AbstractIsotropicCompressibleMaterialLaw.cpp

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*/

#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
     * because it runs at compile time checking templates I think.
     */
    assert((DIM==2) || (DIM==3)); // LCOV_EXCL_LINE
    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<2>;
template class AbstractIsotropicCompressibleMaterialLaw<3>;