Fragmentation is often of interest to scientists and engineers because it affects many systems. In particle technology, it can be desirable or something to be avoided. For example, particle fracture is desired when trying to reduce particle size; but it is unwanted in solid catalysts in a fluidized bed.

In modeling particulate processes, it is necessary to account for particle breakage. At the macro-scale, researchers often use breakage distribution functions to describe the particle size distribution produced by a parent particle breaking. Many of the breakage distribution functions are empirical. At the micro-scale, researchers often model the fracture of an individual particle using fundamental fracture mechanics. The fracture mechanics are often represented by a branching crack model. However, the fracture mechanics are not usually connected to the breakage distribution functions.

This work discusses the connection between a branching crack model and the resulting macro-scale breakage distribution functions. More specifically, a branching crack model is used to develop bivariate breakage functions that include both size and shape. The development and the resulting functions will be presented.