From 2260d903747179778b7dea86a01ca4f07d42a426 Mon Sep 17 00:00:00 2001
From: Jonathan Youett <youett@mi.fu-berlin.de>
Date: Fri, 29 Mar 2013 12:44:22 +0000
Subject: [PATCH] add functions that compute the nonlinear and linearised
strain tensors
[[Imported from SVN: r11276]]
---
dune/elasticity/common/elasticityhelpers.hh | 55 +++++++++++++++++++++
1 file changed, 55 insertions(+)
diff --git a/dune/elasticity/common/elasticityhelpers.hh b/dune/elasticity/common/elasticityhelpers.hh
index 49c2e1b..c5357b6 100644
--- a/dune/elasticity/common/elasticityhelpers.hh
+++ b/dune/elasticity/common/elasticityhelpers.hh
@@ -9,6 +9,61 @@ namespace Dune {
namespace Elasticity {
+ /** \brief Compute nonlinear strain tensor from a displacement gradient.
+ *
+ * \param grad The gradient of the direction in which the linearisation is computed.
+ * \param strain The tensor to store the strain in.
+ */
+ template <int dim>
+ void computeNonlinearStrain(const Dune::FieldMatrix<double, dim, dim>& grad, SymmetricTensor<dim>& strain) {
+ strain = 0;
+ for (int i=0; i<dim ; ++i) {
+ strain(i,i) +=grad[i][i];
+
+ for (int k=0;k<dim;++k)
+ strain(i,i) += 0.5*grad[k][i]*grad[k][i];
+
+ for (int j=i+1; j<dim; ++j) {
+ strain(i,j) += 0.5*(grad[i][j] + grad[j][i]);
+ for (int k=0;k<dim;++k)
+ strain(i,j) += 0.5*grad[k][i]*grad[k][j];
+ }
+ }
+ }
+
+ /** \brief Compute linearised strain at the identity from a given displacement gradient.
+ *
+ * \param grad The gradient of the direction in which the linearisation is computed.
+ * \param strain The tensor to store the strain in.
+ */
+ template <int dim>
+ void computeLinearisedStrain(const Dune::FieldMatrix<double, dim, dim>& grad, SymmetricTensor<dim>& strain) {
+ for (int i=0; i<dim ; ++i)
+ {
+ strain(i,i) = grad[i][i];
+ for (int j=i+1; j<dim; ++j)
+ strain(i,j) = 0.5*(grad[i][j] + grad[j][i]);
+ }
+ }
+
+
+ /** \brief Compute linearised strain at a prescribed configuration in the direction of a given displacement gradient.
+ *
+ * \param grad The gradient of the direction in which the linearisation is computed.
+ * \param conf The deformation gradient(!) of the configuration at which the linearisation is evaluated.
+ * \param strain The tensor to store the strain in.
+ */
+ template <int dim>
+ void computeLinearisedStrain(const Dune::FieldMatrix<double, dim, dim>& grad, const Dune::FieldMatrix<double, dim, dim>& conf,
+ SymmetricTensor<dim>& strain) {
+ strain = 0;
+ for (int i=0;i<dim; i++)
+ for (int j=i;j<dim;j++)
+ for (int k=0;k<dim;k++)
+ strain(i,j)+= grad[k][i]*conf[k][j]+conf[k][i]*grad[k][j];
+ strain *= 0.5;
+ }
+
/** \brief The penalty term \f$ \Gamma \f$ */
double Gamma(double x) {
return x*x - std::log(x);
--
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