AbstractIsotropicIncompressibleMaterialLaw.cpp

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*/

#include "AbstractIsotropicIncompressibleMaterialLaw.hpp"

template<unsigned DIM>
AbstractIsotropicIncompressibleMaterialLaw<DIM>::~AbstractIsotropicIncompressibleMaterialLaw()
{
}

template<unsigned DIM>
void AbstractIsotropicIncompressibleMaterialLaw<DIM>::ComputeStressAndStressDerivative(
        c_matrix<double,DIM,DIM>& rC,
        c_matrix<double,DIM,DIM>& rInvC,
        double                    pressure,
        c_matrix<double,DIM,DIM>& rT,
        FourthOrderTensor<DIM,DIM,DIM,DIM>&   rDTdE,
        bool                      computeDTdE)
{
    assert((DIM==2) || (DIM==3)); // LCOV_EXCL_LINE

    static c_matrix<double,DIM,DIM> identity = identity_matrix<double>(DIM);

    double I1 = Trace(rC);
    double I2 = SecondInvariant(rC);

    double  w1 = Get_dW_dI1(I1, I2);
    double  w2; // only computed if DIM==3

    // Compute stress:  **** See FiniteElementImplementations document. ****
    //
    //  T = dW_dE
    //    = 2 * w1 * dI1_dC_MN   +   2 * w2 * dI1_dC_MN  -  p * invC
    //    = 2 * w1 * delta_MN    +   2 * w2 * (I1 delta_MN - C_MN)  -  p * invC
    //
    //  (where w1 = dW/dI1, etc).

    rT = 2*w1*identity - pressure*rInvC;
    if (DIM==3)
    {
        w2 = Get_dW_dI2(I1, I2);
        rT += 2*w2*(I1*identity - rC);
    }

    // Compute stress derivative if required:   **** See FiniteElementImplementations document. ****
    //
    // The stress derivative dT_{MN}/dE_{PQ} is
    //
    //  dT_dE =    4 * w11 * dI1_dC_MN * dI1_dC_PQ
    //           + 4 * w1  * d2I1_dC2
    //           + 4 * w22 * dI2_dC_MN * dI2_dC_PQ
    //           + 4 * w2  * d2I2_dC2
    //           + 4 * w12 * (dI1_dC_MN*dI2_dC_PQ + dI1_dC_PQ*dI2_dC_MN)
    //           - 2 * pressure * d_invC_dC;
    //
    // where
    //   dI1_dC_MN = (M==N); // ie delta_{MN}
    //   dI1_dC_PQ = (P==Q);
    //   d2I1_dC2  = 0;
    //
    //   dI2_dC_MN = I1*(M==N)-C[M][N];
    //   dI2_dC_PQ = I1*(P==Q)-C[P][Q];
    //   d2I2_dC2  = (M==N)*(P==Q)-(M==P)*(N==Q);
    //
    //   d_invC_dC = -invC[M][P]*invC[Q][N];
    //
    if (computeDTdE)
    {
        double w11 = Get_d2W_dI1(I1,I2);

        double w12;
        double w22;

        if (DIM==3)
        {
            w22 = Get_d2W_dI2(I1, I2);
            w12 = Get_d2W_dI1I2(I1, I2);
        }

        for (unsigned M=0; M<DIM; M++)
        {
            for (unsigned N=0; N<DIM; N++)
            {
                for (unsigned P=0; P<DIM; P++)
                {
                    for (unsigned Q=0; Q<DIM; Q++)
                    {
                        rDTdE(M,N,P,Q) =   4 * w11  * (M==N) * (P==Q)
                                         + 2 * pressure * rInvC(M,P) * rInvC(Q,N);

                        if (DIM==3)
                        {
                            rDTdE(M,N,P,Q) +=   4 * w22   * (I1*(M==N) - rC(M,N)) * (I1*(P==Q) - rC(P,Q))
                                              + 4 * w2    * ((M==N)*(P==Q) - (M==P)*(N==Q))
                                              + 4 * w12 * ((M==N)*(I1*(P==Q) - rC(P,Q)) + (P==Q)*(I1*(M==N) - rC(M,N)));
                        }
                    }
                }
            }
        }
    }
}

template<>
double AbstractIsotropicIncompressibleMaterialLaw<2>::GetZeroStrainPressure()
{
    return 2*Get_dW_dI1(2,0);
}

template<>
double AbstractIsotropicIncompressibleMaterialLaw<3>::GetZeroStrainPressure()
{
    return 2*Get_dW_dI1(3,3) + 4*Get_dW_dI2(3,3);
}

// Explicit instantiation
template class AbstractIsotropicIncompressibleMaterialLaw<2>;
template class AbstractIsotropicIncompressibleMaterialLaw<3>;