IN PARTIAL FOLFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN MECHANICAL ENGINEERING

This is a study of a bifurcation problem for a solid circular cylinder which is made of a particular class of homogeneous, isotropic, compressible elastic material. The surface of the cylinder is subjected to a purely radial stretch X (>I) and the cylinder is assumed to be in a state of plane strain. One solution to this problem, for all values of A, is that of a pure homogeneous stretching in which the cylinder expands radially. However, a second (singular) solution bifurcates from this homogeneous solution at a critical value of the stretch X (=Acr) at which the homogeneous solution becomes unstable. For X>Xcr, a circular cylindrical cavity forms at the axis of the cylinder. In this study we have two purposes. The first is to determine an explicit analytical solution to the bifurcation problem for a broad class of com~ressible elastic materials. The second is to examine the dependerce of various physical quantities (such as the critical stres