Fragmentation of a circular disc by projectiles

The fragmentation of a two-dimensional circular disc by lateral impact is investigated using a cell model of brittle solid. The disc is composed of numerous unbreakable randomly shaped convex polygons connected together by simple elastic beams that break when bent or stretched beyond a certain limit. We found that the fragment mass distribution follows a power law with an exponent close to 2 independent of the system size. We also observed two types of crack patterns: radial cracks starting from the impact point and cracks perpendicular to the radial ones. Simulations revealed that there exists a critical projectile energy, above which the target breaks into numerous smaller pieces, and below which it suffers only damage in the form of cracks. Our theoretical results are in a reasonable agreement with recent experimental findings on the fragmentation of discs.