skip to main content

Title: Tiling Patterns and the Mechanical Properties of Topologically Interlocked Materials
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 more » 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. « less
Authors:
Award ID(s):
1662177
Publication Date:
NSF-PAR ID:
10121875
Journal Name:
Proceedings of the 56th Annual Technical Meeting of the Society of Engineering Science
Sponsoring Org:
National Science Foundation
More Like this
  1. This research presents an experimental program executed to understand the strength and stiffness properties of hollow built-up glass compression members that are intended for use in the modular construction of all glass, compression-dominant, shell-type structures. The proposed compression-dominant geometric form has been developed using the methods of form finding and three-dimensional graphical statics. This research takes the first steps towards a new construction methodology for glass structures where individual hollow glass units (HGU) are assembled using an interlocking system to form large, compression-dominant, shell-type structures, thereby exploiting the high compression strength of glass. In this study, an individual HGU hasmore »an elongated hexagonal prism shape and consists of two deck plates, two long side plates, and four short side plates, as is shown in Figure 1. Connections between glass plates are made using a two-sided transparent structural adhesive tape. The test matrix includes four HGUs, two each fabricated with 1 mm and 2 mm thick adhesive tape. All samples are dimensioned 64 cm on the long axis of symmetry, 51 cm on the short axis of symmetry, and are 10 cm in width. Glass plates are all 10 mm thick annealed float glass with geometric fabrication done using 5-axis abrasive water jet cutting. HGU assembly is accomplished using 3D printed truing clips and results in a rigid three-dimensional glass frame. Testing was done with the HGU oriented such that load was introduced on the short side edges of the two deck plates, resulting in an asymmetric load-support condition. A soft interface material was used between the HGU and steel plates of the hydraulic actuator and support for the purpose of avoiding premature cracking from local stress concentrations on the glass edges at the load and support locations. Force was applied in displacement control at 0.25 mm/minute with a full array of displacement and strain sensors. Test results for load vs. center deck plate transverse deflection are shown in Figure 2. All samples failed explosively by flexural buckling with no premature cracking on the load and support edges of the deck plates. Strain and deformation data clearly show the presence of second-order behavior resulting from bending deformation perpendicular to the plane of the deck plates. In general, linear axial behavior transitions to nonlinear second-order behavior, with increasing rates in deflection and strain growth, ultimately ending in glass fracture on the tension surfaces of the buckled deck plates. The failure resulted in near-complete disintegration of the deck plates, but with no observable cracking in any side plates and a secure connection on all adhesive tape. Results of the experimental program clearly demonstrate the feasibility of using HGUs for modular construction of compression dominant all-glass shell-type structures. This method of construction can significantly reduce the self-weight of the structure, and it will inspire the use of sustainable materials in the construction of efficient structures.« less
  2. 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 weightsmore »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.« less
  3. Kachanov, M. ; Rajagopal, K.R. (Ed.)
    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 assembledmore »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.« less
  4. Topologically interlocked stereotomic material (TISM) systems are load-carrying assemblies of unit elements interacting by contact and friction. Past research on these material systems has demonstrated attractive mechanical response characteristics, including damage tolerance, impact resistance, adaptive property control, tuneable acoustical characteristics, as well as disassembly and reuse. In this work, we aim to expand the range of topologically interlocked material systems for which such response is found. The theory of tessellations is the underpinning to create new material systems. We present a comparative study on the deflection response to transverse loading for two underlying tessellations and boundary conditions. Williams, A., &more »Siegmund, T. (2018). Tesselations and Percolations in Topologically Interlocked Stereotomic Material Systems. In T. Siegmund & F. Barthelat (Eds.) Proceedings of the IUTAM Symposium Architectured Materials Mechanics, September 17-19, 2018 , Chicago, IL: Purdue University Libraries Scholarly Publishing Services, 2018. https://docs.lib.purdue.edu/iutam/presentations/abstracts/79« less
  5. 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 sizemore »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.« less