Saturday, January 19, 2013

Topological interlocking structures

I recently came across an interesting paper done by a team of physicists and mathematicians titled The Concept of Topological Interlocking in Engineering  by AV Dyskin, Y Estrin, E. Pasternak, HC Khor andAJ Kanel-Belov of the Department of Civil Resource Engineering, the University of Western Australia, Australia; Institut fur Werkstoffkunde und Werkstofftechnik, Technische UniversitatClausthatl, Germany; and Unversity of Bremen, Germany (Materials Science and Engineering, Volume 31, Issue 6,August 12, 2011, pp.1189-1194).

The work described in this paper by this team is very similar to some of the work I have been conducting over the past 20 years or so.  First, they identify their inspiration as occurring in the biology of nature, as I have also done (see “Nature’s Masons” on this blog). 

Secondly, they describe how a structure assembled from their interlocking units is toughened, as it is resistant to crack propagation between adjacent interlocking units (as I have also described several times on this blog, e.g. “Harder, stronger, stiffer, tougher”). 

Third, they provide a rounded edge to their interlocking shapes, so as not to focus stress, as I have also described on this blog (see “The art of limits (and the limits of art”).

The authors point to the failure of thermal tiles on thespace shuttle Columbia as one example of how their concept of “topological interlocking” can be advantageous by providing a toughened structure held together by geometry alone; which is at the very heart of my own work.  The authors' system is comprised of parts interlocked with the concave features of one block interlocking with convex parts of another block, and vice-versa.  This is precisely how my dual-inverse mirror plane (dimp) arrangement works also. 

They assembled flat (planar) sections of structure using various polyhedral arrangements and tested these for strength.  They found that the resulting planar configurations could withstand significant stress tests, and furthermore that loss of one or more interlocking block did not necessarily result in failure of the structure.  Again, this is what I have been saying about my own system for years.

The work of this team is very interesting, and validates and substantiates much of what I have been saying for years.  Their system does lack a few of the advantages to be found in the designs I have developed.  First, their topological interlocking units create an undercut, or draft, or negative angle which cannot be readily released from a simple two-piece mold (unlike my system).  Secondly, their system is not capable of conjugate shearing in the same ease of manner which triangular shapes inherently allow.  Third, they build flat planar structures, and their system does not allow for a radial (spherical and cylindrical) structure as readily, as easily and as strongly as my system does (my system can also do flat planar structures).

I was delighted to see this work and realize that other teams of engineers share the same insight into the advantages inherent in a system comprised of interlocking unit shapes.


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