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

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.