Fracture mechanics and complexity sciences – Part I. Order emerging from complex systems: Fractals and renormalization group

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 heterogeneous and random systems and the route towards instability and chaos arising from simple nonlinear rules. In this paper (Part I), the former trend will be illustrated by means of two fracture mechanics applications, whereas the latter trend will be treated in the companion paper. The first application concerns the occurrence of self-similarity and fractal patterns in material damage and deformation of heterogeneous materials, and the apparent scaling of the nominal mechanical properties of disordered materials. The second application deals with criticality in the acoustic emissions of damaged structures and with scaling in the time-to-failure.