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
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
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
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).
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
Scienceticker.de , in the
Focus of Physical Review
Nature milestones and even in
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.
A movie of the simulation of the explosion of a
thin shell and of a
thick shell give insight into the dynamics of
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:
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:
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
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.