Design of Flat Vaults with Topological Interlocking Solids

This paper investigates the principles that regulate complex stereotomic constructions as a starting point for the design of a new two-dimensional floor structure based on the principles of TIM (Topological Interlocking Materials). These interlocking systems use an assembly of identical Platonic solids which, due to the mutual bearing between adjacent units and the presence of a global peripheral constraint, lock together to form pure geometric shapes. This type of structure offers several advantages such as a high energy dissipation capacity and tolerance towards localised failure, which has made it a popular research topic over the last 30 years. The current research project includes a case study of an assembly of interlocking cubes to create a “flat vault”. The resulting vault design features a striking appearance and its geometry may be manipulated to achieve different two-dimensional solutions, provided certain geometric conditions necessary for the stability of the system are followed.

Floor Slabs Made from Topologically Interlocking Prefabs of Small Size

In this article, the issue of constructing slabs from unified small elements, which are connected together into a stable structure by topological interlocking, is considered. The state-of-the-art methods in this topic are presented, as well as the results of the author’s original research. The author has expanded the well-known concept of shaping square slabs from square prefabs by the aggregation of triangular and hexagonal slabs from prefabs in the shape of equilateral triangles, regular hexagons, and rhombuses. Each of the slabs can be modelled with upper and bottom surfaces, either both relief, both smooth, or one relief and the other smooth. The slabs can be modelled in different ways, and each one results in intriguing floor and ceiling patterns. All of the slabs can co-operate with grillages made of steel beams, which can be constructed before filling with the prefabricated slab, which is a novel idea. Reversing the assembly order, as compared to that used in the literature, is made possible thanks to division of these elements into parts, to form a keystone which is inserted into the slab as a final step.

Scaling, Growth, and Size Effects on the Mechanical Behavior of a Topologically Interlocking Material Based on Tetrahedra Elements

The present study is concerned with the deformation response of an architectured material system, i.e., a 2D-material system created by the topological interlocking assembly of polyhedra. Following the analogy of granular crystals, the internal load transfer is considered along well-defined force networks, and internal equivalent truss structures are used to describe the deformation response. Closed-form relationships for stiffness, strength, and toughness of the topologically interlocked material system are presented. The model is validated relative to direct numerical simulation results. The topologically interlocked material system characteristics are compared with those of monolithic plates. The architectured material system outperforms equivalent size monolithic plates in terms of toughness for nearly all possible ratios of modulus to the strength of the material used to make the building blocks and plate, respectively. In addition, topologically interlocked material systems are shown to provide better strength characteristics than a monolithic system for low strength solids.