Eur. Phys. J. B (2015) 88: 91
https://doi.org/10.1140/epjb/e2015-50703-8

Regular Article

A continuum framework for mechanics of fractal materials II: elastic stress fields ahead of cracks in a fractal medium

Grupo “Mecánica Fractal”, ESIME-Zacatenco, Instituto Politécnico Nacional, México D.F. 07738, Mexico

^a e-mail: abalankin@ipn.mx

Received: 12 October 2014
Received in final form: 18 December 2014
Published online: 8 April 2015

Abstract

This paper is devoted to the crack mechanics in heterogeneous materials with fractal (micro-)structures. Specifically, stress concentrations ahead of straight notches and self-affine cracks in fractal media are studied within a fractal continuum framework. A model of fractal continuum with fractal boundaries accounting for the metric, topological, and connectivity properties of the material microstructure and crack is employed for homogenization of crack problems in fractal media. It is found that the fractal nature of material heterogeneity can either delay or assist the crack initiation and propagation, depending on the interplay between metric and topological properties of the fractal domain.