SchmidCostaExponentialLaw2d.cpp

00001 /*
00002 
00003 Copyright (C) University of Oxford, 2005-2010
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 "SchmidCostaExponentialLaw2d.hpp"
00030 
00031 SchmidCostaExponentialLaw2d::SchmidCostaExponentialLaw2d()
00032 {
00033     mA = 0.221;    // kiloPascals, presumably, althought the paper doesn't say.
00034                    // gives results matching Pole-zero anyway.
00035 
00036     double bff = 42.5; // dimensionless
00037     double bfs = 11.0; // dimensionless
00038     double bss = 18.6; // dimensionless
00039 
00040     mB.resize(2);
00041     mB[0].resize(2);
00042     mB[1].resize(2);
00043 
00044     mB[0][0] = bff;
00045     mB[0][1] = bfs;
00046     mB[1][0] = bfs;
00047     mB[1][1] = bss;
00048 
00049     for (unsigned M=0; M<2; M++)
00050     {
00051         for (unsigned N=0; N<2; N++)
00052         {
00053             mIdentity(M,N) = M==N ? 1.0 : 0.0;
00054         }
00055     }
00056 
00057     mpChangeOfBasisMatrix = NULL;
00058 }
00059 
00060 void SchmidCostaExponentialLaw2d::ComputeStressAndStressDerivative(c_matrix<double,2,2>& rC,
00061                                                                    c_matrix<double,2,2>& rInvC,
00062                                                                    double                pressure,
00063                                                                    c_matrix<double,2,2>& rT,
00064                                                                    FourthOrderTensor<2>& rDTdE,
00065                                                                    bool                  computeDTdE)
00066 {
00067     static c_matrix<double,2,2> C_transformed;
00068     static c_matrix<double,2,2> invC_transformed;
00069 
00070     // The material law parameters are set up assuming the fibre direction is (1,0,0)
00071     // and sheet direction is (0,1,0), so we have to transform C,inv(C),and T.
00072     // Let P be the change-of-basis matrix P = (\mathbf{m}_f, \mathbf{m}_s, \mathbf{m}_n).
00073     // The transformed C for the fibre/sheet basis is C* = P^T C P.
00074     // We then compute T* = T*(C*), and then compute T = P T* P^T.
00075 
00076     if(mpChangeOfBasisMatrix)
00077     {
00078         // C* = P^T C P, and ditto inv(C)
00079         C_transformed = prod(trans(*mpChangeOfBasisMatrix),(c_matrix<double,2,2>)prod(rC,*mpChangeOfBasisMatrix));          // C*    = P^T C    P
00080         invC_transformed = prod(trans(*mpChangeOfBasisMatrix),(c_matrix<double,2,2>)prod(rInvC,*mpChangeOfBasisMatrix));   // invC* = P^T invC P
00081     }
00082     else
00083     {
00084         C_transformed = rC;
00085         invC_transformed = rInvC;
00086     }
00087 
00088     // compute T*
00089 
00090     c_matrix<double,2,2> E = 0.5*(C_transformed - mIdentity);
00091 
00092     double Q = 0;
00093     for (unsigned M=0; M<2; M++)
00094     {
00095         for (unsigned N=0; N<2; N++)
00096         {
00097             Q += mB[M][N]*E(M,N)*E(M,N);
00098         }
00099     }
00100 
00101     double multiplier = mA*exp(Q-1);
00102     rDTdE.Zero();
00103 
00104     for (unsigned M=0; M<2; M++)
00105     {
00106         for (unsigned N=0; N<2; N++)
00107         {
00108             rT(M,N) = multiplier*mB[M][N]*E(M,N) - pressure*invC_transformed(M,N);
00109 
00110             if (computeDTdE)
00111             {
00112                 //dTdE(M,N,M,N) = multiplier * mB[M][N];
00113                 for (unsigned P=0; P<2; P++)
00114                 {
00115                     for (unsigned Q=0; Q<2; Q++)
00116                     {
00117                         rDTdE(M,N,P,Q) =   multiplier * mB[M][N] * (M==P)*(N==Q)
00118                                         +  2*multiplier*mB[M][N]*mB[P][Q]*E(M,N)*E(P,Q)
00119                                         +  2*pressure*invC_transformed(M,P)*invC_transformed(Q,N);
00120                     }
00121                 }
00122             }
00123         }
00124     }
00125 
00126     // now do:   T = P T* P^T   and   dTdE_{MNPQ}  =  P_{Mm}P_{Nn}P_{Pp}P_{Qq} dT*dE*_{mnpq}
00127     if(mpChangeOfBasisMatrix)
00128     {
00129         static c_matrix<double,2,2> T_transformed_times_Ptrans;
00130         T_transformed_times_Ptrans = prod(rT, trans(*mpChangeOfBasisMatrix));
00131 
00132         rT = prod(*mpChangeOfBasisMatrix, T_transformed_times_Ptrans);  // T = P T* P^T
00133 
00134         // dTdE_{MNPQ}  =  P_{Mm}P_{Nn}P_{Pp}P_{Qq} dT*dE*_{mnpq}
00135         if (computeDTdE)
00136         {
00137             static FourthOrderTensor<2> temp;
00138             temp.SetAsProduct(rDTdE, *mpChangeOfBasisMatrix, 0);
00139             rDTdE.SetAsProduct(temp, *mpChangeOfBasisMatrix, 1);
00140             temp.SetAsProduct(rDTdE, *mpChangeOfBasisMatrix, 2);
00141             rDTdE.SetAsProduct(temp, *mpChangeOfBasisMatrix, 3);
00142         }
00143     }
00144 }
00145 
00146 double SchmidCostaExponentialLaw2d::GetA()
00147 {
00148     return mA;
00149 }
00150 
00151 std::vector<std::vector<double> > SchmidCostaExponentialLaw2d::GetB()
00152 {
00153     return mB;
00154 }
00155 
00156 double SchmidCostaExponentialLaw2d::GetZeroStrainPressure()
00157 {
00158     return 0.0;
00159 }

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