An official website of the United States government
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.
more »
« less
ABAQUS Python Code for the Simulation of Topologically Interlocked Material Systems Based on Archimedean and Laves Tilings
A set of six python scripts that parametrically generate ABAQUS models to simulate the response of topologically interlocked material systems based on the Archimedean and Laves tilings subjected to body force and displacement loading. These scripts were created to conduct research for a thesis in fulfillment of a Master of Science in Mechanical Engineering degree at Purdue University titled "Load Response of Topologically Interlocked Material Systems - Archimedean and Laves Tilings." There is one file for each of the [44], [3.6.3.6], [3.4.6.4], [36], (4.82), and (4.6.12) tilings. Many parameters can be altered including specifications for the symmetry condition of the frame, the load type and direction, the block dimensions, and the number of blocks. Additionally, there are parameters for the material properties, mesh density, simulation settings, etc. A gap may also be added between blocks to enable 3D printing of the entire assembly.
more »
« less
- Award ID(s):
- 1662177
- PAR ID:
- 10531683
- Publisher / Repository:
- Purdue University Research Repository
- Date Published:
- Subject(s) / Keyword(s):
- Tessellations Topologically Interlocked Material Systems Finite Element Analysis
- Format(s):
- Medium: X
- Location:
- Purdue University Research Repository
- Right(s):
- CC0 1.0 Universal
- Institution:
- Purdue University
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
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.more » « less
-
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., & 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/79more » « less
-
The present study focuses on the mechanical chirality in plate-type topologically interlocked material systems. Topologically interlocked material (TIM) systems are a class of dense architectured materials for which the mechanical response emerges from the elastic behavior of the building blocks and the contact-frictions interactions between the blocks. The resulting mechanical behavior is strongly non-linear due to the stability-instability characteristics of the internal load transfer pattern. Two tessellations are considered (square and hexagonal) and patches from each are used as templates. While individual building blocks are achiral, chirality emerges from the assembly pattern. The measure of \textit{microstructure circulation} is introduced to identify the geometric chirality of TIM systems. TIM systems identified as geometrically chiral are demonstrated to possess mechanical chiral response with a force-torque coupling under transverse mechanical loading of the TIM plate. The chiral length is found to be constant during the elastic response, yet size-dependent. During nonlinear deformation, the chiral length scale increases significantly and again exhibits a strong size dependence. The principle of dissection is introduced to transform non-chiral TIM systems into chiral ones. In the linear deformation regime, the framework of chiral elasticity is shown to be applicable. In the non-linear deformation regime, chirality is found to strongly affect the mechanical behavior more significantly than in the linear regime. Experiments on selected TIM systems validate key findings of the main computational study with the finite element method.more » « less
-
Topologically interlocked stereotomic material systems are load-carrying assemblies of unit elements interacting by contact and friction. This contribution summarizes research on such material systems in a variety of configurations based on tessellation geometry and percolation, and it considers external rigid confined, external flexible confined, internal flexible confined, as well as considers the unit elements as solids (elastic and elastic-brittle) or shells (elastic), and under consideration of a range of assembly geometries. Siegmund, T. (2018). Topologically Interlocked Material Systems: From a Material Design Concept to Properties. 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/70more » « less
