PolynomialMaterialLaw3d.cpp

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*/

#include "PolynomialMaterialLaw3d.hpp"

double PolynomialMaterialLaw3d::Get_dW_dI1(double I1, double I2)
{
    double ret = 0.0;
    // notes: use ints not unsigned as doing p-1
    // (except indexing from p=1 because multiplying by p, but
    // still safer to use ints)
    for (int p=1; p<=(int)mN; p++)
    {
        for (int q=0; q<=(int)mN-p; q++)
        {
            ret += mAlpha[p][q] * p * pow(I1-3,p-1) * pow(I2-3,q);
        }
    }

    return ret;
}

double PolynomialMaterialLaw3d::Get_dW_dI2(double I1, double I2)
{
    double ret = 0.0;
    // notes: use ints not unsigned as doing q-1
    // (except indexing from q=1 because multiplying by q, but
    // still safer to use ints)
    for (int p=0; p<=(int)mN; p++)
    {
        for (int q=1; q<=(int)mN-p; q++)
        {
            ret += mAlpha[p][q] * q * pow(I1-3,p) * pow(I2-3,q-1);
        }
    }
    return ret;
}

double PolynomialMaterialLaw3d::Get_d2W_dI1(double I1, double I2)
{
    double ret = 0.0;

    // notes: use ints not unsigned as doing p-1
    // (except indexing from p=2 because multiplying by p(p-1), but
    // still safer to use ints)
    for (int p=2; p<=(int)mN; p++)
    {
        for (int q=0; q<=(int)mN-p; q++)
        {
            ret += mAlpha[p][q] * p * (p-1) * pow(I1-3,(p-1)*(p-2)) * pow((double)I2-3,(double)q);
        }
    }
    return ret;
}

double PolynomialMaterialLaw3d::Get_d2W_dI2(double I1, double I2)
{
    double ret = 0.0;

    // notes: use ints not unsigned as doing q-1
    // (except indexing from q=2 because multiplying by q(q-1), but
    // still safer to use ints)
    for (int p=0; p<=(int)mN; p++)
    {
        for (int q=2; q<=(int)mN-p; q++)
        {
            ret += mAlpha[p][q] * q * (q-1) * pow((double)I1-3,(double)p) * pow(I2-3,(q-1)*(q-2));
        }
    }
    return ret;
}

double PolynomialMaterialLaw3d::Get_d2W_dI1I2(double I1, double I2)
{
    double ret = 0.0;

    // notes: use ints not unsigned as doing p-1
    // (except indexing from p=1,q=1 because multiplying by pq, but
    // still safer to use ints)
    for (int p=1; p<=(int)mN; p++)
    {
        for (int q=1; q<=(int)mN-p; q++)
        {
            ret += mAlpha[p][q] * p * q * pow(I1-3,p-1) * pow(I2-3,q-1);
        }
    }
    return ret;
}

double PolynomialMaterialLaw3d::GetAlpha(unsigned i, unsigned j)
{
    assert(i+j > 0);
    assert(i+j <= mN);

    return mAlpha[i][j];
}

PolynomialMaterialLaw3d::PolynomialMaterialLaw3d(unsigned n, std::vector<std::vector<double> > alpha)
{
    if (n==0)
    {
        EXCEPTION("n must be positive");
    }

    mN = n;

    // error checking: must have alpha[p][q]=0 if p+q>n
    for (unsigned p=0; p<=mN; p++)
    {
        if (alpha[p].size() < mN+1-p)
        {
            EXCEPTION("alpha not big enough");
        }

        for (unsigned q=0; q<alpha[p].size(); q++)
        {
            if ((p+q>mN) && (fabs(alpha[p][q]) > 1e-12))
            {
                EXCEPTION("alpha[" << p << "][" << q << "] should be zero, as p+q > " << n);
            }
        }
    }

    mAlpha = alpha;
}

std::vector<std::vector<double> > PolynomialMaterialLaw3d::GetZeroedAlpha(unsigned n)
{
    std::vector<std::vector<double> > alpha(n+1);

    for (unsigned i=0; i<n+1; i++)
    {
        alpha[i].resize(n+1);
        for (unsigned j=0; j<n+1; j++)
        {
            alpha[i][j] = 0.0;
        }
    }

    return alpha;
}