Computations and Mechanics of Convex Interlocking

Interdisciplinary Areas: Future Manufacturing

Project Description

Convex solids of specific shape can be arranged in a planar tiling such that they cannot be extracted or pushed into a void underneath the tiling. Note that no adhesives or fasteners of any kind are used. Examples include anti-prisms and all Platonic polyhedra. Prior published work has shown such systems to possess interesting mechanical behavior and multifunctional properties, and realizations exist in architectural floor and wall coverings, and in mechanical engineering systems for thermal control or battery systems packaging. To-date, a planar tiling must be enclosed in a frame so as to block lateral motion of tiles.
We propose research into nonplanar tiling, such as cylinders and hemispheres. The core question is how to assign the role of the enclosing frame of a planar tiling to the geometric shape. For example, in a cylindrical tiling part of a frame is obviated by the closed rings. Only a top and bottom lid should be necessary. Similarly, hemispheric tiling should topologically require no frame, just a foundation.
By executing this research we aim to create new multifunctional structural and material systems.

Start Date

Spring 2019

Postdoc Qualifications

The successful candidate will have expertise in geometric modeling and computations, ideally in computer-aided design (CAD) and finite element analysis. S/he will be fluent in algorithm design and analysis, to the extent of devising superior computational strategies and understanding and defending the choices. Mathematical maturity is expected.  


Thomas Siegmund,, School of Mechanical Engineering,

Christoph Hoffmann,, Computer Science 


1. C. Khor, A. Dyskin, E. Pasternak, Y. Estrin and A. Kanel-Belov, "Integrity and fracture of plate-like assemblies of topologically interlocked elements," Structural Integrity and Fracture: Proceedings of the International Conference, SIF 2002, pp. 449-456, 25-28 September 2002. 

2. S. Khandelwal, T. Siegmund, R. Cipra and J. Bolton, "Transverse loading of cellular topologically interlocked materials," International Journal of Solids and Structures, vol. 49, no. 18, pp. 2394-2403, 15 September 2012. 

3. S. Khandelwal, Hybrid and smart Topologically Interlocking Materials, vol. 145, Open Access Dissertations, 2013. 

4. O. Tessmann, "Topological Interlocking Assemblies," in Proceedings of the 30th eCAADe Conference, Czech Technical University in Prague, 2012. 

5. M. Weizmann, O. Amir and Y. J. Grobman, "Topological interlocking in buildings: A case for the design and construction of floors," Automation in Construction, vol. 72, no. 1, pp. 18-25, December 2016.