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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

$\begin{array}{ccc}\hfill l& \hfill =\hfill & 1\mathrm{m}\hfill \\ \hfill z_0& \hfill =\hfill & 0.05\mathrm{m}\hfill \\ \hfill \kappa & \hfill =\hfill & {10}^8\mathrm{Pa}\hfill \\ \hfill \mu & \hfill =\hfill & 280709\mathrm{Pa}\hfill \\ \hfill J_{\mathrm{m}}& \hfill =\hfill & 1.1575\hfill \\ \hfill {\mu }^{\mathrm{aniso}}& \hfill =\hfill & 26000\mathrm{Pa}\hfill \\ \hfill J_{\mathrm{m}}^{\mathrm{aniso}}& \hfill =\hfill & 1.044\hfill \\ \hfill \beta & \hfill =\hfill & \frac{\pi }{2}\hfill \end{array}$

Theory

Deflection is given by formula:

FE Model

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

Results