PoleZeroMaterialLaw.cpp

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*/

#include "PoleZeroMaterialLaw.hpp"

template<unsigned DIM>
PoleZeroMaterialLaw<DIM>::PoleZeroMaterialLaw()
{
}

template<unsigned DIM>
void PoleZeroMaterialLaw<DIM>::SetParameters(std::vector<std::vector<double> > k,
                                             std::vector<std::vector<double> > a,
                                             std::vector<std::vector<double> > b)
{
    if (DIM!=2 && DIM !=3)
    {
        EXCEPTION("Can only have a 2 or 3d incompressible pole-zero law");
    }

    assert(k.size()==DIM);
    assert(a.size()==DIM);
    assert(b.size()==DIM);

    for (unsigned i=0; i<DIM; i++)
    {
        assert(k[i].size()==DIM);
        assert(a[i].size()==DIM);
        assert(b[i].size()==DIM);

        for (unsigned j=0; j<DIM; j++)
        {
            assert( k[i][j] = k[j][i] );
            assert( a[i][j] = a[j][i] );
            assert( b[i][j] = b[j][i] );
        }
    }

    mK = k;
    mA = a;
    mB = b;

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

template<unsigned DIM>
PoleZeroMaterialLaw<DIM>::PoleZeroMaterialLaw(std::vector<std::vector<double> > k,
                                              std::vector<std::vector<double> > a,
                                              std::vector<std::vector<double> > b)
{
    SetParameters(k,a,b);
}


template<unsigned DIM>
void PoleZeroMaterialLaw<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)
{
    static c_matrix<double,DIM,DIM> C_transformed;
    static c_matrix<double,DIM,DIM> 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,DIM,DIM> E = 0.5*(C_transformed - mIdentity);

    for (unsigned M=0; M<DIM; M++)
    {
        for (unsigned N=0; N<DIM; N++)
        {
            double e = E(M,N);
            {
                double b = mB[M][N];
                double a = mA[M][N];
                double k = mK[M][N];

                //if this fails one of the strain values got too large for the law
                if (e>=a)
                {
                    EXCEPTION("E_{MN} >= a_{MN} - strain unacceptably large for model");
                }

                rT(M,N) =   k
                          * e
                          * (2*(a-e) + b*e)
                          * pow(a-e,-b-1)
                          - pressure*invC_transformed(M,N);
            }
        }
    }

    if (computeDTdE)
    {
        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) = 2 * pressure * invC_transformed(M,P) * invC_transformed(Q,N);
                    }
                }

                double e = E(M,N);

                double b = mB[M][N];
                double a = mA[M][N];
                double k = mK[M][N];

                rDTdE(M,N,M,N) +=   k
                                  * pow(a-e, -b-2)
                                  * (
                                       2*(a-e)*(a-e)
                                     + 4*b*e*(a-e)
                                     + b*(b+1)*e*e
                                    );
            }
        }
    }

    // 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);
}

template<unsigned DIM>
double PoleZeroMaterialLaw<DIM>::GetZeroStrainPressure()
{
    return 0.0;
}

template<unsigned DIM>
void PoleZeroMaterialLaw<DIM>::ScaleMaterialParameters(double scaleFactor)
{
    assert(scaleFactor > 0.0);
    for (unsigned i=0; i<mK.size(); i++)
    {
        for (unsigned j=0; j<mK[i].size(); j++)
        {
            mK[i][j] /= scaleFactor;
        }
    }
}

// Explicit instantiation

template class PoleZeroMaterialLaw<2>;
template class PoleZeroMaterialLaw<3>;