Dynamic fragmentation: Geometric approach

Abstract

Dynamic fragmentation is a complex and common phenomenon in nature and technological systems. The main task in fragmentation modeling is determination of the fragment size (or mass) distribution law. There are several approaches to the fragmentation problem – empirical, probabilistic, energetic, approach based on fracture mechanics, etc. In the present paper we consider a general approach based on the simple assumption of random geometric partition of a body, following early Lineau [1], Mott [2] and well-known Grady-Kipp work [3]. Starting from the Poisson distribution of fracture sites (points, lines or planes), size distribution laws are derived for 1D, 2D and 3D geometries. Geometric fragmentation models based on the Mott and Grady-Kipp approaches are discussed, as well as the model originated from the Voronoi diagrams. The results of presented models are compared with numerical simulations and experimental data, showing significant compatibility with certain limitations.