AbstractIsotropicCompressibleMaterialLaw.cpp

/*

Copyright (C) University of Oxford, 2005-2011

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 "AbstractIsotropicCompressibleMaterialLaw.hpp"

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

template<unsigned DIM>
void AbstractIsotropicCompressibleMaterialLaw<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)
{
    /*
     * 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

    assert(pressure==0.0);

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

    double I1 = Trace(rC);
    double I2 = SecondInvariant(rC);
    double I3 = Determinant(rC);

    static c_matrix<double,DIM,DIM> dI2dC;
    dI2dC = I1*identity - rC;              // MUST be on separate line to above!

    double w1 = Get_dW_dI1(I1,I2,I3);
    double w2 = Get_dW_dI2(I1,I2,I3);
    double w3 = Get_dW_dI3(I1,I2,I3);


    // Compute stress:  **** See FiniteElementImplementations document. ****
    //
    //  T = dW_dE
    //    = 2 dW_dC
    //    = 2 (  w1 dI1/dC   +  w2 dI2/dC      +   w3 dI3/dC )
    //    = 2 (  w1 I        +  w2 (I1*I - C)  +   w3 I3 inv(C) )
    //
    //  where w1 = dW/dI1, etc
    //
    rT = 2*w1*identity + 2*w3*I3*rInvC;
    if (DIM==3)
    {
        rT += 2*w2*dI2dC;
    }

    // Compute stress derivative if required:  **** See FiniteElementImplementations document. ****
    //
    // The stress derivative dT_{MN}/dE_{PQ} is
    //
    //
    //  dT_dE = 2 dT_dC
    //        = 4  d/dC ( w1 I  +  w2 (I1*I - C)  +   w3 I3 inv(C) )
    //  so (in the following ** represents outer product):
    //  (1/4) dT_dE =        w11 I**I          +    w12 I**(I1*I-C)           +     w13 I**inv(C)
    //                  +    w21 (I1*I-C)**I   +    w22 (I1*I-C)**(I1*I-C)    +     w23 (I1*I-C)**inv(C)           +   w2 (I**I - dC/dC)
    //                  +    w31 I3 inv(C)**I  +    w32 I3 inv(C)**(I1*I-C)   +  (w33 I3 + w3) inv(C)**inv(C)      +   w3 d(invC)/dC
    //
    //  Here, I**I represents the tensor A[M][N][P][Q] = (M==N)*(P==Q) // ie delta(M,N)delta(P,Q),   etc
    //

    if (computeDTdE)
    {
        double  w11    = Get_d2W_dI1(I1,I2,I3);
        double  w22    = Get_d2W_dI2(I1,I2,I3);
        double  w33    = Get_d2W_dI3(I1,I2,I3);

        double  w23  = Get_d2W_dI2I3(I1,I2,I3);
        double  w13  = Get_d2W_dI1I3(I1,I2,I3);
        double  w12  = Get_d2W_dI1I2(I1,I2,I3);

        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)
                                         + 4 * w13  * I3 * ( (M==N) * rInvC(P,Q)  +  rInvC(M,N)*(P==Q) )  // the w13 and w31 terms
                                         + 4 * (w33*I3 + w3) * I3 * rInvC(M,N) * rInvC(P,Q)
                                         - 4 * w3 * I3 * rInvC(M,P) * rInvC(Q,N);

                        if (DIM==3)
                        {
                            rDTdE(M,N,P,Q) +=   4 * w22  * dI2dC(M,N) * dI2dC(P,Q)
                                              + 4 * w12  * ((M==N)*dI2dC(P,Q) + (P==Q)*dI2dC(M,N))          // the w12 and w21 terms
                                              + 4 * w23 * I3 * ( dI2dC(M,N)*rInvC(P,Q) + rInvC(M,N)*dI2dC(P,Q)) // the w23 and w32 terms
                                              + 4 * w2   * ((M==N)*(P==Q) - (M==P)*(N==Q));
                        }
                    }
                }
            }
        }
    }
}

// Explicit instantiation

//template class AbstractIsotropicCompressibleMaterialLaw<1>;
template class AbstractIsotropicCompressibleMaterialLaw<2>;
template class AbstractIsotropicCompressibleMaterialLaw<3>;