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# Conformal Contact Between a Rubber Band and Rigid Cylinders

[+] Author and Article Information
Takuya Morimoto

Graduate School of Science and Engineering, Yamagata University, Jonan 4-3-16, Yonezawa, Yamagata 992-8510, Japanmorimoto@yz.yamagata-u.ac.jp

Hiroshi Iizuka

Graduate School of Science and Engineering, Yamagata University, Jonan 4-3-16, Yonezawa, Yamagata 992-8510, Japanh-iizuka@yz.yamagata-u.ac.jp

J. Appl. Mech 79(4), 044504 (May 09, 2012) (4 pages) doi:10.1115/1.4005566 History: Received June 06, 2011; Revised September 26, 2011; Posted January 31, 2012; Published May 09, 2012; Online May 09, 2012

## Abstract

We consider a conformal contact problem between a rubber band and rigid cylinders that involves geometrical and material nonlinearities. The rubber band is assumed to be incompressible, neo-Hookean rubber. From the geometry and elasticity of the band, we present simple formulas to estimate the force–stretch relations and the contact pressure distributions on the cylinder. We show that the theoretical results are in good agreement with those of the finite element analysis when the rubber band is thin enough to be negligible to the bending stiffness. This verifies that the theory can effectively take into account both the material and geometrical nonlinearities of the band under the present conditions.

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## Figures

Figure 4

Contact pressure distribution along the arc length s with various stretches λ =  {1.11,1.42,1.74,2.05} under the fixed values of r/R=  0.4 and h0 /R=  0.04. The closed and open symbols denote the FEA results with friction (μ =  0.5) and without friction (μ =  0), respectively.

Figure 3

(a) Reaction force-displacement responses with various cylinder radii r=  {20,30,40} [mm]. (b) Collapsed response between the dimensionless reaction force P¯0 and the stretch λ with various dimensionless band thicknesses r/R=  {0.2,0.3,0.4}. The closed and open symbols denote the FEA results with friction (μ =  0.5) and without friction (μ =  0), respectively.

Figure 2

(a) Reaction force-displacement responses with various band thicknesses h0  = { 4,8,20,40} [mm]. (b) Collapsed response between the dimensionless reaction force P¯ and the initial stretch λ with various dimensionless band thicknesses h0 /R. The closed and open symbols denote the FEA results with friction (μ =  0.5) and without friction (μ =  0), respectively.

Figure 1

Schematic configurations of static contact between a rubber band and a rigid pulley. Three configurations are shown in this figure: Initial configuration (I) is shows that the undeformed rubber band is initially touched with both the left-side and right-side cylinders at the inside. Then, the right-side cylinder is moved to the outward direction of the center of the band radius R until δ = δ 0 , which is configuration (II). Finally, the band is stretched with the amount of displacement δ * by the additional movement of the right-side cylinder.

## Errata

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