = size;
        if (!dir_.empty())
        {
            for (const auto &m : dir_)
            {
                assert((m.rows() == size && m.cols() == size) || (m.rows() == size && m.cols() == 1));
            }
        }
    }
 
    Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic, 1, 3, 3> FiberDirection::operator()(double px, double py, double pz, double x, double y, double z, double t, int el_id) const
    {
        assert(dir_.size() == 1 || el_id < dir_.size());
 
        const auto &tmp = dir_.size() == 1 ? dir_[0] : dir_[el_id];
        Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic, 1, 3, 3> res;
        res.resize(tmp.rows(), tmp.cols());
        for (int i = 0; i < tmp.rows(); ++i)
        {
            for (int j = 0; j < tmp.cols(); ++j)
            {
                res(i, j) = tmp(i, j)(x, y, z, t, el_id);
 
                assert(!std::isnan(res(i, j)));
                assert(!std::isinf(res(i, j)));
            }
        }
        return res;
    }
 
    Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic, 1, 6, 6> FiberDirection::stiffness_rotation_voigt(double px, double py, double pz, double x, double y, double z, double t, int el_id) const
    {
        // Rotate stiffness mtx in voigt notation according to:
        // https://scicomp.stackexchange.com/questions/35600/4th-order-tensor-rotation-sources-to-refer
 
        Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic, 1, 3, 3> rot = (*this)(px, py, pz, x, y, z, t, el_id);
        Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic, 1, 6, 6> res;
 
        int dim = rot.rows();
 
        static const double sqrt2 = std::sqrt(2.0);
 
        if (dim == 2)
        {
            res.resize(3, 3);
            // Still need to compute for 2d
            assert(false);
            // res << rot(0, 0) * rot(0, 0), rot(0, 1) * rot(0, 1), 0,
            //  rot(1, 0) * rot(1, 0), rot(1, 1) * rot(1, 1), 0,
            //  0, 0, 1;
        }
        else
        {
            assert(dim == 3);
            res.resize(6, 6);
            res << rot(0, 0) * rot(0, 0), rot(0, 1) * rot(0, 1), rot(0, 2) * rot(0, 2), sqrt2 * rot(0, 1) * rot(0, 2), sqrt2 * rot(0, 0) * rot(0, 2), sqrt2 * rot(0, 0) * rot(0, 1),
                rot(1, 0) * rot(1, 0), rot(1, 1) * rot(1, 1), rot(1, 2) * rot(1, 2), sqrt2 * rot(1, 1) * rot(1, 2), sqrt2 * rot(1, 0) * rot(1, 2), sqrt2 * rot(1, 0) * rot(1, 1),
                rot(2, 0) * rot(2, 0), rot(2, 1) * rot(2, 1), rot(2, 2) * rot(2, 2), sqrt2 * rot(2, 1) * rot(2, 2), sqrt2 * rot(2, 0) * rot(2, 2), sqrt2 * rot(2, 0) * rot(2, 1),
                sqrt2 * rot(1, 0) * rot(2, 0), sqrt2 * rot(1, 1) * rot(2, 1), sqrt2 * rot(1, 2) * rot(2, 2), rot(1, 1) * rot(2, 2) + rot(1, 2) * rot(2, 1), rot(1, 0) * rot(2, 2) + rot(1, 2) * rot(2, 0), rot(1, 0) * rot(2, 1) + rot(1, 1) * rot(2, 0),
                sqrt2 * rot(0, 0) * rot(2, 0), sqrt2 * rot(0, 1) * rot(2, 1), sqrt2 * rot(0, 2) * rot(2, 2), rot(0, 1) * rot(2, 2) + rot(0, 2) * rot(2, 1), rot(0, 0) * rot(2, 2) + rot(0, 2) * rot(2, 0), rot(0, 0) * rot(2, 1) + rot(0, 1) * rot(2, 0),
                sqrt2 * rot(0, 0) * rot(1, 0), sqrt2 * rot(0, 1) * rot(1, 1), sqrt2 * rot(0, 2) * rot(1, 2), rot(0, 1) * rot(1, 2) + rot(0, 2) * rot(1, 1), rot(0, 0) * rot(1, 2) + rot(0, 2) * rot(1, 0), rot(0, 0) * rot(1, 1) + rot(0, 1) * rot(1, 0);
        }
 
        return res;
    }
 
    void FiberDirection::add_multimaterial(const int index, const json &dir, const std::string &unit)
    {
        for (int i = dir_.size(); i <= index; ++i)
        {
            dir_.emplace_back();
        }
 
        if (dir.size() == 3 || dir.size() == 2)
        {
            const int size = dir.size();
            const int other_size = dir[0].is_array() ? size : 1;
 
            assert(size == size_);
            dir_[index].resize(size, other_size);
            for (int i = 0; i < size; ++i)
            {
                if (other_size == 1)
                {
                    if (dir[i].is_array())
                    {
                        log_and_throw_error(fmt::format("Fiber must be a {} vector, row {} is {}", size, i, dir[i].dump()));
                    }
                    dir_[index](i, 0).init(dir[i]);
                    dir_[index](i, 0).set_unit_type(unit);
                    continue;
                }
                if (dir[i].size() != size)
                {
                    log_and_throw_error(fmt::format("Fiber must be {}x{}, row {} is {}", size, other_size, i, dir[i].dump()));
                }
                for (int j = 0; j < size; ++j)
                {
                    dir_[index](i, j).init(dir[i][j]);
                    dir_[index](i, j).set_unit_type(unit);
                }
            }
            has_rotation_ = true;
        }
        else if (dir.size() == 9 || dir.size() == 4)
        {
            const int size = dir.size() == 9 ? 3 : 2;
            assert(size == size_);
            dir_[index].resize(size, size);
            for (int i = 0; i < size; ++i)
            {
                for (int j = 0; j < size; ++j)
                {
                    dir_[index](i, j).init(dir[i * size + j]);
                    dir_[index](i, j).set_unit_type(unit);
                }
            }
            has_rotation_ = true;
        }
        else if (dir.empty())
        {
            dir_[index].resize(size_, size_);
            for (int i = 0; i < size_; ++i)
            {
                for (int j = 0; j < size_; ++j)
                {
                    dir_[index](i, j).init(i == j ? 1.0 : 0.0);
                    dir_[index](i, j).set_unit_type(unit);
                }
            }
            has_rotation_ = false;
        }
        else
        {
            log_and_throw_error("Fiber direction must be a 3x3 or 2x2 matrix");
        }
    }
 
    // template instantiation
    template double ElasticityTensor::compute_stress<3>(const std::array<double, 3> &strain, const int j) const;
    template double ElasticityTensor::compute_stress<6>(const std::array<double, 6> &strain, const int j) const;
 
} // namespace polyfem::assembler