characteristics of the grinding materials. During the cataracting motion where the charge material inside a mill follows a parabolic path [@data], most of the materials are ground as hard balls fall back onto them. There is particular interest in the net energy required to achieve a certain size reduction and the the energy distribution of the fragments during the grinding process. The efficiency of the mills could be controlled if the breakage characteristics of the grinding materials were better understood. Our current work can provide some valuable information for the modernization of the mill design.

Model
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In order to study fragmentation of granular solids, we performed molecular dynamic (MD) simulations in two dimensions. To better capture the complex structure of a real solid, we used randomly generated convex polygons that interact with each other elastically. The model consists of three major parts, namely, the construction of a Voronoi cellular structure, the introduction of the elastic behavior, and finally the breaking of the solid. This section gives a detailed overview of these three steps.

In order to take into account the complex structure of the granular solid, we use randomly generated convex polygons, [*i.e.*]{} we divide the solid into grains 