Theoretical analysis of the particle fragmentation process requires a proper choice of the breakage functions. In this work we construct the breakage functions on a basis of numerical modelling. Four types of the breakage functions are obtained. We demonstrate that if the average number of fragments at a single breakage event is larger than two, then the breakage kernel is asymmetric. Also a possibility of double-peaked kernels is shown. (C) 2012 Elsevier Ltd. All rights reserved.