Mass-velocity correlation in impact induced fragmentation of heterogeneous solids

We study the impact fragmentation of disorderedsolids by means of a discrete element model focusing on thevelocity and mass-velocity correlation of fragments. Simula-tions are performed with plate-like objects varying the platethickness and the impact velocity in broad ranges. Dependingon the impact velocity the breakup process has two differentoutcomes: at low velocities the sample gets only damaged,to achieve fragmentation, where no large residues survive,the impact velocity has to surpass a critical value. In thefragmented phase the velocity components of fragments arepower law distributed with a stretched exponential cutoff,where the impact velocity and plate thickness mainly controlthe standard deviation of the distributions. Mass velocity cor-relation is only pointed out for thin plates, while it disappearsfor three-dimensional bulk samples. In the damage phase ofthin plates the mass and velocity of fragments proved to bestrongly correlated, however, in the fragmented phase corre-lation occurs in the vicinity of the critical velocity and it islimited to the large fragments only. The correlation functiondecays as a power law with different exponents for small andlarge fragments in good agreement with recent experimentalfindings. We show that the mass-velocity correlation origi-nates from the spatial dependence of the mass and velocityof pieces inside the fragmenting body