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n-ary fragmentation model with nearest point flaw and maximal net force fracture

Abstract:

A n-ary fragmentation model is introduced as a generalization of Ref. [G. Hernandez, Two-dimensional model for binary fragmentation process with random system of forces, random stopping and material resistance, Physica A 323 (1) (2003) 1-8]. Its main assumptions are: Continuous bi-dimensional material; Uniform and independent random distribution of the net forces (fx, fy); Every fragment fracture stops with constant probability p. Furthermore, the material has q random point flaws that interact with the maximal net forces to produce the fracture. By medium-scale simulations, it was obtained an approximate power law for the fragment size distribution with an exponent in the range [1.01, 1.15]. The simulations show close resemblance to actual fragmentation of brittle materials. © 2006 Elsevier B.V. All rights reserved.