From 7a1ddb37307b40f7ef87940b34ff2b21e66a9324 Mon Sep 17 00:00:00 2001
From: Jonathan Youett <youett@mi.fu-berlin.de>
Date: Tue, 16 Apr 2013 14:50:47 +0000
Subject: [PATCH] add methods to compute the linearization of the determinante
of a deformation gradient
[[Imported from SVN: r11286]]
---
dune/elasticity/common/elasticityhelpers.hh | 32 +++++++++++++++++++++
1 file changed, 32 insertions(+)
diff --git a/dune/elasticity/common/elasticityhelpers.hh b/dune/elasticity/common/elasticityhelpers.hh
index c5357b6..f083430 100644
--- a/dune/elasticity/common/elasticityhelpers.hh
+++ b/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) {
--
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