A continuum model of interlocking structural systems

Abstract

Masonry systems made of interlocking square-cut stones have long been studied by mathematicians and architects. It so happens that, under appropriate boundary conditions, ashlars interlock, and a stable structure results. Recently, the idea that new masonry-like materials can be designed on the basis of this archetypal principle has been put forward and applications have been proposed under the name of topological interlocking materials.

In this paper, a mathematical model is proposed, that describes these materials as a special class of continua with microstructure. The system is viewed as a continuous body, the material elements of which are ashlar blocks endowed with an interaction structure based, to within certain approximations, on their interlocking geometry. The case of rigid ashlars with purely plastic interactions is developed in detail.