add methods to compute the linearization of the determinante of a deformation gradient

[[Imported from SVN: r11286]]

dune/elasticity/common/elasticityhelpers.hh

@@ -123,7 +123,39 @@ namespace Dune {
                 - (Delta<(p+1)%3,(q-1)%3>::delta+u[(p+1)%3][(q-1)%3])
                 * (Delta<(p+2)%3,(q-2)%3>::delta+u[(p+2)%3][(q-2)%3]);
         }
+         
+        /** \brief Compute linearization of the determinant of a deformation gradient
+         *
+         *  \param u The displacement gradient(!) at which the determinant is evaluated
+         */
+        void linearizedDefDet(const Dune::FieldMatrix<double,3,3>& u, Dune::FieldMatrix<double,3,3>& linDet) {
+
+            linDet = 0;
+            for (int i=0; i<2; i++)                       
+                for (int j=(i+1)%3; j<3; j++) {
+                    int k=(j+1)%3 + (j+1)/3;          
+                    linDet[i][j] = u[j][k]*u[k][i] - u[j][i]*(1+u[k][k]);
+                    linDet[j][i] = u[k][j]*u[i][k] - u[i][j]*(1+u[k][k]);
+            }    
+
+            // the diagonal parts
+            for (int i=0; i<3; i++)
+                linDet[i][i] = (u[(i+1)%3][(i+1)%3]+1)*(u[(i+2)%3][(i+2)%3]+1)-u[(i+1)%3][(i+2)%3]*u[(i+2)%3][(i+1)%3]
+        }
         
+        /** \brief Compute linearization of the determinant of a deformation gradient
+         *
+         *  \param u The displacement gradient(!) at which the determinant is evaluated
+         */
+        void linearizedDefDet(const Dune::FieldMatrix<double,2,2>& u, Dune::FieldMatrix<double,2,2>& linDet) {
+
+            linDet = 0;
+            for (int i=0; i<2; i++) {
+                linDet[i][i] = 1+u[(i+1)%2][(i+1)%2];
+                linDet[i][(i+1)%2] = -u[(i+1)%2][i];
+            }
+        }
+
         // \parder {det I + u}{ u_pq }
         template <int p, int q>
         double det_du_tmpl(const Dune::FieldMatrix<double,2,2>& u) {