AbstractIsotropicIncompressibleMaterialLaw.cpp

/*

Copyright (C) University of Oxford, 2005-2010

University of Oxford means the Chancellor, Masters and Scholars of the
University of Oxford, having an administrative office at Wellington
Square, Oxford OX1 2JD, UK.

This file is part of Chaste.

Chaste is free software: you can redistribute it and/or modify it
under the terms of the GNU Lesser General Public License as published
by the Free Software Foundation, either version 2.1 of the License, or
(at your option) any later version.

Chaste is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
License for more details. The offer of Chaste under the terms of the
License is subject to the License being interpreted in accordance with
English Law and subject to any action against the University of Oxford
being under the jurisdiction of the English Courts.

You should have received a copy of the GNU Lesser General Public License
along with Chaste. If not, see <http://www.gnu.org/licenses/>.

*/

#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>&   rDTdE,
        bool                      computeDTdE)
{
    // this is covered, but gcov doesn't see this as being covered
    // for some reason, maybe because of optimisations
    #define COVERAGE_IGNORE
    assert((DIM==2) || (DIM==3));
    #undef COVERAGE_IGNORE

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

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

    double  dW_dI1 = Get_dW_dI1(I1, I2);
    double  dW_dI2; // only computed if DIM==3

    double  d2W_dI1;
    double  d2W_dI2;
    double  d2W_dI1I2;

    // Compute stress:
    //
    //  T = dW_dE
    //    = 2 * dI1_dC_MN * dI1_dC_MN   +   2 * dI1_dC_MN * dI1_dC_MN  -  p * invC
    //    = 2 * dI1_dC_MN * delta_MN    +   2 * dI1_dC_MN * (I1 delta_MN - C_MN)  -  p * invC

    rT = 2*dW_dI1*identity - pressure*rInvC;
    if (DIM==3)
    {
        dW_dI2 = Get_dW_dI2(I1, I2);
        rT += 2*dW_dI2*(I1*identity - rC);
    }

    // Compute stress derivative if required:
    //
    // The stress derivative dT_{MN}/dE_{PQ} can be expanded to be seen to be
    //
    //  dT_dE =    4 * true_d2WdI1 * dI1_dC_MN * dI1_dC_PQ
    //           + 4 * true_dWdI1  * d2I1_dC2
    //           + 4 * true_d2WdI2 * dI2_dC_MN * dI2_dC_PQ
    //           + 4 * true_dWdI2  * d2I2_dC2
    //           + 4 * true_d2WdI1I2 * (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)
    {
        d2W_dI1 = Get_d2W_dI1(I1,I2);

        if (DIM==3)
        {
            d2W_dI2   = Get_d2W_dI2(I1, I2);
            d2W_dI1I2 = 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 * d2W_dI1  * (M==N) * (P==Q)
                                         + 2 * pressure * rInvC(M,P) * rInvC(Q,N);

                        if (DIM==3)
                        {
                            rDTdE(M,N,P,Q) +=   4 * d2W_dI2   * (I1*(M==N) - rC(M,N)) * (I1*(P==Q) - rC(P,Q))
                                              + 4 * dW_dI2    * ((M==N)*(P==Q) - (M==P)*(N==Q))
                                              + 4 * d2W_dI1I2 * ((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>;