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Two-dimensional model for binary fragmentation process with random system of forces, random stopping and material resistance

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  • Hernandez, Gonzalo

Abstract

This work presents the numerical results obtained from large-scale parallel distributed simulations of a self-similar model for two-dimensional discrete in time and continuous in space binary fragmentation. Its main characteristics are: (1) continuous material; (2) uniform and independent random distribution of the net forces, denoted by fx and fy, that produce the fracture; (3) these net forces act at random positions of the fragments and generate the fracture following a maximum criterion; (4) the fragmentation process has the property that every fragment fracture stops at each time step with an uniform probability p; (5) the material presents an uniform resistance r to the fracture process. Through a numerical study was obtained an approximate power law behavior for the small fragments size distribution for a wide range of the main parameters of the model: the stopping probability p and the resistance r. The visualizations of the model resemble real systems. The approximate power law distribution is a non-trivial result, which reproduces empirical results of some highly energetic fracture processes.

Suggested Citation

  • Hernandez, Gonzalo, 2003. "Two-dimensional model for binary fragmentation process with random system of forces, random stopping and material resistance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 323(C), pages 1-8.
    • Handle: RePEc:eee:phsmap:v:323:y:2003:i:c:p:1-8
    DOI: 10.1016/S0378-4371(03)00032-3
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    Cited by:

    1. Benjamin J Finley & Kalevi Kilkki, 2014. "Exploring Empirical Rank-Frequency Distributions Longitudinally through a Simple Stochastic Process," PLOS ONE, Public Library of Science, vol. 9(4), pages 1-14, April.
    2. Hernandez, Gonzalo & Salinas, Luis & Avila, Andres, 2006. "n-ary fragmentation model with nearest point flaw and maximal net force fracture," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 565-572.

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