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Topologically interlocking material (TIM) systems are composed of convex polyhedral units placed such that building blocks restrict each other’s movement. Here, TIM tubes are considered as rolled monolayers of such assemblies. The deformation response of these assembled tubes under diametrical loading is considered. This investigation employs experiments on additively manufactured physical realizations and finite element analysis with contact interactions. The internal load transfer in topologically interlocking tubes is rationalized through inspection of the distribution of minimum principal stress. A thrust-line (TL) model for the deformation of topologically interlocking tubes is established. The model approximates the deformation behavior of the assembled tubes as the response of a collection of Mises trusses aligned with paths of maximum load transfer in the system. The predictions obtained with the TL-model are in good agreement with results of finite element models. Accounting for sliding between building blocks in the TL-model yields a predicted response more similar to experimental results with additively manufactured tubes. 

A set of three input files for ABAQUS models to simulate the response of tubes built from topologically interlocked building blocks. 

This data set contains STL files to use for 3D printing of tubes made of topologically interlocked building blocks. 

LEGOs are one of the most popular toys and are known to be useful as instructional tools in STEM education. In this work, we used LEGO structures to demonstrate the energetic size effect on structural strength. Many material's fexural strength decreases with increasing structural size. We seek to demonstrate this effect in LEGO beams. Fracture experiments were performed using 3-point bend beams built of 2 X 4 LEGO blocks in a periodic staggered arrangement. LEGO wheels were used as rollers on either ends of the specimens which were weight compensated by adding counterweights. [1] Specimens were loaded by hanging weights at their midspan and the maximum sustained load was recorded. Specimens with a built-in defect (crack) of half specimen height were considered. Beam height was varied from two to 32 LEGO blocks while keeping the in-plane aspect ratio constant. The specimen thickness was kept constant at one LEGO block. Slow-motion videos and sound recordings of fractures were captured to determine how the fracture originated and propagated through the specimen. Flexural stress was calculated based on nominal specimen dimensions and fracture toughness was calculated following ASTM E-399 standard expressions from Srawley (1976). [2] The results demonstrate that the LEGO beams indeed exhibit a size effect on strength. For smaller beams the Uexural strength is higher than for larger beams. The dependence of strength on size is similar to that of Bažant’s size effect law [3] . Initiation of failure occurs consistently at the built-in defect. The staggered arrangement causes persistent crack branching which is more pronounced in larger specimens. The results also show that the apparent fracture toughness increases as the specimen size decreases. Further ongoing investigations consider the effects of the initial crack length on the size effect and the fracture response. The present work demonstrates that LEGO structures can serve as an instructional tool. We demonstrate principles of non-linear elastic fracture mechanics and highlight the importance of material microstructure (architecture) in fracture response. The experimental method is reproducible in a classroom setting without the need for complex facilities. This work was partially supported by the National Science Foundation (NSF) under the award #1662177 and the School of Mechanical Engineering at Purdue University. The authors acknowledge the support of Dr. Thomas Siegmund and Glynn Gallaway. [1] Khalilpour, S., BaniAsad, E. and Dehestani, M., 2019. A review on concrete fracture energy and effective parameters. Cement and Concrete research, 120, pp.294-321. [2] Srawley, J.E., 1976, January. Wide range stress intensity factor expressions for ASTM E 399 standard fracture toughness specimens. In Conf. of Am. Soc. for Testing and Mater., Committee E-24 (No. E-8654). [3] Bažant, Z.P., 1999. Size effect on structural strength: a review. Archive of applied Mechanics, 69(9), pp.703-725. 

A set of three input files for ABAQUS models to simulate the response of interlocked irregular square tilings subjected to displacement loading. 

Abstract 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. 

Topologically interlocked materials (TIMs) are material systems consisting of one or more repeating unit blocks assembled in a planar configuration such that each block is fully constrained geometrically by its neighbours. The assembly is terminated by a frame that constrains the outermost blocks. The resulting plate-like structure does not use any type of adhesive or fastener between blocks but is capable of carrying transverse loads. These material systems are advantageous due to their potential attractive combination of strength, toughness, and damage tolerance as compared to monolithic plates, especially when using lower strength materials. TIMs are damage tolerant due to the fact that cracks in any single block cannot propagate to neighbouring blocks. Many configurations of TIMs have been conceptualized in the past, particularly in architecture, but less work has been done to understand the mechanics of such varied assembly architectures. This work seeks to expand our knowledge of how TIM architecture is related to TIM mechanics. The present study considers TIMs created from the Archimedean and Laves tessellations. Each tessellation is configured as a TIM by projecting each edge of a tile at alternating angles from the normal to the tiling plane. For each tiling, multiple symmetries exist depending on where the frame is placed relative to the tiling. Six unique tilings and their multiple symmetries and load directions were considered, resulting in 19 unique TIM configurations. All TIM configurations were realized with identical equivalent overall assembly dimensions. The radius of the inscribed circle of the square and hexagon frames were the same, as well as the thickness of the assemblies. The tilings were scaled to possess the similar same number of building blocks within the frame. Finite element models were created for each configuration and subjected to two load types under quasi-static conditions: a prescribed displacement applied at the center of the assembly, and by a gravity load. The force deflection response of all TIM structures was found to be similar to that of a Mises truss, comprised of an initial positive stiffness followed by a period of negative stiffness until failure of the assembly. This response is indeed related to the internal working of load transfer in TIMs. Owing to the granular type character of the TIM assembly, the stress distribution follows a force-network. The key findings of this study are: • The load transfer in TIMs follows from force networks and the geometry of the force network is associated with the dual tessellation of the respective TIM system. • In TIMs based on Laves tessellations (centered around a vertex of the tiling rather than the center of a tile), displayed chirality and exerted a moment normal to the tile plane as they were loaded. • TIMs resulting from tessellations with more than one unique tile, such as squares and octagons, are asymmetric along the normal to the tile plane causing a dependence of the load response to the direction of the transverse load. Work is underway to transform these findings into general rules allowing for a predictive relationship between material architecture and mechanical response of TIM systems. This material is based upon work supported by the National Science Foundation under Grant No. 1662177.