Topologically interlocking material (TIM) systems are constrained assemblies of building blocks with geometry such that individual unit elements cannot be removed from the assembly without complete disassembly. These assemblies can bear load in the absence of adhesive bonds. TIM systems with scutoid‐shaped building blocks are investigated. Scutoids are prism‐like shapes with two polygonal faces and contain vertices on the lateral sides which enable geometric interlocking. The quasi‐static mechanical behavior of two types of scutoid‐based TIM systems is investigated and compared to reference tetrahedron‐based TIM systems. TIM systems are realized as plate‐type assemblies and a central point‐force load is considered. The computational analysis is conducted with the finite‐element method. Scutoid‐based TIM systems are found, in aggregate, to match or exceed the performance of the tetrahedra‐based systems. It is documented that TIM systems in general, but scutoid‐based systems in particular, emerge to possess chiral characteristics. The combination of building block symmetry and assembly symmetry together determines the type of chirality in the mechanical response. Experimental data validates the computational finding. In summary, considering scutoids as building blocks for load‐carrying TIM assemblies opens the pathway to new classes of mechanical behavior in systems where structure and microstructure strongly interact with each other.
more » « less- Award ID(s):
- 1662177
- NSF-PAR ID:
- 10499819
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Advanced Engineering Materials
- ISSN:
- 1438-1656
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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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
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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 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.more » « less
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Topologically Interlocked Material systems are a class of architectured materials. TIM systems are assembled from individual building blocks and are confined by an external frame. In particular, 2D, plate-type assemblies are considered. This publication contains files for the numerical analysis of the mechanical behavior of TIM systems through the use of finite element analysis. ABAQUS model files (inp format) for the study of the chiral/achiral response are provided. Files chirality_s1_in.inp are for type I square assemblies. n=3,5,7,9 Files chirality_s2_in.inp are for type II square assemblies. n=4,6,8,10 Files chirality_h1_in.inp are for type I hexagon assemblies. n=2,3,4,5 Files chirality_h2_in.inp are for type II hexagon assemblies. n=2,3,4,5 File chirality_s1i5_center_dissection.inp is for an assembly with a dissection of the central tile of type I square assembly with n=5. File chirality_s2i6_center_dissection.inp is for an assembly with a dissection of the central tile of type II square assembly with n=6. File chirality_s1i5_center_surrounding_dissection.inp is for an assembly with dissections of the tiles surrounding the center tile of type I square assembly with n=5. File chirality_h1i3_center_dissection.inp is for an assembly with a dissection of the central tile of type I hexagon assembly with n=3. File chirality_h2i3_center_dissection.inp is for an assembly with a dissection of the central tile of type II hexagon assembly with n=3. File chirality_h1i3_center_surrounding_dissection.inp is for an assembly with dissections of the tiles surrounding the center tile of type I hexagon assembly with n=3.more » « less
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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
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This publication provides files for the finite element simulation of the mechanical behavior of a set of topologically interlocked material (TIM) systems. Files are to be executed with the FE code ABAQUS (TM), Simulia Inc., or need a file translator to be used by other codes if needed. Files are provided for even (i=10) and odd (i=11) numbered square assemblies of (i x i) blocks confined by a rigid frame and subjected to a transverse displacement load at the assembly center. The following files are provided: The simulations are executed as explicit dynamic simulations with a mass-scale approach to extract the quasi-static response. Building blocks are linear elastic and interact with neighbors by contact and friction. The following files are provided BR_tet_i6.inp: File for a TIM system constructed from regular, truncated tetrahedra shaped building blocks. An assembly of 6 x 6 blocks. This is the reference model 1. BR_tet_i8.inp: File for a TIM system constructed from regular, truncated tetrahedra shaped building blocks. An assembly of 8 x 8 blocks. This is the reference model 1. BR_tet_i10.inp: File for a TIM system constructed from regular, truncated tetrahedra shaped building blocks. An assembly of 10 x 10 blocks. This is the reference model 1. BR_tet_i12.inp: File for a TIM system constructed from regular, truncated tetrahedra shaped building blocks. An assembly of 12 x 12 blocks. This is the reference model 1. BR_tet_i5.inp: File for a TIM system constructed from regular, truncated tetrahedra shaped building blocks. An assembly of 5 x 5 blocks. This is the reference model 2. BR_tet_i7.inp: File for a TIM system constructed from regular, truncated tetrahedra shaped building blocks. An assembly of 7 x 7 blocks. This is the reference model 2. BR_tet_i9.inp: File for a TIM system constructed from regular, truncated tetrahedra shaped building blocks. An assembly of 9 x 9 blocks. This is the reference model 2. BR_tet_i11.inp: File for a TIM system constructed from regular, truncated tetrahedra shaped building blocks. An assembly of 11 x 11 blocks. This is the reference model 2. BT1_tet_i6.inp: File for a TIM system constructed from single-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 6 x 6 blocks. BT1_tet_i8.inp: File for a TIM system constructed from single-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 8 x 8 blocks. BT1_tet_i10.inp: File for a TIM system constructed from single-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 10 x 10 blocks. BT1_tet_i12.inp: File for a TIM system constructed from single-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 12 x 12 blocks. BT1_tet_i5.inp: File for a TIM system constructed from single-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 5 x 5 blocks. BT1_tet_i7.inp: File for a TIM system constructed from single-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 7 x 7 blocks. BT1_tet_i9.inp: File for a TIM system constructed from single-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 9 x 9 blocks. BT1_tet_i11.inp: File for a TIM system constructed from single-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 11 x 11 blocks. BT2_tet_i6.inp: File for a TIM system constructed from double-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 6 x 6 blocks. BT2_tet_i8.inp: File for a TIM system constructed from double-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 8 x 8 blocks. BT2_tet_i10.inp: File for a TIM system constructed from double-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 10 x 10 blocks. BT2_tet_i12.inp: File for a TIM system constructed from double-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 12 x 12 blocks. BT2_tet_i5.inp: File for a TIM system constructed from double-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 5 x 5 blocks. BT2_tet_i7.inp: File for a TIM system constructed from double-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 7 x 7 blocks. BT2_tet_i9.inp: File for a TIM system constructed from double-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 9 x 9 blocks. BT2_tet_i11.inp: File for a TIM system constructed from double-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 11 x 11 blocks. BT1_tet_i6_0_34.inp: File for a TIM system constructed from single-skewed, truncated tetrahedra shaped building blocks. Skew angle is 17 degree. An assembly of 6 x 6 blocks. BT1_tet_i8_0_34.inp: File for a TIM system constructed from single-skewed, truncated tetrahedra shaped building blocks. Skew angle is 17 degree. An assembly of 8 x 8 blocks. BT1_tet_i10_0_34.inp: File for a TIM system constructed from single-skewed, truncated tetrahedra shaped building blocks. Skew angle is 17 degree. An assembly of 10 x 10 blocks. BT1_tet_i12_0_34.inp: File for a TIM system constructed from single-skewed, truncated tetrahedra shaped building blocks. Skew angle is 17 degree. An assembly of 12 x 12 blocks. BT1_tet_i5_0_34.inp: File for a TIM system constructed from single-skewed, truncated tetrahedra shaped building blocks. Skew angle is 17 degree. An assembly of 5 x 5 blocks. BT1_tet_i7_0_34.inp: File for a TIM system constructed from single-skewed, truncated tetrahedra shaped building blocks. Skew angle is 17 degree. An assembly of 7 x 7 blocks. BT1_tet_i9_0_34.inp: File for a TIM system constructed from single-skewed, truncated tetrahedra shaped building blocks. Skew angle is 17 degree. An assembly of 9 x 9 blocks. BT1_tet_i11_0_34.inp: File for a TIM system constructed from single-skewed, truncated tetrahedra shaped building blocks. Skew angle is 17 degree. An assembly of 11 x 11 blocks. BT2_tet_i6_0_34.inp: File for a TIM system constructed from double-skewed, truncated tetrahedra shaped building blocks. Skew angle is 17 degree. An assembly of 6 x 6 blocks. BT2_tet_i8_0_34.inp: File for a TIM system constructed from double-skewed, truncated tetrahedra shaped building blocks. Skew angle is 17 degree. An assembly of 8 x 8 blocks. BT2_tet_i10_0_34.inp: File for a TIM system constructed from double-skewed, truncated tetrahedra shaped building blocks. Skew angle is 17 degree. An assembly of 10 x 10 blocks. BT2_tet_i12_0_34.inp: File for a TIM system constructed from double-skewed, truncated tetrahedra shaped building blocks. Skew angle is 17 degree. An assembly of 12 x 12 blocks. BT2_tet_i5_0_34.inp: File for a TIM system constructed from double-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 5 x 5 blocks. BT2_tet_i7_0_34.inp: File for a TIM system constructed from double-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 7 x 7 blocks. BT2_tet_i9_0_34.inp: File for a TIM system constructed from double-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 9 x 9 blocks. BT2_tet_i11_0_34.inp: File for a TIM system constructed from double-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 11 x 11 blocks.more » « less