Equilibrium Paths of Polygonally Damaging Structures Part Two: One-Dimensional Example for Nonsmooth Damage and Localization

In the first part of the paper, stability analysis of nonlinearly inelastic damaging structures is shown by applying polygonal approximation for the nonlinear material functions. The basis of the nonsmooth stability analysis together with a lot of numerical illustrations has originally been laid down in the papers of M. Kurutz (1989, 1993a, 1993b, 1995). In the first part of this paper, the theoretical bases of the nonsmooth damage and localization instabilities of structures having polygonal stress-strain diagrams are presented. In the second part, the numerical illustrations are shown. The presented example aims to follow the famous historical example of Shanley (1947), related to the elasto-plastic behaviour of the Euler-column. By using a very simple mechanical model of the problem, the damage behaviour of the plastic hinges of the buckled state can be analysed.