CompressibleExponentialLaw.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 "CompressibleExponentialLaw.hpp"
00030 
00031 template<unsigned DIM>
00032 CompressibleExponentialLaw<DIM>::CompressibleExponentialLaw()
00033 {
00034     mA = 0.88;  // kPa
00035 
00036     double bff = 18.5; // dimensionless
00037     double bss = 3.58; // dimensionless
00038     double bnn = 3.58; // dimensionless
00039     double bfn = 2.8;  // etc
00040     double bfs = 2.8;
00041     double bsn = 2.8;
00042 
00043     mCompressibilityParam = 100.0;
00044 
00045     mB.resize(DIM);
00046     for (unsigned i=0; i<DIM; i++)
00047     {
00048         mB[i].resize(DIM);
00049     }
00050 
00051     mB[0][0] = bff;
00052     mB[0][1] = mB[1][0] = bfs;
00053     mB[1][1] = bss;
00054 
00055     if (DIM > 2)
00056     {
00057         mB[2][2] = bnn;
00058         mB[0][2] = mB[2][0] = bfn;
00059         mB[2][1] = mB[1][2] = bsn;
00060     }
00061 
00062     for (unsigned M=0; M<DIM; M++)
00063     {
00064         for (unsigned N=0; N<DIM; N++)
00065         {
00066             mIdentity(M,N) = M==N ? 1.0 : 0.0;
00067         }
00068     }
00069 }
00070 
00071 template<unsigned DIM>
00072 void CompressibleExponentialLaw<DIM>::ComputeStressAndStressDerivative(c_matrix<double,DIM,DIM>& rC,
00073                                                                        c_matrix<double,DIM,DIM>& rInvC,
00074                                                                        double                pressure /* not used */,
00075                                                                        c_matrix<double,DIM,DIM>& rT,
00076                                                                        FourthOrderTensor<DIM,DIM,DIM,DIM>& rDTdE,
00077                                                                        bool                  computeDTdE)
00078 {
00079     static c_matrix<double,DIM,DIM> C_transformed;
00080     static c_matrix<double,DIM,DIM> invC_transformed;
00081 
00082     // The material law parameters are set up assuming the fibre direction is (1,0,0)
00083     // and sheet direction is (0,1,0), so we have to transform C,inv(C),and T.
00084     // Let P be the change-of-basis matrix P = (\mathbf{m}_f, \mathbf{m}_s, \mathbf{m}_n).
00085     // The transformed C for the fibre/sheet basis is C* = P^T C P.
00086     // We then compute T* = T*(C*), and then compute T = P T* P^T.
00087 
00088     ComputeTransformedDeformationTensor(rC, rInvC, C_transformed, invC_transformed);
00089 
00090     // Compute T*
00091 
00092     c_matrix<double,DIM,DIM> E = 0.5*(C_transformed - mIdentity);
00093 
00094     double QQ = 0;
00095     for (unsigned M=0; M<DIM; M++)
00096     {
00097         for (unsigned N=0; N<DIM; N++)
00098         {
00099             QQ += mB[M][N]*E(M,N)*E(M,N);
00100         }
00101     }
00102 
00103     double multiplier = mA*exp(QQ)/2;
00104     rDTdE.Zero();
00105 
00106     double J = sqrt(Determinant(rC));
00107 
00108     for (unsigned M=0; M<DIM; M++)
00109     {
00110         for (unsigned N=0; N<DIM; N++)
00111         {
00112             rT(M,N) = multiplier*mB[M][N]*E(M,N) + mCompressibilityParam * J*log(J)*invC_transformed(M,N);
00113 
00114             if (computeDTdE)
00115             {
00116                 for (unsigned P=0; P<DIM; P++)
00117                 {
00118                     for (unsigned Q=0; Q<DIM; Q++)
00119                     {
00120                         rDTdE(M,N,P,Q) =    multiplier * mB[M][N] * (M==P)*(N==Q)
00121                                          +  2*multiplier*mB[M][N]*mB[P][Q]*E(M,N)*E(P,Q)
00122                                          +  mCompressibilityParam * (J*log(J) + J) * invC_transformed(M,N) * invC_transformed(P,Q)
00123                                          -  mCompressibilityParam * 2*J*log(J) * invC_transformed(M,P) * invC_transformed(Q,N);
00124                     }
00125                 }
00126             }
00127         }
00128     }
00129 
00130     // Now do:   T = P T* P^T   and   dTdE_{MNPQ}  =  P_{Mm}P_{Nn}P_{Pp}P_{Qq} dT*dE*_{mnpq}
00131     this->TransformStressAndStressDerivative(rT, rDTdE, computeDTdE);
00132 }
00133 
00135 // Explicit instantiation
00137 
00138 template class CompressibleExponentialLaw<2>;
00139 template class CompressibleExponentialLaw<3>;
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