From b59599cda45de5187c28d31ca6eefa7ea4e43958 Mon Sep 17 00:00:00 2001 From: Andreas Dutzler Date: Wed, 27 Sep 2023 10:12:14 +0200 Subject: [PATCH] Update example_neohooke.md --- docs/examples/example_neohooke.md | 11 ++++++++--- 1 file changed, 8 insertions(+), 3 deletions(-) diff --git a/docs/examples/example_neohooke.md b/docs/examples/example_neohooke.md index b603069..a2ae761 100644 --- a/docs/examples/example_neohooke.md +++ b/docs/examples/example_neohooke.md @@ -9,9 +9,14 @@ parent: Examples This is a very basic example on how to implement a nearly-incompressible version of the Neo-Hookean material model in a commercial FEM package (HYPELA2 for Marc). As no special two- or three-field variational principle is used in this example, it is not suitable for nearly-incompressible material behaviour. Otherwise the elements tend to show excessive volumetric locking during deformation and hence, wrong results are calculated. -The strain energy density function per unit reference volume is additively splitted into an isochoric and volumetric contribution. The first one is assumed to be proportional to the first invariant of the isochoric part of the right Cauchy-Green deformation tensor whereas the volumetric part is only a function of the volumetric ratio (the determinant of the deformation gradient). - -$$ \psi(\mathbf{C}) = \psi(\mathbf{\hat C}) + U(J) $$ +The strain energy density function per unit reference volume is additively splitted into an isochoric and volumetric contribution, see $$\eqref{eq:psi}$$. The first one is assumed to be proportional to the first invariant of the isochoric part of the right Cauchy-Green deformation tensor whereas the volumetric part is only a function of the volumetric ratio (the determinant of the deformation gradient). + +$$ +\begin{equation} +\psi(\mathbf{C}) = \psi(\mathbf{\hat C}) + U(J) +\label{eq:psi} +\end{equation} +$$