Fracture mechanics and complexity sciences – Part II. Complex behaviour emerging from simple nonlinear rules: Catastrophes and chaos

摘要

The so-called Complexity Sciences are a topic of fast growing interest inside the scientific community. Aim of this paper is to provide an insight into the role of complexity in the field of Materials Science and Fracture Mechanics. The paper is divided into two parts, which deal with the two opposite natural trends of composite systems: order and structure emerging from large, complicated systems and the route towards randomness and chaos arising from simple nonlinear rules. The former trend has been illustrated in the companion paper (Part I); on the other hand, this part will focus on the latter trend. The first example concerns the snap-back instabilities in the structural behaviour of composite structures, which are illustrated in the framework of Catastrophe Theory; the second application deals with the transition towards chaos in the dynamics of cracked beams.