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.
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The present study focuses on the mechanical chirality in platetype 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 contactfrictions interactions between the blocks. The resulting mechanical behavior is strongly nonlinear due to the stabilityinstability 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 forcetorque coupling under transverse mechanical loading of the TIM plate. The chiral length is found to be constant during the elastic response, yet sizedependent. During nonlinear deformation, the chiral length scale increases significantly and again exhibits a strong size dependence. The principle of dissection is introduced to transform nonchiral TIM systems into chiral ones. In the linear deformation regime, the framework of chiral elasticity is shown to be applicable. In the nonlinear 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 » « lessFree, publiclyaccessible full text available April 1, 2025

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 massscale approach to extract the quasistatic 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 singleskewed, 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 singleskewed, 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 singleskewed, 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 singleskewed, 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 singleskewed, 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 singleskewed, 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 singleskewed, 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 singleskewed, 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 doubleskewed, 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 doubleskewed, 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 doubleskewed, 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 doubleskewed, 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 doubleskewed, 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 doubleskewed, 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 doubleskewed, 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 doubleskewed, 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 singleskewed, 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 singleskewed, 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 singleskewed, 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 singleskewed, 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 singleskewed, 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 singleskewed, 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 singleskewed, 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 singleskewed, 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 doubleskewed, 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 doubleskewed, 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 doubleskewed, 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 doubleskewed, 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 doubleskewed, 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 doubleskewed, 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 doubleskewed, 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 doubleskewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 11 x 11 blocks.more » « less

A series of files for the execution of finite element simulations of topologically interlocked assemblies are provided and can be executed with the finite element code ABAQUS (or similar). In all files the following structure is present:  For each part of the assembly (frame, indenter, building block), a definition of nodes (*node) and sets of nodes (*nset), elements (*element) and set of elements (*elset) is provided.  Instances of parts are defined an placed in the assembly at position according to the assembly plan.  Parts frame and indenter are defined as rigid bodies (*rigid body) . Building blocks as linear elastic (*elastic).  Boundary conditions and constraints are defined (*boundary)  Surfaces (*surface), surface behavior (*surface behavior) and contact interactions (*contact) are given.  A mass scaled explicit solution is used (*dynamic, explicit)  Computed values are recorded (*node output, *energy output, *element output) ABAQUS inp file for a 6 by 6 assembly of hexagonal scutoids, coefficient of friction 0.4: HexScutoid6x6mu4.inp ABAQUS inp file for a 6 by 6 assembly of hexagonal scutoids, all building blocks fused to a monolithic system: HexScutoid6x6mu4_fused.inp ABAQUS inp file for a 7 by 7 assembly of hexagonal scutoids, coefficient of friction 0.4: HexScutoid6x6mu4.inp ABAQUS inp file for a 6 by 6 assembly of pentagonal scutoids, coefficient of friction 0.4: PentagonScutoid6x6mu4.inp ABAQUS inp file for a 7 by 7 assembly of pentagonal scutoids, coefficient of friction 0.4: PentagonScutoid6x6mu4.inp ABAQUS inp file for a 6 by 6 assembly of tetrahedra, coefficient of friction 0.4: Tetrahedra6x6mu4.inp ABAQUS inp file for a 7 by 7 assembly of tetrahedra, coefficient of friction 0.4: Tetrahedra7x7mu4.inp This work was supported by NSF Award 16622177.more » « less

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.more » « less

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, platetype 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

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 thrustline (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 TLmodel are in good agreement with results of finite element models. Accounting for sliding between building blocks in the TLmodel yields a predicted response more similar to experimental results with additively manufactured tubes.more » « less