A full 3-D material stability analysis of a classical elasto-plastic medium through a linear perturbation approach

Abstract

In this paper, the linear perturbation theory is used to study material instability in a classical elasto-plastic model. In this framework, the well known Rice criterion of bifurcation into localized modes is found to be a limiting case corresponding to unbounded growth of perturbation. In the first part, derived expression of the critical plastic modulus is numerically plotted versus the spherical coordinates of the potential normal to the localization band in order to describe the whole space. In the second part, conditions of occurrence of the other types of instability are established, namely divergence and flutter types of instability, and modelling details influencing them checked. These conditions are also relative to the parameter of growth of perturbations which can be plotted versus the plastic modulus considered as the loading parameter. When several modes of instability are possible, an hierarchy is established.