Instability of a hollow rubber-like cylinder under initial stress

Abstract In this paper, the problem of a rubber-like hollow circular cylinder subjected to a finite uniform initial stress in the axial direction is considered. An infinitesimal axial-symmetric deformation is then superposed on the prestressed hollow cylinder and the axial-symmetric instability of the cylinder caused by the initial stress is investigated. The analysis is based on the general theory of mechanics of incremental deformations established by Biot[ll]. It is shown that introducing a displacement potential function, φ, the field equation previously derived by Sun[15] is obtained. The solution of this field equation is shown to be given in terms of modified Bessel functions of the first and the second kind in r and trigonometric functions of z . By satisfying the homogeneous boundary conditions, the characteristic equation governing stability of the hollow cylinder is obtained. Numerical results examining the critical initial stress as a function of the slenderness ratio and the geometry of the cylinder are presented and discussed.