Plastic bifurcation and postbifurcation analysis for generalized standard continua

Abstract

The present work is concerned with the bifurcation and postbifurcation analysis of a class of rate independent plasticity models obeying Hill's maximum dissipation principle. A variational inequality approach, which differs from the classical formulation of the plastic bifurcation problem, is employed. The rate n bifurcation problem is formulated and sufficient conditions for uniqueness of the corresponding boundary value problem are given. A connection is made with Hill's nonbifurcation criterion. In addition. the issue of the postbifurcation behavior of the solid is addressed in this more general context showing the possibility of angular as well as smooth bifurcations of rate n > 1.Finally an example, capable of exhibiting both an angular as well as a smooth bifurcation is analysed using the general formulation derived in this work. The presentation is concluded with some comments and comparisons of the present methodology with the classical approach.