## Benchmark UP3

### Uniaxial Extension (Anisotropic Case)

This is an extension of benchmark UP2 for the case of an arbitrary value of fiber angle $0\le \beta \le 2$  in case of the anisotropic Gent material. The uniaxial loading is set to value ${p}_{1}=-240\mathrm{kPa}$.

Boundary conditions at $x=0$:

##### Parameters

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

##### Theory

The theory yields two nonlinear algebraic equations, which are solved by means of the Newton method. For details see [Stembera, 2013].

##### FE Model

To discretize the bar we used $2×2×40=160$ BRICK60 elements.

##### Results

Fiber angle Theory femCalc (BRICK60)
$\beta \text{\hspace{0.17em}}\left[{}^{\circ }\right]$ $\phi \text{\hspace{0.17em}}\left[{}^{\circ }\right]$ ${u}_{x}\text{\hspace{0.17em}}\left[\mathrm{m}\right]$ ${u}_{x}\text{\hspace{0.17em}}\left[\mathrm{m}\right]$ $\text{Ratio}\text{\hspace{0.17em}}\left[\mathrm{-}\right]$
$90$ $0$ $0.1955$ $0.1961$ $1.003$
$60$ $30$ $0.2343$ $0.2349$ $1.003$
$30$ $60$ $0.2794$ $0.2800$ $1.002$
$0$ $90$ $0.2707$ $0.2714$ $1.003$