AbstractIsotropicIncompressibleMaterialLaw.cpp

00001 /*
00002 
00003 Copyright (C) University of Oxford, 2005-2011
00004 
00005 University of Oxford means the Chancellor, Masters and Scholars of the
00006 University of Oxford, having an administrative office at Wellington
00007 Square, Oxford OX1 2JD, UK.
00008 
00009 This file is part of Chaste.
00010 
00011 Chaste is free software: you can redistribute it and/or modify it
00012 under the terms of the GNU Lesser General Public License as published
00013 by the Free Software Foundation, either version 2.1 of the License, or
00014 (at your option) any later version.
00015 
00016 Chaste is distributed in the hope that it will be useful, but WITHOUT
00017 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
00018 FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
00019 License for more details. The offer of Chaste under the terms of the
00020 License is subject to the License being interpreted in accordance with
00021 English Law and subject to any action against the University of Oxford
00022 being under the jurisdiction of the English Courts.
00023 
00024 You should have received a copy of the GNU Lesser General Public License
00025 along with Chaste. If not, see <http://www.gnu.org/licenses/>.
00026 
00027 */
00028 
00029 #include "AbstractIsotropicIncompressibleMaterialLaw.hpp"
00030 
00031 template<unsigned DIM>
00032 AbstractIsotropicIncompressibleMaterialLaw<DIM>::~AbstractIsotropicIncompressibleMaterialLaw()
00033 {
00034 }
00035 
00036 template<unsigned DIM>
00037 void AbstractIsotropicIncompressibleMaterialLaw<DIM>::ComputeStressAndStressDerivative(
00038         c_matrix<double,DIM,DIM>& rC,
00039         c_matrix<double,DIM,DIM>& rInvC,
00040         double                    pressure,
00041         c_matrix<double,DIM,DIM>& rT,
00042         FourthOrderTensor<DIM,DIM,DIM,DIM>&   rDTdE,
00043         bool                      computeDTdE)
00044 {
00045     /*
00046      * This is covered, but gcov doesn't see this as being covered
00047      * for some reason, maybe because of optimisations.
00048      */
00049     #define COVERAGE_IGNORE
00050     assert((DIM==2) || (DIM==3));
00051     #undef COVERAGE_IGNORE
00052 
00053     static c_matrix<double,DIM,DIM> identity = identity_matrix<double>(DIM);
00054 
00055     double I1 = Trace(rC);
00056     double I2 = SecondInvariant(rC);
00057 
00058     double  w1 = Get_dW_dI1(I1, I2);
00059     double  w2; // only computed if DIM==3
00060 
00061     // Compute stress:  **** See FiniteElementImplementations document. ****
00062     //
00063     //  T = dW_dE
00064     //    = 2 * w1 * dI1_dC_MN   +   2 * w2 * dI1_dC_MN  -  p * invC
00065     //    = 2 * w1 * delta_MN    +   2 * w2 * (I1 delta_MN - C_MN)  -  p * invC
00066     //
00067     //  (where w1 = dW/dI1, etc).
00068 
00069     rT = 2*w1*identity - pressure*rInvC;
00070     if (DIM==3)
00071     {
00072         w2 = Get_dW_dI2(I1, I2);
00073         rT += 2*w2*(I1*identity - rC);
00074     }
00075 
00076     // Compute stress derivative if required:   **** See FiniteElementImplementations document. ****
00077     //
00078     // The stress derivative dT_{MN}/dE_{PQ} is
00079     //
00080     //  dT_dE =    4 * w11 * dI1_dC_MN * dI1_dC_PQ
00081     //           + 4 * w1  * d2I1_dC2
00082     //           + 4 * w22 * dI2_dC_MN * dI2_dC_PQ
00083     //           + 4 * w2  * d2I2_dC2
00084     //           + 4 * w12 * (dI1_dC_MN*dI2_dC_PQ + dI1_dC_PQ*dI2_dC_MN)
00085     //           - 2 * pressure * d_invC_dC;
00086     //
00087     // where
00088     //   dI1_dC_MN = (M==N); // ie delta_{MN}
00089     //   dI1_dC_PQ = (P==Q);
00090     //   d2I1_dC2  = 0;
00091     //
00092     //   dI2_dC_MN = I1*(M==N)-C[M][N];
00093     //   dI2_dC_PQ = I1*(P==Q)-C[P][Q];
00094     //   d2I2_dC2  = (M==N)*(P==Q)-(M==P)*(N==Q);
00095     //
00096     //   d_invC_dC = -invC[M][P]*invC[Q][N];
00097     //
00098     if (computeDTdE)
00099     {
00100         double w11 = Get_d2W_dI1(I1,I2);
00101 
00102         double w12;
00103         double w22;
00104 
00105         if (DIM==3)
00106         {
00107             w22 = Get_d2W_dI2(I1, I2);
00108             w12 = Get_d2W_dI1I2(I1, I2);
00109         }
00110 
00111         for (unsigned M=0; M<DIM; M++)
00112         {
00113             for (unsigned N=0; N<DIM; N++)
00114             {
00115                 for (unsigned P=0; P<DIM; P++)
00116                 {
00117                     for (unsigned Q=0; Q<DIM; Q++)
00118                     {
00119                         rDTdE(M,N,P,Q) =   4 * w11  * (M==N) * (P==Q)
00120                                          + 2 * pressure * rInvC(M,P) * rInvC(Q,N);
00121 
00122                         if (DIM==3)
00123                         {
00124                             rDTdE(M,N,P,Q) +=   4 * w22   * (I1*(M==N) - rC(M,N)) * (I1*(P==Q) - rC(P,Q))
00125                                               + 4 * w2    * ((M==N)*(P==Q) - (M==P)*(N==Q))
00126                                               + 4 * w12 * ((M==N)*(I1*(P==Q) - rC(P,Q)) + (P==Q)*(I1*(M==N) - rC(M,N)));
00127                         }
00128                     }
00129                 }
00130             }
00131         }
00132     }
00133 }
00134 
00135 template<>
00136 double AbstractIsotropicIncompressibleMaterialLaw<2>::GetZeroStrainPressure()
00137 {
00138     return 2*Get_dW_dI1(2,0);
00139 }
00140 
00141 template<>
00142 double AbstractIsotropicIncompressibleMaterialLaw<3>::GetZeroStrainPressure()
00143 {
00144     return 2*Get_dW_dI1(3,3) + 4*Get_dW_dI2(3,3);
00145 }
00146 
00148 // Explicit instantiation
00150 
00151 template class AbstractIsotropicIncompressibleMaterialLaw<2>;
00152 template class AbstractIsotropicIncompressibleMaterialLaw<3>;
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