Stress Concentration in a Rubber Sheet Under Axially Symmetric Stretching

[+] Author and Article Information
Wei Hsuin Yang

Department of Engineering Mechanics, The University of Michigan, Ann Arbor, Mich.

J. Appl. Mech 34(4), 942-946 (Dec 01, 1967) (5 pages) doi:10.1115/1.3607860 History: Received December 28, 1966; Revised June 14, 1967; Online September 14, 2011


A class of axially symmetric problems, concerning a highly elastic, circular rubber sheet with (a) a centered circular hole, (b) a rigid circular inclusion under outward radial loading at outer boundary, and (c) a rigid outer boundary and a concentric hole under inward radial loading around the hole, is solved. The solution of (a) has been obtained by Rivlin and Thomas [1] by solving simultaneously a set of differential equations numerically. In this paper, their equations are reduced to a single second-order differential equation governing the deformation function ρ(r). This is further reduced to two decoupled first-order equations after introducing the phase plane (λ1 – λ2 plane). The solutions are obtained conveniently in the phase plane by Picard’s method and by straightforward numerical integration.

Copyright © 1967 by ASME
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