Department of Mathematics University of Haifa
Mathematics Club
Speaker: Prof. Alexei Kanel-Belov
Bar-Ilan University
Title: Interlocking of convex polyhedra:
towards a geometric theory of fragmented solids
Date: Tuesday, January 13, 2004
Place: Room 614 (old room 1621) in the Science & Education Building,
University of Haifa
(On 6th floor, across the street from the main building).
Time: 12:10 PM
Note: the talk will be given in English!
Abstract:
Consider a set of contacting convex figures in R^2. It is not
difficult to prove that one of these figures can be moved out of
the set by translation without disturbing others. Therefore, any
set of planar figures can be disassembled by moving all figures
one b one (as opposed to simple homothetic motion of the plane, which
automatically puts the figures out of contact with each other). One
may think that this statement holds for higher dimensions as well.
However, attempts to generalize it to R^3 have been unsuccessful. And
recently quite unexpectedly interlocking structures of convex bodies
were found such that every body was locked! These structures
cannot be disassembled by removing individual bodies one by one.
The author proposed a follows mechanical use of this effect. In a
small grain there is no room for cracks, and crack propagation
should be arrested on the boundary of the grain. On the other hand,
grains keep each other. So it is possible to get "materials without
crack propagation" and get new use of sparse materials, say ceramics.
Quite unexpectedly, such structures can be assembled with any
type of platonic polyhedra, and they have a geometric beauty. The
talk will be devoted to such structures. They may be interesting in
nanotechnology.
1. Gal'perin, G.A., 1985, Russian Math. Surveys, 40, 229.
2. Kanel, A. Ya., 2001, A story of an olympiad problem, Matematicheskoe
prosveshchenie, 3, No. 5, 207-208 (in Russian).
Dyskin, A.V., Y. Estrin, A.J. Kanel-Belov & E. Pasternak, 2001. A new
concept in design of materials and structures: Assemblies of interlocked
tetrahedron-shaped elements. Scripta Materialia, 44, 2689-2694.
Estrin, Y., A.V. Dyskin, E Pasternak, H.C. Khor & A J Kanel-Belov 2003.
Topological interlocking of protective tiles for Space Shuttle. Phil. Mag.
Letters, 83, 351-355.
Dyskin, A.V., Estrin, Y., Kanel-Belov, A.J. and Pasternak, E. 2003.
Topological interlocking of platonic solids: A way to new materials and
structures, Phil. Mag. Letters Vol. 83, No. 3, 197-203.
For further information, or to be put on our mailing list, contact:
David Blanc (tel. 8249758, room 604, e-mail blanc@math.haifa.ac.il)
or Anna Melnikov (tel. 8240054, room 611, e-mail anna@math.haifa.ac.il)
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Technion Math Net-2 (TECHMATH2)
Editor: Eddy Mayer-Wolf
Announcement from: David Blanc