skip to main content


Title: Mechanics of tubes composed of interlocking building blocks
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
Award ID(s):
1662177
NSF-PAR ID:
10330626
Author(s) / Creator(s):
;
Editor(s):
Kachanov, M.; Rajagopal, K.R.
Date Published:
Journal Name:
International journal of engineering science
Volume:
174
ISSN:
0020-7225
Page Range / eLocation ID:
103654
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. 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
  2. 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
  3. An approach for modeling topologically interlocked building blocks that can be assembled in a water‐tight manner (space filling) to design a variety of spatial structures is introduced. This approach takes inspiration from recent methods utilizing Voronoi tessellation of spatial domains using symmetrically arranged Voronoi sites. Attention is focused on building blocks that result from helical stacking of planar 2‐honeycombs (i.e., tessellations of the plane with a single prototile) generated through a combination of wallpaper symmetries and Voronoi tessellation. This unique combination gives rise to structures that are both space‐filling (due to Voronoi tessellation) and interlocking (due to helical trajectories). Algorithms are developed to generate two different varieties of helical building blocks, namely, corrugated and smooth. These varieties result naturally from the method of discretization and shape generation and lead to distinct interlocking behavior. In order to study these varieties, finite‐element analyses (FEA) are conducted on different tiles parametrized by 1) the polygonal unit cell determined by the wallpaper symmetry and 2) the parameters of the helical line generating the Voronoi tessellation. Analyses reveal that the new design of the geometry of the building blocks enables strong variation of the engagement force between the blocks.

     
    more » « less
  4. Abstract Additively manufactured (AM) metallic materials often comprise as-printed dislocation cells inside grains. These dislocation cells can give rise to substantial microscale internal stresses in both initial undeformed and plastically deformed samples, thereby affecting the mechanical properties of AM metallic materials. Here we develop models of microscale internal stresses in AM stainless steel by focusing on their back stress components. Three sources of microscale back stresses are considered, including the printing and deformation-induced back stresses associated with as-printed dislocation cells as well as the deformation-induced back stresses associated with grain boundaries. We use a three-dimensional discrete dislocation dynamics model to demonstrate the manifestation of printing-induced back stresses. We adopt a dislocation pile-up model to evaluate the deformation-induced back stresses associated with as-printed dislocation cells. The extracted back stress relation from the pile-up model is incorporated into a crystal plasticity model that accounts for the other two sources of back stresses as well. The crystal plasticity finite element simulation results agree with the experimentally measured tension-compression asymmetry and macroscopic back stress, the latter of which represents the effective resultant of microscale back stresses of different origins. Our results provide an in-depth understanding of the origins and evolution of microscale internal stresses in AM metallic materials. 
    more » « less
  5. Additive manufacturing has been used to develop a variety of scaffold designs for clinical and industrial applications. Mechanical properties (i.e., compression, tension, bending, and torsion response) of these scaffolds are significantly important for load-bearing orthopaedic implants. In this study, we designed and additively manufactured porous metallic biomaterials based on two different types of triply periodic minimal surface structures (i.e., gyroid and diamond) that mimic the mechanical properties of bone, such as porosity, stiffness, and strength. Physical and mechanical properties, including compressive, tensile, bending, and torsional stiffness and strength of the developed scaffolds, were then characterised experimentally and numerically using finite element method. Sheet thickness was constant at 300 μm, and the unit cell size was varied to generate different pore sizes and porosities. Gyroid scaffolds had a pore size in the range of 600–1200 μm and a porosity in the range of 54–72%, respectively. Corresponding values for the diamond were 900–1500 μm and 56–70%. Both structure types were validated experimentally, and a wide range of mechanical properties (including stiffness and yield strength) were predicted using the finite element method. The stiffness and strength of both structures are comparable to that of cortical bone, hence reducing the risks of scaffold failure. The results demonstrate that the developed scaffolds mimic the physical and mechanical properties of cortical bone and can be suitable for bone replacement and orthopaedic implants. However, an optimal design should be chosen based on specific performance requirements. 
    more » « less