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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

$\begin{array}{ccc}\hfill l& \hfill =\hfill & 1\mathrm{m}\hfill \\ \hfill z_0& \hfill =\hfill & 0.05\mathrm{m}\hfill \\ \hfill \kappa & \hfill =\hfill & {10}^8\mathrm{Pa}\hfill \\ \hfill \mu & \hfill =\hfill & 280709\mathrm{Pa}\hfill \\ \hfill J_{\mathrm{m}}& \hfill =\hfill & 1.1575\hfill \\ \hfill {\mu }^{\mathrm{aniso}}& \hfill =\hfill & 26000\mathrm{Pa}\hfill \\ \hfill J_{\mathrm{m}}^{\mathrm{aniso}}& \hfill =\hfill & 1.044\hfill \end{array}$

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 $2\times 2\times 40=160$ BRICK60 elements.

Results