From f0d7143851fb1902fff5649f31954c7e8ed35cf1 Mon Sep 17 00:00:00 2001 From: Andreas Dutzler Date: Wed, 27 Sep 2023 14:32:45 +0200 Subject: [PATCH] Update example_neohooke.md --- docs/examples/example_neohooke.md | 12 +++--------- 1 file changed, 3 insertions(+), 9 deletions(-) diff --git a/docs/examples/example_neohooke.md b/docs/examples/example_neohooke.md index 32dd18b..c302b3f 100644 --- a/docs/examples/example_neohooke.md +++ b/docs/examples/example_neohooke.md @@ -12,17 +12,11 @@ This is a very basic example on how to implement a nearly-incompressible version The strain energy density function per unit reference volume is additively splitted into an isochoric and volumetric contribution, see Eq. $$\eqref{eq:psi}$$. 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), see Eq. $$\eqref{eq:psi-nh}$$. $$ -\begin{equation} - \psi(\mathbf{C}) = \psi(\mathbf{\hat C}) + U(J) - \label{eq:psi} -\end{equation} -$$ - -$$ -\begin{equation} +\begin{align} + \psi(\mathbf{C}) = \psi(\mathbf{\hat C}) + U(J) \nonumber \\ \psi(\mathbf{C}) = \text{C}_{10} (\text{I}_\mathbf{\hat C}-3) + \frac{\kappa}{2} (J-1)^2 \label{eq:psi-nh} -\end{equation} +\end{align} $$ We get the second Piola-Kirchhoff stress with the derivative of the strain energy density function per unit reference volume with respect to one half of the right Cauchy-Green deformation tensor as shown in Eq. $$\eqref{eq:pk2-nh}$$.