Topological interlocking of platonic solids: A way to new materials and structures

Mathematics under the Microscope

“…Remarkably, one can place congruent Platonic solids in an interlocked regular pattern [278,279,280]; see Figure 10 form of, say, octahedral crystals, and, moreover, can be manufactured only as relatively small crystals, the possibility of an interlocked regular pattern leads to the idea of making composite materials from separate, but interlocked, crystals. There is another benefit in this approach: failure of materials is in many cases associated with propagation of macroscopic fractures.…”

“…Since many hard crystals have octahedral shape, this pattern is of serious practical interest. After Dyskin et al [280] Spatial configurations of interlocked octahedra are paradoxical and beautiful. But it is Noskov's expansion procedure (see Page 235) which is the true marvel: you can reverse it and make it into a manufacturing process for the mass production of new composite materials: place crystals in appropriately positioned nests in a low density foamy material (something like styrofoam), at comfortable distances one from another, like glass Christmas tree decorations in their protective packaging.…”

Mechanics of Multiscale Energy Dissipation in Topologically Interlocked Materials-11.1 STIR

“…These unique characteristics of TIMs provide unique properties that can be utilize to create adaptive and configurable structures to harsh conditions such as random and harmonic vibrations, thermal loads, repetitive shocks and acoustic attenuation. For example, Dyskin et al [4,5,7,9,10] introduced the general concept of TIM, and demonstrated the requirements for basic elements to assemble a TIM tile.…”

“…Proposed by Glickman [8] with the name of G-Block for the reduction of sub-structure and diminished maintenance cost for paving system, expanded, generalized and termed with the current name by Dyskin et al [4,9,10], TIMs can be considered as novel mechanical meta-materials as these derive their unique properties not from composition but structure. Forces and energy can only be transmitted through the contact surfaces; accordingly, there are no tensile forces developed when TIMs carry loads.…”

“…In particular, the study is concerned with one class of segmented hybrids, Topologically Interlocked Material assemblies, TIMs. In a TIM system, each individual unit element is topologically confined by its neighbors due to the oblique angles of the basic unit elements; therefore no binders are necessary to maintain the integrity of the assembly [4][5][6][7][8].…”