Instability of a Bell Constrained Cylindrical Lhbe Under end Thrust-Part 2: Examples, Thin Libe Analysis

Abstract

This paper is a continuation of an earlier work that analyzed the elastic stability of a homogeneous, isotropic, Bell constrained cylindrical tube of uniform cross section subjected to axial end thrust. Here, the focus is on some applications. Four kinds of material models are considered: a simple hyperelastic Bell material model, Bell's empirical material model, and two new theoretical models, one being similar to a wellknown biomaterial model. Numerical results for a thick-walled tube and a solid bar are illustrated graphically The thin-walled tube problem, however, is studied analytically for a general class of Bell constrained materials, and the critical stretch and corresponding critical load are derived. The load result is shown to be consistent with the classical solution obtained by Southwell and Dean.