Most natural fragmentation processes generate a yet unexplained power law distribution in the fragment size distribution. With Gonzalo HernŠndez we got some insight into the mechanism leading to this power law through a simple stochastic model ( published in Physica A 215 , 420 (1995)).


Much more realistic but also computer intensive calculations were performed with FerenÁ Kun imulating the smashing of a wall due to the impact of a projectile , the explosion of a solid block and the debris produced by the collision of two fragile objects (see our paper (Comp. Meth. in Appl. Mech. and Eng., 138 , 3-18 (1996))). The figure shows three snapshots of the collision between two discs simulated by FerenÁ Kun. For more detail see our paper (Int.J.Mod.Phys.C. 7 , 837 (1996)). Particularly interesting was the discovery that there exists a critical energy above which one obtains fragments of all sizes as published in Physical Reviev E Vol.59, p.2623 (1999). With Bhupalendra Behera we continued working on this field by studying the dependence of the fragmentation transition on collision angles and impact velocities as shown in our recent paper which was published in Jour.Phys.Cond.Mat. Vol. 17, p. S2439 (2005) and the distribution of fragments close to the critical fragmentation energy as described in our preprint submitted to EPJE. Fragmentation in different geometries was also studied with Gian Antonio d'Addetta as published in Comp.Ass. Mech. and Eng. Sci., Vol.6, p.385-402 (1999).

With Jan Astrom we simulated quasi-static fragmentation. A packing of discs is compressed uniaxially and a disc breaks in several fragments. The paper is published in Eur.Phys.J. B, Vol. 5, p. 551 (1998). The resulting configurations after several breaking iterations depend strongly on the local fracture mechanisms. We also studied fragmentation in shear bands as discussed in our paper published in Europ. Phys. J. E, Vol.4, p.273-279 (2001).

Photo Our last contribution to the understanding of fragmentation is the explosion and the impact against a hard wall of shells. The classical natural shell is a the shell of an egg. We exploded hollow eggs injecting hydrogen and measured the fragment size distribution using a scanner. The power-law distribution matches very well with simulations using our discrete element technique and the exponent is different from that of 2d or 3d bulk fragmentation. These results have been published in a paper in Phys.Rev.Lett. Vol. 93, 035504 (2004) and more details can be found in a paper published in Phys.Rev.E, Vol.71, 016108 (2005). There have also been several articles in journals on this issue like the following in Der Spiegel from July 19, 2004 and several presentations in the TV, the , , in the Focus of Physical Review and in Nature milestones and even in russian . Photos of an exploding and an impacting egg can be seen to the right and the corresponding simulations of spherical shells give a fragmentation pattern are shown below in green on orange for two different energies. Photo A movie of the simulation of the explosion of a thin shell and of a thick shell give insight into the dynamics of fragmentation.

Below you see some high precision fotos of the eggs-plosion made in the lab of Knut Jurgen Malløy in Oslo with a camera of 15.000 images per second:

Photo Photo Photo

You see tensile cracks starting at the bottom of the egg and the resulting fragments later been broken through bending in the orthogonal direction.

Below you see some high precision fotos of glass balls (from Christmas trees) with 30.000 images per second:

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As opposed to the eggs here rupture is much faster. Many cracks start from a single point which we call "hotspots" and form long fragments which later burst in pieces due to collisions.

Below a foto with the egg-team (Ferenç Kun and Falk Wittel):


With Gabor Timar, Jan Bloemer and FerenÁ Kun we simulated what happens to fragmentation when the material has plastic yield under shear. Interestingly the universality class is changed dramatically as we showed with experiments and simulations in our paper in Phys.Rev.Lett. Vol. 104, 095502 (2010). The comparison of an fragmented polypropylene sphere and the simulation was also exhibited on the cover shown here.


Recently we also simulated the fragmentation of multicrystaline grains as described in our paper .

You can also download a talk that I gave in several occasions on the subject.