Due to mechanical stress, bulk material is crushed and fines are produced. This can either be desired in comminution processes or undesired in conveying and storage processes. In this work a novel breakage model for the Discrete Element Method is presented to allow a prediction of the resulting particle size distribution after damaging events. The breakage model is based on a probabilistic particle replacement strategy. Depending on the load, the initial particle is replaced by a breakage pattern tessellated with the Voronoi algorithm. Replacement probabilities and breakage patterns follow results from breakage tests. In contrast to other replacement models, mass and volume remain constant. Initial particles are polyhedral and can be of any shape. Crushing processes with multiple breakage can be simulated. The computational scheme is described in detail. The model was verified and validated with trials of shatter tests and two conveying processes with blast furnace sinter from two different industrial partners.