Dynamical systems in material instability of cracked medium

Abstract

The paper deals with rate-dependent and rate-independent smeared crack models by considering them as a dynamical system. In such approach one of the most important mode of material instability, the strain localization can be studied as a static bifurcation of a steady-state solution. Then the uniqueness of the solution is lost at the loss of (Liapunov) stability. In terms of the theory of dynamical system for a rate-independent crack model this phenomenon happens in an ungeneric structurally unstable way. In the paper we show that by adding a rate-dependent term the system of the basic equations regains structural stability.