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1. Tessellations in Topologically Interlocked Stereotomic Material Systems

   Williams, A; Siegmund, T (September 2018, Proceedings of the IUTAM Symposium Architectured Materials Mechanics)

   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/79 

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2. Chirality in topologically interlocked material systems

   https://doi.org/10.1016/j.mechmat.2024.104956  

   Kim, Dong Young; Siegmund, Thomas (April 2024, Mechanics of Materials)

   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. 

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

   https://doi.org/10.1115/1.4044025  

   Short, M.; Siegmund, T. (November 2019, Journal of Applied Mechanics)

   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. 

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4. ABAQUS Python Code for the Simulation of Topologically Interlocked Material Systems Based on Archimedean and Laves Tilings

   https://doi.org/10.4231/JBKY-JH21  

   Williams, Andrew; Siegmund, Thomas; Siegmund, Thomas (January 2020, Purdue University Research Repository)

   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. 

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5. ABAQUS Code for the Simulation of Wave propagation in a Row of Tetrahedra

   https://doi.org/10.4231/R0S6-0P69  

   Ballance, Tanner; Siegmund, Thomas; Siegmund, Thomas (January 2024, Purdue University Research Repository)

   This publication contains ABAQUS inp files supporting the publication Numerical study on wave propagation in a row of topologically interlocked tetrahedra in Granular Matter (2023), 25 (1) This study is concerned with the mechanics of wave propagation in a type of architectured, granular, material system. Specifically, we investigate wave propagation in a topologically interlocked material (TIM) system. TIM systems are assemblies of polyhedrons in which individual polyhedrons cannot be removed from the assembly without complete disassembly due to the geometric interlocking of the polyhedrons. The study employs an explicit finite element code to compute phase velocities, amplitude distributions, and wave patterns in a linear assembly of topologically interlocking tetrahedra. Tetrahedra are considered fully 3D linear elastic bodies interacting with neighboring tetrahedra by contact and friction. This publication contains the following inp files for use with the FE code ABAQUS: FullChainMu0V01Linear.inp -- A row of tetrahedra, constant contact stiffness, no friction, impact velocity 1.0 m/s. FullChainMu5V01Linear.inp -- A row of tetrahedra, constant contact stiffness, Coulomb friction with coefficient of friction 0.5, impact velocity 1.0 m/s. ExpAV01.inp -- A row of tetrahedra, variable contact stiffness, no friction, impact velocity 1.0 m/s. ExpBV01.inp -- A row of tetrahedra, variable contact stiffness, no friction, impact velocity 1.0 m/s. PartiallyFused.inp -- A row of tetrahedra with several tetrahedra fused together, constant contact stiffness, no friction, impact velocity 1.0 m/s. PartiallyFusedFric.inp -- A row of tetrahedra with several tetrahedra fused together, constant contact stiffness, Coulomb friction with coefficient of friction 0.5, impact velocity 1.0 m/s. 

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