Post-bifurcation behavior in the plastic range

In the first part of the paper a simple model is used to introduce some of the analytical and physical features of post-bifurcation phenomena in continuous elastic-plastic systems. An analysis is presented for the initial post-bifurcation behavior of a class of elastic-plastic solids subject to loads characterized by a single load parameter. Bifurcations which occur at the lowest possible load are singled out for attention. The theory makes connection with Hill's general theory of bifurcation and uniqueness in elastic-plastic solids and Koiter's general approach to the initial post-buckling behavior of conservative elastic systems. Buckling of an axially compressed column in the plastic range is used to illustrate the theory.