Benchmark UP5

Cylinder Torsion

Let us test the forces required to sustain a torsion of a cylinder. The cylinder is supposed to have length l, diameter D and to be made of the Neo-Hookean material. The cylinder radius is denoted by a=D2.

Image depicts meshed cylinder under torsinal loading (dimensions).
Parameters

D = 1 m l = 1 m κ = 107 Pa μ = 280709 Pa

Theory

The cylinder lower base is fully fixed and the cylinder upper base is subjected to the surface load according to the theoretical formula given in [Taber, 2004]

σzz = -2θ2 ra r˜ Ψiso I1 |J=1 dr˜ σθz = 2θr Ψiso I1 |J=1

After exerting coresponding surface loading on the upper base of the cylinder, a value of θ is numerically measured and compared with its assumed value.

Results

Theory femCalc (BRICK24) femCalc (BRICK24)
K=4, N=960 K=6, N=3240
θ[rad] θ[rad] Ratio[-] θ[rad] Ratio[-]
0.1 0.1007 1.007 0.0997 0.997
0.2 0.2019 1.010 0.1998 1.001
0.3 0.3035 1.012 0.3003 1.001
0.4 0.4053 1.013 0.4014 1.003
0.5 0.5072 1.014 0.5026 1.005
0.6 0.6082 1.014 0.6034 1.006
0.7 0.7071 1.010 0.7024 1.003
0.8 0.8021 1.003 0.7975 0.997
0.9 0.8912 0.990 0.8864 0.985
1.0 0.9723 0.972 0.9671 0.967