AbstractMaterialLaw.cpp

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*/
 
#include "AbstractMaterialLaw.hpp"
 
template<unsigned DIM>
AbstractMaterialLaw<DIM>::AbstractMaterialLaw()
    : mpChangeOfBasisMatrix(nullptr)
{
}
 
template<unsigned DIM>
void AbstractMaterialLaw<DIM>::ComputeCauchyStress(c_matrix<double,DIM,DIM>& rF,
                                                   double pressure,
                                                   c_matrix<double,DIM,DIM>& rSigma)
{
    double detF = Determinant(rF);
 
    c_matrix<double,DIM,DIM> C = prod(trans(rF), rF);
    c_matrix<double,DIM,DIM> invC = Inverse(C);
 
    c_matrix<double,DIM,DIM> T;
 
    static FourthOrderTensor<DIM,DIM,DIM,DIM> dTdE; // not filled in, made static for efficiency
 
    ComputeStressAndStressDerivative(C, invC, pressure, T, dTdE, false);
 
    /*
     * Looping is probably more eficient then doing rSigma = (1/detF)*rF*T*transpose(rF),
     * which doesn't seem to compile anyway, as rF is a Tensor<2,DIM> and T is a
     * SymmetricTensor<2,DIM>.
     */
    for (unsigned i=0; i<DIM; i++)
    {
        for (unsigned j=0; j<DIM; j++)
        {
            rSigma(i,j) = 0.0;
            for (unsigned M=0; M<DIM; M++)
            {
                for (unsigned N=0; N<DIM; N++)
                {
                    rSigma(i,j) += rF(i,M)*T(M,N)*rF(j,N);
                }
            }
            rSigma(i,j) /= detF;
        }
    }
}
 
template<unsigned DIM>
void AbstractMaterialLaw<DIM>::Compute1stPiolaKirchoffStress(c_matrix<double,DIM,DIM>& rF,
                                                             double pressure,
                                                             c_matrix<double,DIM,DIM>& rS)
{
    c_matrix<double,DIM,DIM> C = prod(trans(rF), rF);
    c_matrix<double,DIM,DIM> invC = Inverse(C);
 
    c_matrix<double,DIM,DIM> T;
 
    static FourthOrderTensor<DIM,DIM,DIM,DIM> dTdE; // not filled in, made static for efficiency
 
    ComputeStressAndStressDerivative(C, invC, pressure, T, dTdE, false);
 
    rS = prod(T, trans(rF));
}
 
template<unsigned DIM>
void AbstractMaterialLaw<DIM>::Compute2ndPiolaKirchoffStress(c_matrix<double,DIM,DIM>& rC,
                                                             double pressure,
                                                             c_matrix<double,DIM,DIM>& rT)
{
    c_matrix<double,DIM,DIM> invC = Inverse(rC);
 
    static FourthOrderTensor<DIM,DIM,DIM,DIM> dTdE; // not filled in, made static for efficiency
 
    ComputeStressAndStressDerivative(rC, invC, pressure, rT, dTdE, false);
}
 
// LCOV_EXCL_START
template<unsigned DIM>
void AbstractMaterialLaw<DIM>::ScaleMaterialParameters(double scaleFactor)
{
    EXCEPTION("[the material law you are using]::ScaleMaterialParameters() has not been implemented\n");
}
// LCOV_EXCL_STOP
 
template<unsigned DIM>
void AbstractMaterialLaw<DIM>::SetChangeOfBasisMatrix(c_matrix<double,DIM,DIM>& rChangeOfBasisMatrix)
{
    mpChangeOfBasisMatrix = &rChangeOfBasisMatrix;
}
 
template<unsigned DIM>
void AbstractMaterialLaw<DIM>::ResetToNoChangeOfBasisMatrix()
{
    mpChangeOfBasisMatrix = nullptr;
}
 
template<unsigned DIM>
void AbstractMaterialLaw<DIM>::ComputeTransformedDeformationTensor(c_matrix<double,DIM,DIM>& rC, c_matrix<double,DIM,DIM>& rInvC,
                                                                   c_matrix<double,DIM,DIM>& rCTransformed, c_matrix<double,DIM,DIM>& rInvCTransformed)
{
    // Writing the local coordinate system as fibre/sheet/normal, as in cardiac problems..
 
    // 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.
    if (mpChangeOfBasisMatrix)
    {
        // C* = P^T C P, and ditto inv(C)
        rCTransformed = prod(trans(*mpChangeOfBasisMatrix),(c_matrix<double,DIM,DIM>)prod(rC,*mpChangeOfBasisMatrix));         // C*    = P^T C    P
        rInvCTransformed = prod(trans(*mpChangeOfBasisMatrix),(c_matrix<double,DIM,DIM>)prod(rInvC,*mpChangeOfBasisMatrix));   // invC* = P^T invC P
    }
    else
    {
        rCTransformed = rC;
        rInvCTransformed = rInvC;
    }
}
 
template<unsigned DIM>
void AbstractMaterialLaw<DIM>::TransformStressAndStressDerivative(c_matrix<double,DIM,DIM>& rT,
                                                                  FourthOrderTensor<DIM,DIM,DIM,DIM>& rDTdE,
                                                                  bool transformDTdE)
{
    //  T = P T* P^T   and   dTdE_{MNPQ}  =  P_{Mm}P_{Nn}P_{Pp}P_{Qq} dT*dE*_{mnpq}
    if (mpChangeOfBasisMatrix)
    {
        static c_matrix<double,DIM,DIM> T_transformed_times_Ptrans;
        T_transformed_times_Ptrans = prod(rT, trans(*mpChangeOfBasisMatrix));
 
        rT = prod(*mpChangeOfBasisMatrix, T_transformed_times_Ptrans);  // T = P T* P^T
 
        // dTdE_{MNPQ}  =  P_{Mm}P_{Nn}P_{Pp}P_{Qq} dT*dE*_{mnpq}
        if (transformDTdE)
        {
            static FourthOrderTensor<DIM,DIM,DIM,DIM> temp;
            temp.template SetAsContractionOnFirstDimension<DIM>(*mpChangeOfBasisMatrix, rDTdE);
            rDTdE.template SetAsContractionOnSecondDimension<DIM>(*mpChangeOfBasisMatrix, temp);
            temp.template SetAsContractionOnThirdDimension<DIM>(*mpChangeOfBasisMatrix, rDTdE);
            rDTdE.template SetAsContractionOnFourthDimension<DIM>(*mpChangeOfBasisMatrix, temp);
        }
    }
}
 
// Explicit instantiation
template class AbstractMaterialLaw<2>;
template class AbstractMaterialLaw<3>;