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

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.