MooneyRivlin3ParamElasticity.hpp

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#pragma once
 
#include <polyfem/assembler/GenericElastic.hpp>
#include <polyfem/assembler/MatParams.hpp>
 
// non linear MooneyRivlin material model
namespace polyfem::assembler
{
    class MooneyRivlin3ParamElasticity : public GenericElastic<MooneyRivlin3ParamElasticity>
    {
    public:
        MooneyRivlin3ParamElasticity();
 
        // sets material params
        void add_multimaterial(const int index, const json &params, const Units &units) override;
 
        const GenericMatParam &c1() const { return c1_; }
        const GenericMatParam &c2() const { return c2_; }
        const GenericMatParam &c3() const { return c3_; }
        const GenericMatParam &d1() const { return d1_; }
 
        std::string name() const override { return "MooneyRivlin3Param"; }
        std::map<std::string, ParamFunc> parameters() const override;
 
        template <typename T>
        T elastic_energy(
            const RowVectorNd &p,
            const double t,
            const int el_id,
            const DefGradMatrix<T> &def_grad) const
        {
            const double c1 = c1_(p, t, el_id);
            const double c2 = c2_(p, t, el_id);
            const double c3 = c3_(p, t, el_id);
            const double d1 = d1_(p, t, el_id);
 
            const T J = polyfem::utils::determinant(def_grad);
            const auto right_cauchy_green = def_grad * def_grad.transpose();
 
            const auto powJ = pow(J, -2. / 3);
            const auto TrB = right_cauchy_green.trace();
            const auto I1_tilde = powJ * (TrB + (3 - size())) - 3;
            const auto second_invariant_val = (size() == 3) ? 0.5 * (TrB * TrB - (right_cauchy_green * right_cauchy_green).trace()) : TrB + J * J;
            const auto I2_tilde = (powJ * powJ) * second_invariant_val - 3;
 
            const T val = c1 * I1_tilde + (c2 + c3 * I1_tilde) * I2_tilde + d1 * (J - 1) * (J - 1);
 
            return val;
        }
 
    private:
        GenericMatParam c1_;
        GenericMatParam c2_;
        GenericMatParam c3_;
        GenericMatParam d1_;
    };
} // namespace polyfem::assembler