## Benchmark UP2

### Uniaxial Extension

A bar of length $l$, depth and width ${z}_{0}$, fixed at one side in the same way as in the benchmark UP1 (transverse deformation is not resctricted) and axially loaded on the other side by pressure ${p}_{1}=-480\mathrm{kPa}$.

Four materials were tested:

• Neo-Hookean
• Mooney-Rivlin
• Gent
• Anisotropic Gent

Boundary conditions at $x=0$:

##### Parameters

$\begin{array}{ccc}\hfill l& \hfill =\hfill & 1\mathrm{m}\hfill \\ \hfill {z}_{0}& \hfill =\hfill & 0.05\mathrm{m}\hfill \\ \hfill \kappa & \hfill =\hfill & {10}^{8}\mathrm{Pa}\hfill \\ \hfill \mu & \hfill =\hfill & 280709\mathrm{Pa}\hfill \\ \hfill {J}_{m}& \hfill =\hfill & 1.1575\hfill \\ \hfill {\mu }^{\mathrm{aniso}}& \hfill =\hfill & 26000\mathrm{Pa}\hfill \\ \hfill {J}_{m}^{\mathrm{aniso}}& \hfill =\hfill & 1.044\hfill \\ \hfill \beta & \hfill =\hfill & \frac{\pi }{2}\hfill \end{array}$

##### Theory

Deflection is given by formula:

${\sigma }_{11}=2\frac{\partial {\Psi }_{\text{iso}}}{\partial {I}_{1}}{|}_{J=1}\left({\lambda }^{2}-\frac{1}{\lambda }\right)+2\frac{\partial {\Psi }_{\text{iso}}}{\partial {I}_{2}}{|}_{J=1}\left(\lambda -\frac{1}{\mathrm{{\lambda }^{2}}}\right)+2\left[\frac{\partial {\Psi }_{\text{iso}}}{\partial {J}_{4}}{|}_{J=1}\right]\left(\lambda \right)\cdot {\lambda }^{2}$
##### FE Model

In ANSYS the problem is solved using $2×2×40=160$ HYPER58 elements. In femCalc the same number of BRICK60 elements was used.

##### Results

Material Theory ANSYS (HYPER58) femCalc (BRICK60)
Type ${u}_{}\text{\hspace{0.17em}}\left[\mathrm{m}\right]$ ${u}_{}\text{\hspace{0.17em}}\left[\mathrm{m}\right]$ Ratio ${u}_{}\text{\hspace{0.17em}}\left[\mathrm{m}\right]$ Ratio
Neo-Hookean $0.5365$ $0.5381$ $1.003$ $0.5383$ $1.003$
Mooney-Rivlin $0.6541$ $0.6559$ $1.003$ $0.6562$ $1.003$
Gent $0.3813$ $-$ $-$ $0.3825$ $1.003$
Anisotropic Gent $0.3047$ $-$ $-$ $0.3057$ $1.003$