Chaste Release::3.1
SchmidCostaExponentialLaw2d.cpp
00001 /*
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00034 */
00035 
00036 #include "SchmidCostaExponentialLaw2d.hpp"
00037 
00038 SchmidCostaExponentialLaw2d::SchmidCostaExponentialLaw2d()
00039 {
00040     mA = 0.221;    // kiloPascals, presumably, although the paper doesn't say.
00041                    // gives results matching Pole-zero anyway.
00042                    // Obtained from Table 1 of Schmid reference (see class doxygen), the mu (mean) value.
00043 
00044     double bff = 42.5; // dimensionless
00045     double bfs = 11.0; // dimensionless
00046     double bss = 18.6; // dimensionless
00047 
00048     mB.resize(2);
00049     mB[0].resize(2);
00050     mB[1].resize(2);
00051 
00052     mB[0][0] = bff;
00053     mB[0][1] = bfs;
00054     mB[1][0] = bfs;
00055     mB[1][1] = bss;
00056 
00057     for (unsigned M=0; M<2; M++)
00058     {
00059         for (unsigned N=0; N<2; N++)
00060         {
00061             mIdentity(M,N) = M==N ? 1.0 : 0.0;
00062         }
00063     }
00064 }
00065 
00066 void SchmidCostaExponentialLaw2d::ComputeStressAndStressDerivative(c_matrix<double,2,2>& rC,
00067                                                                    c_matrix<double,2,2>& rInvC,
00068                                                                    double                pressure,
00069                                                                    c_matrix<double,2,2>& rT,
00070                                                                    FourthOrderTensor<2,2,2,2>& rDTdE,
00071                                                                    bool                  computeDTdE)
00072 {
00073     static c_matrix<double,2,2> C_transformed;
00074     static c_matrix<double,2,2> invC_transformed;
00075 
00076     // The material law parameters are set up assuming the fibre direction is (1,0,0)
00077     // and sheet direction is (0,1,0), so we have to transform C,inv(C),and T.
00078     // Let P be the change-of-basis matrix P = (\mathbf{m}_f, \mathbf{m}_s, \mathbf{m}_n).
00079     // The transformed C for the fibre/sheet basis is C* = P^T C P.
00080     // We then compute T* = T*(C*), and then compute T = P T* P^T.
00081 
00082     ComputeTransformedDeformationTensor(rC, rInvC, C_transformed, invC_transformed);
00083 
00084     // Compute T*
00085 
00086     c_matrix<double,2,2> E = 0.5*(C_transformed - mIdentity);
00087 
00088     double Q = 0;
00089     for (unsigned M=0; M<2; M++)
00090     {
00091         for (unsigned N=0; N<2; N++)
00092         {
00093             Q += mB[M][N]*E(M,N)*E(M,N);
00094         }
00095     }
00096 
00097     double multiplier = mA*exp(Q)/2;
00098     rDTdE.Zero();
00099 
00100     for (unsigned M=0; M<2; M++)
00101     {
00102         for (unsigned N=0; N<2; N++)
00103         {
00104             rT(M,N) = multiplier*mB[M][N]*E(M,N) - pressure*invC_transformed(M,N);
00105 
00106             if (computeDTdE)
00107             {
00108                 for (unsigned P=0; P<2; P++)
00109                 {
00110                     for (unsigned Q=0; Q<2; Q++)
00111                     {
00112                         rDTdE(M,N,P,Q) =   multiplier * mB[M][N] * (M==P)*(N==Q)
00113                                         +  2*multiplier*mB[M][N]*mB[P][Q]*E(M,N)*E(P,Q)
00114                                         +  2*pressure*invC_transformed(M,P)*invC_transformed(Q,N);
00115                     }
00116                 }
00117             }
00118         }
00119     }
00120 
00121     // Now do:   T = P T* P^T   and   dTdE_{MNPQ}  =  P_{Mm}P_{Nn}P_{Pp}P_{Qq} dT*dE*_{mnpq}
00122     this->TransformStressAndStressDerivative(rT, rDTdE, computeDTdE);
00123 }
00124 
00125 double SchmidCostaExponentialLaw2d::GetA()
00126 {
00127     return mA;
00128 }
00129 
00130 std::vector<std::vector<double> > SchmidCostaExponentialLaw2d::GetB()
00131 {
00132     return mB;
00133 }
00134 
00135 double SchmidCostaExponentialLaw2d::GetZeroStrainPressure()
00136 {
00137     return 0.0;
00138 }