Benchmark UP2

Uniaxial Extension

A bar of length l, depth and width z0, 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 p1=-480 kPa.

Four materials were tested:

  • Neo-Hookean
  • Mooney-Rivlin
  • Gent
  • Anisotropic Gent
Image depicts cantilever dimensions, loading and boundary conditions.

Boundary conditions at x=0:

Image depicts cantilever boundary conditions.
Parameters

l = 1 m z0 = 0.05 m κ = 108 Pa μ = 280709 Pa Jm = 1.1575 μaniso = 26000 Pa Jmaniso = 1.044 β = π2

Theory

Deflection is given by formula:

σ11 =2 Ψiso I1 |J=1 (λ2-1λ) +2 Ψiso I2 |J=1 (λ-1λ2) +2 [ Ψiso J4 |J=1 ] (λ) λ2
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 umax [m] umax [m] Ratio umax [m] 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