On the bifurcation and postbifurcation analysis of elastic-plastic solids under general prebifurcation conditions

Abstract

work we have studied the bifurcation and postbifurcation of elastic-plastic solids whose behavior near the critical point could not be idealized as hypoelastic and thus the "hypoelastic comparison solid" concept of R. Hill's theory is no longer applicable. First a simple continuous model is considered in order to illustrate the different possibilities in the stability behavior of the structures considered here. Next, a general three-dimensional stability analysis for a broad class of rate independent elastic-plastic solids is presented. It is found that for all the constitutive theories considered and for all possible prebifurcation solutions, the bifurcation functional is a simple generalization of Hill's. A completely different postbifurcation analysis is needed, however, in the case where the "hypoelastic comparison solid" concept cannot be used.