Statistics of structure within solid fragments studied by 2D simulation

Abstract

A strongly fragmented two-dimensional medium was generated by a large number (103–104) of randomly thrown linear cracks. Various properties of fragments (e.g., number, size, shape, perimeter length, number of sides, and internal structure) were analyzed by computational geometry using a plane sweep algorithm. Asymptotically, for high crack density, the simulated fragment sizes follow the Mott distribution formula (cumulative number decreases exponentially with linear fragment size). Fragment structure, due to dangling or fully internal cracks, is identified with internal damage. The magnitude of damage as function of crack density is obtained by computation and analysis and is shown to reach a constant value asymptotically. By our results, a blasting operation leading to crack growth increases the ratio of small fragments in relation to larger ones.