SchmidCostaExponentialLaw2d.cpp

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#include "SchmidCostaExponentialLaw2d.hpp"

SchmidCostaExponentialLaw2d::SchmidCostaExponentialLaw2d()
{
    mA = 0.221;    // kiloPascals, presumably, although the paper doesn't say.
                   // gives results matching Pole-zero anyway.
                   // Obtained from Table 1 of Schmid reference (see class doxygen), the mu (mean) value.

    double bff = 42.5; // dimensionless
    double bfs = 11.0; // dimensionless
    double bss = 18.6; // dimensionless

    mB.resize(2);
    mB[0].resize(2);
    mB[1].resize(2);

    mB[0][0] = bff;
    mB[0][1] = bfs;
    mB[1][0] = bfs;
    mB[1][1] = bss;

    for (unsigned M=0; M<2; M++)
    {
        for (unsigned N=0; N<2; N++)
        {
            mIdentity(M,N) = M==N ? 1.0 : 0.0;
        }
    }
}

void SchmidCostaExponentialLaw2d::ComputeStressAndStressDerivative(c_matrix<double,2,2>& rC,
                                                                   c_matrix<double,2,2>& rInvC,
                                                                   double                pressure,
                                                                   c_matrix<double,2,2>& rT,
                                                                   FourthOrderTensor<2,2,2,2>& rDTdE,
                                                                   bool                  computeDTdE)
{
    static c_matrix<double,2,2> C_transformed;
    static c_matrix<double,2,2> invC_transformed;

    // The material law parameters are set up assuming the fibre direction is (1,0,0)
    // and sheet direction is (0,1,0), so we have to transform C,inv(C),and T.
    // Let P be the change-of-basis matrix P = (\mathbf{m}_f, \mathbf{m}_s, \mathbf{m}_n).
    // The transformed C for the fibre/sheet basis is C* = P^T C P.
    // We then compute T* = T*(C*), and then compute T = P T* P^T.

    ComputeTransformedDeformationTensor(rC, rInvC, C_transformed, invC_transformed);

    // Compute T*

    c_matrix<double,2,2> E = 0.5*(C_transformed - mIdentity);

    double QQ = 0;
    for (unsigned M=0; M<2; M++)
    {
        for (unsigned N=0; N<2; N++)
        {
            QQ += mB[M][N]*E(M,N)*E(M,N);
        }
    }

    double multiplier = mA*exp(QQ)/2;
    rDTdE.Zero();

    for (unsigned M=0; M<2; M++)
    {
        for (unsigned N=0; N<2; N++)
        {
            rT(M,N) = multiplier*mB[M][N]*E(M,N) - pressure*invC_transformed(M,N);

            if (computeDTdE)
            {
                for (unsigned P=0; P<2; P++)
                {
                    for (unsigned Q=0; Q<2; Q++)
                    {
                        rDTdE(M,N,P,Q) =   multiplier * mB[M][N] * (M==P)*(N==Q)
                                        +  2*multiplier*mB[M][N]*mB[P][Q]*E(M,N)*E(P,Q)
                                        +  2*pressure*invC_transformed(M,P)*invC_transformed(Q,N);
                    }
                }
            }
        }
    }

    // Now do:   T = P T* P^T   and   dTdE_{MNPQ}  =  P_{Mm}P_{Nn}P_{Pp}P_{Qq} dT*dE*_{mnpq}
    this->TransformStressAndStressDerivative(rT, rDTdE, computeDTdE);
}

double SchmidCostaExponentialLaw2d::GetA()
{
    return mA;
}

std::vector<std::vector<double> > SchmidCostaExponentialLaw2d::GetB()
{
    return mB;
}

double SchmidCostaExponentialLaw2d::GetZeroStrainPressure()
{
    return 0.0;
}