Tessellation Structures Research Articles

Conceptual Configuration Analysis of Tetrahedral-Octahedral Heterogeneous Unit and Topological Design of Shape Morphing Mechanism

Abstract The truss static structure system has excellent large load and lightweight characteristics. It is easy to embed actuators by substituting specific members in the structure and has the potential for multidimensional space deformation. Inspired by uniform tessellation structures, this article proposes a novel shape morphing mechanism (SMM) based on the combined design of tetrahedral-octahedral heterogeneous units (TOHUs). The relationship between the motion properties and driving configuration of the tetrahedral-octahedral units is analyzed to determine their conceptual configuration based on graph theory. Then, the weighted graph, adjacency matrix, and connection rules are evaluated to synthesize the conceptual structure for the truss mechanism. The results show that this configuration can allow multidimensional continuous deformations, including span, bend, sweep, and twist. A prototype is built to verify its deformability. Finally, the stiffness performance is analyzed based on the matrix displacement method. This research provides a comprehensive design method for constructing SMM, expands the range of combinable units and connection methods, and offers theoretical guidance for the innovative design of multidimensional deformation SMM in aerospace.

Second-order texton feature extraction and pattern recognition of building polygon cluster using CNN network

The cluster patterns of features in map space represent a comprehensive reflection of individual feature geometric attributes and their spatial adjacency relationships. These patterns also embody spatial cognition results under the Gestalt principle. Describing non-linear spatial cluster patterns as effective regular structures is one of the fundamental tasks in deep learning for recognizing feature cluster patterns. In this study, based on the concept of texture co-occurrence matrices from regular gray-scale images, we utilized Voronoi diagrams to construct the tessellation structure of building polygons. Built upon the foundation of first-order texton co-occurrence matrices, we established three-dimensional texton co-occurrence matrices for building polygons, considered five attributes of building size, shape, orientation, and density, and encompassed 64 different combinations of second-order neighboring directions. This matrix concretizes the latent Gestalt spatial characteristics of building polygon clusters into a three-dimensional sparse matrix. It is then used as an input vector to construct a deep convolutional neural network for recognizing building polygon cluster patterns. Through adjustments and optimizations of neural network structure and strategies, along with validation through practical case studies and comparisons with other models, we have demonstrated the effectiveness of the second-order texton co-occurrence matrix in describing the characteristics of building polygon clusters.

Rigid-foldable cylindrical origami with tunable mechanical behaviors

Rigid-foldable origami shows significant promise in advanced engineering applications including deployable structures, aerospace engineering, and robotics. It undergoes deformation solely at the creases during the folding process while maintaining rigidity throughout all facets. However, most types of cylindrical origami, such as Kresling origami, water-bomb origami, and twisted tower origami, lack rigid-foldability. Although shape transformation can be achieved through elastic folding, their limited rigid foldability constrains their engineering applications. To address this limitation, we proposed a type of cylindrical origami inspired by Kresling origami, named foldable prism origami (FP-ori), in this paper. FP-ori possesses not only rigid-foldability but also several tunable properties, including flat-foldability, self-locking, and bistability. The geometric properties of FP-ori were analyzed and the relationship between different parameters and tunable mechanical behaviors were verified through finite element method simulations, as well as experiments using paper models. Furthermore, we proposed stacked structures composed of multiple cubic FP-ori units, the rotation directions of which could be controlled through the combination arrangement. And drawing inspiration from kirigami, a negative Poisson’s ratio tessellation structure was created. These results indicated that FP-ori has substantial potential for broad application in engineering fields.

Habitat Provision and Erosion Are Influenced by Seagrass Meadow Complexity: A Seascape Perspective

Habitat complexity plays a critical role in shaping biotic assemblages and ecosystem processes. While the impacts of large differences in habitat complexity are often well understood, we know less about how subtle differences in structure affect key ecosystem functions or properties such as biodiversity and biomass. The late-successional seagrass Posidonia australis creates vital habitat for diverse fauna in temperate Australia. Long-term human impacts have led to the decline of P. australis in some estuaries of eastern Australia, where it is now classified as an endangered ecological community. We examined the influence of P. australis structural complexity at small (seagrass density) and large (meadow fragmentation) spatial scales on fish and epifauna communities, predation and sediment erosion. Fine-scale spatially balanced sampling was evenly distributed across a suite of environmental covariates within six estuaries in eastern Australia using the Generalised Random Tessellation Structures approach. We found reduced erosion in areas with higher P. australis density, greater abundance of fish in more fragmented areas and higher fish richness in vegetated areas further from patch edges. The abundance of epifauna and fish, and fish species richness were higher in areas with lower seagrass density (seagrass density did not correlate with distance to patch edge). These findings can inform seagrass restoration efforts by identifying meadow characteristics that influence ecological functions and processes.

Characterization of penetrate and interpenetrate tessellated cellular lattice structures for energy absorption

Recently, cellular lattice structures are gaining research attention due to their lightweight and high energy absorption. Interpenetrated lattice structure is a combination of two or more regular lattices with the same volume and without any contact at the unit level. The interpenetrated tessellated lattice (I-PTL) structures are better known for load sharing and energy absorption applications. In the current research, regular unit cell lattices such as cubic, beam lattice, body-centered cubic, and octahedron are considered to fabricate penetrated and interpenetrated cellular lattice structures and tested for energy absorption on quasi-static loading. These structures were fabricated using a Vat polymerization three-dimensional printer and tested as per the American Society for Testing and Materials (ASTM) standards, and the results were compared with numerical simulation using ANSYS. The penetrated tessellated lattice structural and I-PTL behavior deliver energy transfer controlled by the surface and solid joint interactions. The enhancement in mechanical properties is observed with the controllable compliance and specific energy absorption of the lattice structure.

The DLC Coating on 316L Stainless Steel Stochastic Voronoi Tessellation Structures Obtained by Binder Jetting Additive Manufacturing for Potential Biomedical Applications

The DLC coating of samples produced by additive manufacturing with complex shapes is a challenge but also shows the possibility of obtaining a diffusive barrier for biomedical applications. In this study, stochastic porous structures based on Voronoi tessellation were fabricated using binder jetting technology from 316L SS powder and modified using DLC coating. The DLC coating was deposited using the RF PACVD technology. The chamber pressure was 40 Pa with a methane gas flow rate of 60 sccm. The negative bias voltage was 700 V. The deposition time was 5 min. Dimensional analysis was performed using optical microscopy. Surface morphology and topography were evaluated using SEM and confocal microscopy. Raman spectroscopy was used to examine the chemical structure of DLC coating. Finally, the HR TEM was used to evaluate the physicochemical characterization of the DLC coating. The interconnected complex spatial network of the Voronoi structure was accurately duplicated by the binder jetting technology. The obtained substrates were characterized by high roughness (Ra = 6.43 µm). Moreover, the results indicated that the conditions of the RF PACVD process allow for the deposition of the continuous and tightened DLC coating with a thickness from 30 nm to 230 nm and defined the content of Cr2O3 and SiO2.

Design, preparation and characterization of three-dimensional auxetic warp and weft backed weave fabrics based on origami tessellation structures

Materials with a negative Poisson’s ratio (NPR) are also called auxetic materials, which as a branch of mechanical metamaterials have drawn a great deal of attention in many areas. Origami tessellation structures (OTSs) exhibit an in-plane NPR; meanwhile, they may also show an out-of-plane NPR, which may be called three-dimensional (3D) auxetic structures. In the crease pattern of OTSs, there are folding lines in perpendicular directions. Contractions in the warp direction need warp backed weave structures. Herein, warp and weft backed weaves are used together and three OTS Jacquard fabrics are designed. From the physical map, we can see that the elastic warp yarns and elastic weft yarns can form floats in the warp and weft directions, and the flat fabrics can be folded in to 3D OTSs according to the crease patterns designed. The in-plane and out-of-plane Poisson’s ratios of OTSs have been predicted and, subsequently, compared with the experimental results. All OTS fabrics can show an in-plane NPR, two fabrics show out-of-plane NPRs and one shows an out-of-plane positive Poisson’s ratio. A parametric analysis about the interior angle has revealed the interplay between the geometrical parameters of OTSs and the Poisson’s ratio. In various design fields, elastic yarns combined with warp and weft backed weave textile technology can pave the way for realizing new crease pattern fabrics focused on 3D auxetic materials. Theoretical results can provide methodological guidance and technical support for the design and manufacture of OTS fabrics with optimum functional performance or desired aesthetics.

Origami Improved Dielectric Elastomer Actuation for Tunable Lens

Dielectric elastomer actuators (DEAs) have been applied to the tunable solid lens with the unique characteristics of fast response, low consumption, lightweight, and silent operation. However, the performance of the DEA-based contraction tunable solid lens is limited to the small aperture or tuning range compared to the extension tunable solid lens. In this article, to address this issue, a self-recovery origami mechanism with a modified Yoshimura tessellation structure is presented to improve the contraction-tunable lens driven by the truncated cone-shaped DEA. A model using the virtual work principle and spring in-series theory is established to predict the deformation of the tunable lens, and the experimental result verifies the simulation. The experiment demonstrates that the focal length of the 10-mm-diameter solid lens can vary from 45.4 to 37.7 mm, showing a 17% tunability. Results show that combining origami structure with the unique properties of DEA for a tunable solid lens has the potential to expand its application fields.

Ultralight Metamaterial for Sound Absorption Based on Miura‐Ori Tessellation Structures

Herein, electrospinning and paper folding (i.e., origami) techniques are integrated to fabricate a novel ultralight metamaterial for sound absorption based on Miura‐ori tessellation structure, which exists at an extremely low mass density of only 10.64 mg cm−3. Sound absorption tests using an impedance tube demonstrate a significant improvement of sound absorption coefficient and the shift of first resonance absorption frequency to the lower band compared with the plane membrane. Further, the effect on sound absorption performance from three important parameters γ, θ, and a that dominate the shape of Miura‐ori are investigated and understood through the membrane vibration mechanism and Johnson–Alard hard frame model. Meanwhile, to achieve good sound absorption in a broad frequency range, a stacked structure with the double‐cavity‐double‐sandwich model is created, which presents a superior broadband sound absorption and ideal sound absorption in a specific frequency range.

Random Network Transmission and Countermeasures in Containing Global Spread of COVID-19-Alike Pandemic: A Hybrid Modelling Approach

Since the outbreak of the novel coronavirus disease (COVID-19) at the beginning of December 2019, there have been more than 28.69 million cumulative confirmed cases worldwide as of 12th September 2020, affecting over 200 countries and regions with more than 920,463 deaths. The COVID-19 pandemic has been sweeping worldwide with unexpected rapidity. In this paper, a hybrid modelling strategy based on tessellation structure- (TS-) configured SEIR model is adopted to estimate the scale of the pandemic spread. Building on the data pertaining to the global pandemic transmission over the last six months around the world, key impact factors in the transmission and control procedure have been analysed, including isolation rate, number of the infected cases before taking prevention measures, degree of contact scope, and medical level, so as to capture the fundamental factor influencing the pandemic. The quantitative evaluation allowed us to illustrate the magnitude of risks of pandemic and to recommend appropriate national health policy of prevention measures for effectively controlling both intra- and interregional pandemic spread. Our modelling results clearly indicate that the early-stage preventive measures are the most effective action to be taken to contain the pandemic spread of the highly contagious nature of the COVID-19.

Chemical engineering of quasicrystal approximants in lanthanide-based coordination solids

Tessellation of self-assembling molecular building blocks is a promising strategy to design metal-organic materials exhibiting geometrical frustration and ensuing frustrated physical properties. Appearing in two-dimensional quasiperiodic phases, tilings consisting of five-vertex nodes are regarded as approximants for quasicrystals. Unfortunately, these structural motifs are exceedingly rare due to the complications of acquiring five-fold coordination confined to the plane. Lanthanide ions display the sufficient coordinative plasticity, and large ionic radii, to allow their incorporation into irregular molecule-based arrays. We herein present the use of ytterbium(II) as a five-vertex node in a two-dimensional coordination solid, YbI2(4,4′-bipyridine)2.5. The semi-regular Archimedean tessellation structure verges on quasicrystallinity and paves the way for lanthanide-based metal-organic materials with interesting photonic and magnetic properties.

Supramolecular Tessellations at Surfaces by Vertex Design

Assembly and tessellation of organic species at surfaces are important for the design of advanced materials, particularly for the development of spontaneous self-assemblies of supramolecular systems of increasing complexity. However, there are few examples where the ability to steer the system between supramolecular tessellations has been achieved. Here, we demonstrate a series of steps to reduce and then restore molecular symmetry; those variations impact vertex symmetry and thus generate a series of tessellations that reflect the molecular symmetry. We deposit 4,4'-dihydroxybiphenyl on the Ag(111) surface, then anneal at specific temperatures to achieve stepwise dehydrogenation of the terminal hydroxyls. The symmetry of tessellation vertices in the self-assembled structure also changes, as characterized by scanning tunneling microscopy and synchrotron radiation photoemission spectroscopy. This control over vertex geometry and spontaneous tessellation structure extends our understanding of supramolecular design control and advances architectural complexity for the development of functional surfaces.

Piecewise assembled acoustic arrays based on reconfigurable tessellated structures.

Physically reconfigurable, tessellated acoustic arrays inspired by origami structures have recently been leveraged to adaptively guide acoustic energy. Yet, the prior work only examined tessellated arrays composed from uniform folding patterns, so that the limited folding-induced shape change prohibits broad acoustic field tailoring. To explore a wider range of opportunities by origami-inspired acoustic arrays, here, piecewise geometries are assembled from multiple folding patterns so that acoustic transducer elements are reconfigured in more intricate ways upon array folding. An analytical model of assembled geometries and resulting acoustic wave radiation from the oscillating facets is formulated. Using the theoretical tool, parametric investigations are undertaken to study the adaptation of acoustic energy transmission caused by folding and modularity of the array assembly. A proof-of-concept specimen is fabricated and experiments are conducted to validate the theoretical model and to investigate the efficacy of the piecewise acoustic array concept. The total findings reveal that the assembly of tessellated acoustic arrays may emulate the wave radiation emitted by ideal acoustic sources of intricate shapes. Moreover, by exploitation of origami folding actions, the shape adaptations of the proposed arrays permit straightforward wave guiding opportunities for diverse application needs.

Initializing type-2 residual stresses in crystal plasticity finite element simulations utilizing high-energy diffraction microscopy data

Crystal plasticity finite element models have advanced in recent years by increasing their fidelity via incorporating physically based deformation mechanisms and more realistic microstructures. In order to better understand their effectiveness, researchers have looked at comparing their results with that of experiments at the grain level. In most of these efforts, the importance of incorporating initial residual stresses, representing the true grain morphologies, and imposing correct boundary conditions, which may have a significant effect on the results, is often overlooked. This work utilizes an available dataset of high-energy X-ray diffraction microscopy experiments conducted on a titanium alloy, Ti-7Al, providing complete grain averaged elastic strain tensors to investigate these three issues in crystal plasticity models. In this study, a method to initialize grain-level residual stresses is formulated and its effect on the correlation of results between simulations and experiments, is evaluated. The effect of grain morphology on the simulation results is evaluated by comparing results from simulations using exact 3D grain morphology with that of simulations using tessellated grain structures. In addition, the importance of applying physically realistic boundary conditions, obtained directly from experiments is also investigated. The findings of this work indicate that initial residual stresses and physically realistic boundary conditions play a key role in the results obtained from CPFE simulations and it is imperative that more importance is given to them. On the other hand, using exact grain morphology is not of much benefit while comparing data on the grain averaged scale as long as the microstructure contains information about the position of the grains, as is the case with tessellations, although grain morphology plays an important role in predicting intragranular strain localization.

Line segments which are unions of tessellation edges

Planar tessellation structures occur in material science, geology (in rock formations), physics (of foams, for example), biology (especially in epithelial studies) and in other sciences. Their mathematical and statistical study has many aspects to consider. In this paper, line-segments which are either a tessellation edge or a finite union of edges are studied. Our focus is on a sub-class of such line-segments – those we call M-segments – that are not contained in a longer union of edges. These encompass the so-called I-segments that have arisen in many recent tessellation models. We study the expected numbers of edges and cell-sides contained in these M-segments, and the prevalence of these entities. Many examples and figures, including some based on tessellation nesting and superposition, illustrate the theory. M-segments are much more prevalent when a tessellation is not side-to-side, so our paper has theoretical connections with the recent IAS paper by Cowan and Thäle (2014); that paper characterised non side-to-side tessellations.

Lattice structure lightweight triangulation for additive manufacturing

Additive manufacturing offers new available categories of geometries to be built. Among those categories, one can find the well developing field of lattice structures. Attention has been paid on lattice structures for their lightweight and mechanical efficiency ratio, thus leading to more optimized mechanical parts for systems. However this lightness only holds true from a mass related point of view. The files sent to additive manufacturing machines are quite large and can go up to such sizes that machines can freeze and get into malfunction. This is directly related to the lattice structures tendency to be of a high geometric complexity. A large number of vertices and triangles are necessary to describe them geometrically, thus leading to larger file sizes. With the increasing use of lattice structures, the need for their files to be lighter is also rising. This paper aims at proposing a method for tessellating a certain category of such structures, using topologic and geometric criteria to generate as few as possible triangles, thus leading to lightweight files. The triangulation technique is driven by a chordal error that controls the deviation between the exact and tessellated structures. It uses interpolation, boolean as well as triangulation operators. The method is illustrated and discussed through examples from our prototype software.

Modeling structures of open cell foams

This work proposes an original geometrical model based on randomly packed spheres using Laguerre-Voronoi tessellations to simulate geometrical and topological characteristics in the microstructure of open cell foams. The model can be used to analyze the effect of coefficient of variation on the pores distribution in real foams. The distribution of foam-cell volumes in foam structures generated in this work is dependent on the log-normal distribution of sphere volumes in corresponding randomly packed spheres. The statistical data of modeled foam structures, including distribution of the cell volume, face and edge number is very close to the characteristics of real materials. The results also show that a higher coefficient of variation in the sphere diameter would decrease the average number of faces per cell. The average number of faces varies from 13.56 to 14.43 for different coefficients of variation of sphere diameter, while the average number of faces in the Poisson-Voronoi tessellation structures is approximately 15.5. Furthermore, the porosity of foam structures, ε, decreases with the ratio of strut diameter to the average diameter of randomly packed spheres, ds/E(d), while the specific surface area of foams, SV, increases with ds/E(d).

The analysis and measurement of building patterns using texton co-occurrence matrices

ABSTRACTThe representation and analysis of building patterns are critical for characterizing urban scenes and making decisions in urban planning. The evaluation of building patterns is a difficult spatial analysis problem that exhibits properties of symbolization, homogeneity and regularity. Open issues in this field include the development of approaches for representing building patterns and vector-based methods for computing various pattern metrics. In the image analysis domain, there are many methods for pattern recognition (e.g., texture analysis), but there are few corresponding solutions for vector data. The aim of this research is to develop several building pattern metrics and offer a texton co-occurrence matrix (TCM)-based method to quantitatively evaluate the features of building patterns. The procedure first constructs a spatial field based on a Delaunay triangulation skeleton to partition a set of buildings into a set of tessellation cells. The tessellations of building clusters have a similar structure as image representations, in that each cell corresponds to an image pixel. We then use the texton analysis to establish a matrix to describe the tessellation structure, including the neighboring relationships and individual attribute information. Finally, a set of feature descriptors is obtained from the TCM to capture the texture-related information of building groups. Through experiments on building pattern analysis and spatial queries, we show that the results of TCM-based evaluation of building patterns are consistent with those of human cognition.

Effect of mass multiple counting on the elastic properties of open-cell regular porous biomaterials

Low-density open-cell porous structures are widely researched due to their mechanical properties that are close to natural bone and their open-cell interconnected structure that allows for ingrowth of new bone tissue. Different studies have shown that apparent density dominates the mechanical properties of porous lattice structures. Surveying the literature revealed that in the previously published studies, there are inaccuracies in calculating the apparent density. In this study, the effects of considering exact apparent density rather than approximate density on the predicted elastic modulus, yield stress, and Poisson's ratio were investigated. The accuracy of the created models was evaluated by comparing their mechanical properties with corresponding experimental data. Five different types of unit cell, namely cube, rhombic dodecahedron, Weaire–Phelan, Kelvin, and diamond and three different cross-section geometries namely circle, square, and triangle were considered. The effects of unit cell type, cross-section type, and apparent density on the elastic moduli of open-cell tessellated cellular structures were also investigated. Considering exact density instead of approximate density increased the calculated elastic modulus and yield stress of structures with different morphologies by 22%–44% for an apparent density of 50%. Inversely, using exact apparent density instead of approximate apparent density decreased the Poisson's ratio values.

Folding robots and metamaterials

Applied Origami![Figure][1] Folded tessellated structures yield mechanical properties not found in nature CREDIT: JESSE L. SILVERBERG, ARTHUR A. EVANS, LAUREN MCLEOD, RYAN C. HAYWARD, THOMAS HULL, CHRIS D. SANTANGELO, AND ITAI COHEN The same principles used to make origami art can make self-assembling robots and tunable metamaterials—artificial materials engineered to have properties that may not be found in nature (see the Perspective by You). Felton et al. made complex self-folding robots from flat templates. Such robots could potentially be sent through a collapsed building or tunnels and then assemble themselves autonomously into their final functional form. Silverberg et al. created a mechanical metamaterial that was folded into a tessellated pattern of unit cells. These cells reversibly switched between soft and stiff states, causing large, controllable changes to the way the material responded to being squashed. Science , this issue p. [644][2], p. [647][3]; see also p. [623][4] [1]: pending:yes [2]: /lookup/doi/10.1126/science.1252610 [3]: /lookup/doi/10.1126/science.1252876 [4]: /lookup/doi/10.1126/science.1257841