Tessellation Method Research Articles

Energy Absorption Performance of Open-Cell Aluminum Foam and Its Application in Landing Buffer System

The outstanding mechanical properties and lightness of aluminum foam make it attractive as buffering and energy absorption material for spacecraft landing in deep space exploration. In this paper, cell-based model of open-cell aluminum foam has been established by Voronoi tessellation method. Through quantitative comparisons of energy absorption performance between different simulation models, it can be found that the improvement of base material properties can lead to significant enhancement of energy absorption ability, and there is an approximate linear relationship between relative density and relative energy absorption at low speeds. Characteristic deformation mode has been discussed under different compression speeds. The isotropic buffering characteristic of aluminum foam materials has been verified by the simulation of a footpad filled with aluminum foam impacting on a sloping ground.

A high-fidelity crystal-plasticity finite element methodology for low-cycle fatigue using automatic electron backscatter diffraction scan conversion: Application to hot-rolled cobalt–chromium alloy

The common approach to crystal-plasticity finite element modeling for load-bearing prediction of metallic structures involves the simulation of simplified grain morphology and substructure detail. This paper details a methodology for predicting the structure–property effect of as-manufactured microstructure, including true grain morphology and orientation, on cyclic plasticity, and fatigue crack initiation in biomedical-grade CoCr alloy. The methodology generates high-fidelity crystal-plasticity finite element models, by directly converting measured electron backscatter diffraction metal microstructure grain maps into finite element microstructural models, and thus captures essential grain definition for improved microstructure–property analyses. This electron backscatter diffraction-based method for crystal-plasticity finite element model generation is shown to give approximately 10% improved agreement for fatigue life prediction, compared with the more commonly used Voronoi tessellation method. However, the added microstructural detail available in electron backscatter diffraction–crystal-plasticity finite element did not significantly alter the bulk stress–strain response prediction, compared to Voronoi tessellation–crystal-plasticity finite element. The new electron backscatter diffraction-based method within a strain-gradient crystal-plasticity finite element model is also applied to predict measured grain size effects for cyclic plasticity and fatigue crack initiation, and shows the concentration of geometrically necessary dislocations around true grain boundaries, with smaller grain samples exhibiting higher overall geometrically necessary dislocations concentrations. In addition, minimum model sizes for Voronoi tessellation–crystal-plasticity finite element and electron backscatter diffraction–crystal-plasticity finite element models are proposed for cyclic hysteresis and fatigue crack initiation prediction.

Integrated Laser-Induced Breakdown Spectroscopy (LIBS) and Multivariate Wavelet Tessellation: A New, Rapid Approach for Lithogeochemical Analysis and Interpretation

This paper demonstrates a novel approach that uses wavelet tessellation in rapid analysis of raw geochemical data produced by laser-induced breakdown spectroscopy (LIBS) to produce pseudologs that are representative of stratigraphy. Single-line LIBS spectral data for seven major rock-forming elements (Al, Ca, Fe, Mg, Si, Na and K) were collected from a synthetic 22-sample rock-block comprising two distinct lithological groups based on mineralogy, chemistry and texture: plutonic rocks and marble. Seven sublithologies are identified within the rock-block from traditional laboratory whole-rock geochemical analysis: marble, Mg-marble, granite, quartz monzonite, foidolite, granodiorite and gabbroic diorite. Two-domain clustering (k = 2) on raw spectral LIBS data combined with wavelet tessellation was applied to generate a simplified lithological stratigraphy of marble and plutonic rocks and generate a pseudolog identical to the rock-block stratigraphy. A pseudolog generated from seven-domain clustering (k = 7) and wavelet tessellation successfully discriminated most sublithologies within the rock-block slabs, especially marble slabs. Small-scale units were identified within the more mineralogically and geochemically complex plutonic slabs. The spatial resolution of the LIBS analysis, with a measurement spacing of ~0.35 mm, allowed for assessment of individual mineral compositions and rock textures, and small-scale units within the plutonic rocks can be correlated to specific coarse-grained minerals or mineralogical associations. The application of the wavelet tessellation method to raw LIBS geochemical data offers the possibility of rapid and objective lithogeochemical analysis and interpretations which can predate further analysis (quantitative) and supplement geological logging.

Determination of fluid flow adjacent to a gas/liquid interface using particle tracking velocimetry (PTV) and a high-quality tessellation approach

PTV velocity vectors, with high spatial resolution in the flow field, can be used to calculate important flow parameters such as pressure. Determination of such a parameter, which is a function of velocity gradients, entails the velocity vectors to be interconnected by a network of nodes. A tessellated network of the flow field can use the original positions of the PTV particles. This results in a mesh with elements of large aspect ratios, which can produce large numerical errors in the calculation of velocity gradients. In flow scenarios with a moving solid boundary or two-phase interface, a tessellation method is required that can attune to the dynamic topology while capturing the details of the near interface region. Here, we develop a methodology to tessellate two-dimensional (2D) unsteady PTV fields using high quality triangular dynamic meshes, with fine control of the mesh density close to the moving boundaries. To examine the applicability of the method, an experimental setup based on particle shadow velocimetry was conducted, with air and a water/glycerol mixture as the working fluids. Two flow channels of a straight, with a square cross-section of 3 × 3 mm2 and wavy, with a throat width of 0.5 mm were utilized to capture the dynamics of relatively large bubbles with quasi-steady and highly deformable moving interfaces. The versatility of the method was successfully demonstrated by the generation of a high-quality mesh, with controlled sizes and determination of the radial and tangential velocity components at the near interface region for different flow conditions.

Volume statistics as a probe of large-scale structure

We investigate the application of volume statistics to probe the distribution of underdense regions in the large-scale structure of the Universe. This statistic measures the distortion of Eulerian volume elements relative to Lagrangian ones and can be built from tracer particles using tessellation methods. We apply Voronoi and Delaunay tessellation to study the clustering properties of density and volume statistics. Their level of shot-noise contamination is similar, as both methods take into account all available tracer particles in the field estimator. The tessellation causes a smoothing effect in the power spectrum, which can be approximated by a constant window function on large scales. The clustering bias of the volume statistic with respect to the dark matter density field is determined and found to be negative. We further identify the Baryon Acoustic Oscillation (BAO) feature in the volume statistic. Apart from being smoothed out on small scales, the BAO is present in the volume power spectrum as well, without any systematic bias. These observations suggest that the exploitation of volume statistics as a complementary probe of cosmology is very promising.

Fabrication of trabecular-like beta-tricalcium phosphate biomimetic scaffolds for bone tissue engineering

The introduction of 3D printing into the manufacturing of ceramic components offers new possibilities to fabricate porous bioceramic scaffold with biomimetic morphology, customized-designed shape and suitable mechanical property for bone tissue engineering. However, most of 3D printed porous ceramic scaffolds are prepared from the array of unit cells, which do not exploit the whole potential of additive manufacturing. In this paper, a novel biomimetic porous beta-tricalcium phosphate (β-TCP) scaffolds with trabecular-like morphology were obtained based on three dimension (3D) Voronoi tessellation method and generated design. This bionic pore structure is fabricated via photopolymer-based digital light processing (DLP) 3D printing technique, a suitable 30 wt% β-TCP ceramic slurry with the addition of adjuvants was prepared. After optimized debinding-sintering process according the TG-DSC analysis, the β-TCP scaffolds showed fully interconnected trabecular-like pore structure with tailorable pore size (360 μm–1200 μm) and porosity (45%–75%) and compact microstructure. Combining compressive tests and finite element analysis (FEA), the relationship between inputting parameters, pore structure and compressive strength is investigated. Thus, the mechanical strength of the trabecular-like β-TCP scaffolds could be predicted and tuned in the initial generated design stage. In addition, the shrinkage ratio and XRD pattern are also detected. The method proposed in this study may provide an efficient bionic design intended for tissue engineering applications.

Design and properties of biomimetic irregular scaffolds for bone tissue engineering

The treatment of sizeable segmental bone defects remains a challenge encountered by surgeons. In addition to bone transplantation, porous scaffolds have become a common option. Although the mechanical and biological properties of porous scaffold have recently been the subject of intense research, pore irregularity as a critical characteristic has been poorly explored. Therefore, this study aimed to design an irregular biomimetic scaffold for use in bone tissue engineering applications. The irregular scaffold was based on the Voronoi tessellation method for similarity with the primary histomorphological indexes of bone (porosity, trabecular thickness, cortical bone thickness, and surface to volume ratio). Moreover, a new gradient method was adopted, in which porosity was maintained constant, and the strut diameter was changed to generate a gradient in the irregular scaffold. The permeability and stress concentration characteristics of the irregular scaffold were compared against three conventional scaffolds (the octet, body-centered cubic, pillar body-centered cubic). The results illustrated that the microstructure of the irregular scaffold could be controlled similarly to that of the cortical/cancellous bone unit. Simultaneously, a broad range of permeability was identified for the irregular scaffold, and gradient irregular scaffolds performed better in terms of both permeability and stress distribution than regular scaffolds. This study describes a novel method for the design of irregular scaffolds, which have good controllability and excellent permeability.

On the Structural Properties of Voronoi Diagrams

A Voronoi diagram is a tessellation technique, which subdivides space into regions in proximity to a given set of objects called seeds. Patterns emerging naturally in biological processes (for example, in cell tissue) can be modelled in a biomimicry process via Voronoi diagrams. As they originate in nature, we investigate the physical properties of such patterns to determine whether they are optimal given the constraints imposed by surrounding geometry and natural forces. This paper describes under what circumstances the Voronoi tessellation has optimal (structural) properties by surveying recent studies that apply this tessellation technique across different scales. To investigate the properties of random and optimized Voronoi tessellations in comparison to a regular tessellation method, we additionally run and evaluate a simulation in Karamba3D, a parametric structural engineering tool for Rhinoceros3D. The novelty of this research lies in presenting a simple and straightforward simulation of Voronoi diagrams and highlighting how and where their advantages over regular tessellations can be exploited by surveying more advanced approaches as found in literature.

Meso-scale modelling of compressive fracture in concrete with irregularly shaped aggregates

This paper presents a meso-scale modelling framework to investigate the fracture process in concrete subjected to uniaxial and biaxial compression accounting for its mesostructural characteristics. 3D mesostructure of concrete consisting of coarse aggregates, mortar and interfacial transition zone between them was developed using an in-house code based on the Voronoi tessellation and splining method, which enables to generate the realistic-look aggregates with controllable structural features such as content, location, size and shape. Based on the generated 3D mesostructure, the concrete damage plasticity approach was employed to simulate the compressive fracture behaviour of concrete in terms of crack morphology and stress-strain response against the shape parameters of aggregate. Results indicate that the shape of aggregate has a negligible effect on compressive strength of concrete, which is highly associated with the random location and size distribution of aggregate. The aggregate irregularity has a significant influence on crack initiation and growth of concrete.

Cavitation Mean Expectation Time in a Stretched Lennard-Jones Fluid under Confinement.

We investigate the nucleation of cavitation bubbles in a confined Lennard-Jones fluid subjected to negative pressures in a cubic enclosure. We perform molecular dynamics (MD) simulations with tunable interatomic potentials that enable us to control the wettability of solid walls by the liquid, that is, its contact angle. For a given temperature and pressure, as the solid is taken more hydrophobic, we put in evidence, an increase in nucleation probability. A Voronoi tessellation method is used to accurately detect the bubble appearance and its nucleation rate as a function of the contact angle. We adapt classical nucleation theory (CNT) proposed for the heterogeneous case on a flat surface to our situation where bubbles may appear on flat walls, edges, or corners of the confined box. We finally calculate a theoretical mean expectation time in these three cases. The ratio of these calculated values over the homogeneous case is computed and compared successfully against MD simulations. Beyond the infinite liquid case, this work explores the heterogeneous nucleation of cavitation bubbles, not only in the flat surface case but for more complex confining geometries.

Optimized advance front method of packing dense ellipse for generating the convex polygon structure statistically equivalent with real material

A new constructive method, called optimized advance front method (OAFM), for ellipse packing is proposed. The OAFM allows particle rotation at several angles and movement along a local advance front. Combined with the ellipse approximated by four connected arcs and a series of sequential coordinate transformations, the OAFM generates dense ellipse packing with any imposed size, aspect ratio, and orientation distribution at a fastpacking speed, and the generated ellipse packing can satisfy an imposed spatial arrangement. Based on the approximation of ellipses by multicircles, Laguerre Voronoi Tessellation method constructs initial cells. The initial cells are then merged to create the convex polygon with the same size, aspect ratio, orientation, and location as that of the obtained ellipse. Three examples of ellipse packing and convex polygon demonstrate that the convex polygon generated can be statistically equivalent with the real material and satisfy an imposed spatial arrangement.

Modeling of material deformation behavior in micro-forming under consideration of individual grain heterogeneity

Abstract This study aims to develop a model to characterize the inhomogeneous material deformation behavior in micro-forming. First, the influence of individual grain heterogeneity on the deformation behavior of CuZn20 foils was investigated via tensile and micro-hardness tests. The results showed that different from thick sheets, the hardening behavior of grains in the deformation area of thin foils is not uniform. The flow stress of thin foils actually only reflects the average hardening behavior of several easy-deformation-grains, which is the reason that thinner foils own smaller flow stress. Then, a composite modeling method under consideration of individual grain heterogeneity was developed, where the effects of grain orientation and shape are quantitatively represented by the method of flow stress classification and Voronoi tessellation, respectively. This model provides an accurate and effective method to analyze the influence of individual grain heterogeneity on the deformation behavior of the micro-sized material.

Quasi-Icosahedral Clusters in Zr-Based Metallic Glasses

The icosahedral short-range order structure is one of the important local structural units in the field of metallic glasses. Based on the Voronoi tessellation method, the connection modes between shell atoms of Voronoi indexed clusters in ZrCu binary and ZrCuAl ternary metallic glasses were characterized systematically. It was revealed that Voronoi clusters with different connection modes can potentially have the same Voronoi index. By investigating the connection modes of clusters, three types of Voronoi indexed clusters can be defined as quasi-icosahedral clusters, which have the most similar five-fold environments to full icosahedral clusters. It was also found that the full icosahedral clusters and the quasi-icosahedral clusters had similar values for some structural parameters, and that these clusters contain almost all the atoms in these structural models, enhancing the space filling efficiency. Full icosahedral and quasi-icosahedral clusters should be regarded as the building blocks of atomic structures contributing to glass formation in amorphous alloys. This work is helpful for investigating and understanding the various macroscopic properties of metallic glasses at the atomic cluster level.

Numerical simulation of the metal inert gas welding process that considers grain heterogeneity

It is of great significance to reveal the microevolution mechanism of welded structures during thermo-mechanical coupling to improve the welding quality. In this paper, a random microcrystalline structure model for welds is established by the Voronoi tessellation method. According to the nanoindentation results, heterogeneous grains are produced. A welding workpiece model with statistical significance is established. On this basis, the Python script and the birth and death element method are used to realize the transient growth of a weld, and a thermo-mechanical coupling model for the SUS301L-HT stainless steel metal inert gas welding process is established. The temperature field and thermal stress field are calculated. The calculation shows that the thermal stresses along the growth direction of the weld area are in the form of a “trapezoid,” and the stresses at both ends are small. The stress in the vertical direction of the weld has a single peak, and the peak appears in the center of the weld. The stress distribution of the model that considers heterogeneous grains is obviously inhomogeneous compared with that of the traditional model. The thermal stress distribution in the weldment is obviously inhomogeneous due to the heterogeneous grains, the stresses at the boundaries of the adjacent grains in the weldment change abruptly. It is found that the greater the difference in the mechanical properties between grains is, the more obvious the change.

Inferring seismic hazard in Sichuan-Yunnan region of China based on the modern earthquake catalogue (1980-2019)*

Based on the modern earthquake catalogue, the incomplete centroidal voronoi tessellation (ICVT) method was used in this study to estimate the seismic hazard in Sichuan-Yunnan region of China. We calculated spatial distributions of the total seismic hazard and background seismic hazard in this area. The Bayesian delaunay tessellation smoothing method put forward by Ogata was used to calculate the spatial distributions of b-value. The results show that seismic hazards in Sichuan-Yunnan region are high, and areas with relatively high hazard values are distributed along the main faults, while seismic hazards in Sichuan basin are relatively low.

Islamic Geometric Patterns in Higher Dimensions

The purpose of this paper is to develop the Islamic geometric patterns from planar coordinates to three or higher dimensions through their repeat units. We use historical plane methods, polygons in contact (PIC) and point-joined, in our deductive approaches. The mentioned approach makes use of a novel method of tessellation that generates 3D Islamic patterns called “interior polyhedral stellations”. The outputs showed that both the PIC and point-joined methods have strengths and weaknesses. Point-joined stellations are more efficient for regular repeat units and PIC is suitable for complex designs. These two methods can produce a large range of patterns and can be employed simultaneously. This study effectively answers the question regarding the gap between planar design from Muslim achievements and contemporary demands in modern art and architecture. We also propose techniques for constructing aperiodic three-dimension Islamic geometric patterns tessellation and two-point family.

Feature-Aware Uniform Tessellations on Video Manifold for Content-Sensitive Supervoxels.

Over-segmenting a video into supervoxels has strong potential to reduce the complexity of downstream computer vision applications. Content-sensitive supervoxels (CSSs) are typically smaller in content-dense regions (i.e., with high variation of appearance and/or motion) and larger in content-sparse regions. In this paper, we propose to compute feature-aware CSSs (FCSSs) that are regularly shaped 3D primitive volumes well aligned with local object/region/motion boundaries in video. To compute FCSSs, we map a video to a 3D manifold embedded in a combined color and spatiotemporal space, in which the volume elements of video manifold give a good measure of the video content density. Then any uniform tessellation on video manifold can induce CSS in the video. Our idea is that among all possible uniform tessellations on the video manifold, FCSS finds one whose cell boundaries well align with local video boundaries. To achieve this goal, we propose a novel restricted centroidal Voronoi tessellation method that simultaneously minimizes the tessellation energy (leading to uniform cells in the tessellation) and maximizes the average boundary distance (leading to good local feature alignment). Theoretically our method has an optimal competitive ratio O(1), and its time and space complexities are O(NK) and O(N+K) for computing K supervoxels in an N-voxel video. We also present a simple extension of FCSS to streaming FCSS for processing long videos that cannot be loaded into main memory at once. We evaluate FCSS, streaming FCSS and ten representative supervoxel methods on four video datasets and two novel video applications. The results show that our method simultaneously achieves state-of-the-art performance with respect to various evaluation criteria.

Total grain size distribution of components of fallout deposits and implications for magma fragmentation mechanisms: examples from Campi Flegrei caldera (Italy)

In this paper, we present results of the reconstruction of the total grain size distribution (TGSD) of the material erupted during explosive volcanic eruptions at Campi Flegrei (Italy) considering all components (juvenile, lithic and crystal clasts). To date, the few TGSDs made available have been mostly reconstructed by assuming that the tephra deposits consisted of only one component. This simplification can introduce substantial bias in the interpretation of magma fragmentation mechanisms and significantly affect ash dispersion forecasts, since each tephra component has specific aerodynamic characteristics. By means of field investigations and laboratory analyses on samples collected from deposits of the Agnano-Monte Spina and Astroni eruptions, we reconstructed the TGSDs of juvenile, lithic and crystal components via the Voronoi tessellation method. Our results show how the systematic reconstruction of a TGSD, from the component-specific to the bulk TGSD, can provide important information on magma fragmentation mechanisms and wall-rock erosion processes. Results confirm that the bulk TGSD is the combination of the merging of different component subpopulations, according to their own TGSD, density and relative mass proportions. In addition, the integration of component analysis, TGSD and settling velocity data allowed characterization of the aerodynamic behaviour of each component at variable distances from the vent, which can be related to their own parent grain size distribution. The integration of new data from distal tephra deposits for the considered eruptions has thus allowed a reassessment of the erupted volumes of eruptions considered in this research, which are now 3.17 and 0.63 km3, for Agnano-Monte Spina and Astroni, respectively.

Strain rate effects on tensile and compression behavior of nano-crystalline nanoporous gold: A molecular dynamic study

In this study, strain rate effects on the tensile and compressive properties of nano-crystalline nanoporous gold (nc-NPAu) are investigated by performing molecular dynamics simulations. For this purpose, atomistic models of nc-NPAu structures with three different grain sizes are generated through a novel modeling technique based on the Voronoi tessellation method. Additionally, an adaptive common neighbor analysis (aCNA) is carried out to examine the evolution of the crystal structure. In this way, the deformation mechanisms of nc-NPAu atomistic models are thoroughly investigated. The findings point out that mechanical properties of nc-NPAu specimens such as toughness, ultimate and yield strengths grow at increasing strain rates for both tensile and compressive loadings while their elastic moduli exhibit less significant variations at different strain rates. Furthermore, the study also shows that in addition to dislocation motion, several other deformation mechanisms including grain rotation, grain boundary sliding and grain travelling are observed to be effective for nc-NPAu.

Characterizing magma fragmentation and its relationship with eruptive styles of Somma-Vesuvius volcano (Naples, Italy)

Among the active volcanoes worldwide, Somma-Vesuvius is one with the highest volcanic risk as the surrounding areas are highly populated. Somma-Vesuvius is quiescent since 1944, but geological and historical records reveal a frequent violent explosive activity in the last 4000 years, representing a severe risk for the ∼700,000 inhabitants currently living in the area having a high probability for being impacted by pyroclastic density currents (“red zone”) and more than one million people who can be potentially affected by tephra fallout. This study aims to analyze the distribution and grain-size of tephra fallout deposits from several Somma-Vesuvius eruptions of different styles, ranging from Violent Strombolian to sub-Plinian and Plinian, for characterizing the associated magmatic fragmentation through the assessment of their total grain-size distribution (TGSD). Chronologically, we focus on the Avellino (4365 BP) and Pompeii (A.D. 79) Plinian eruptions, the Pollena (A.D. 472) sub-Plinian eruption, and the 1906 and 1944 Violent Strombolian eruptions. The related TGSDs were estimated by means of the Voronoi tessellation method, which requires a suitable number of local grain-size distributions and estimation of the area of minimum tephra loading (zero-line contour). However, field-derived TGSDs can be biased towards the coarse and fine grain-size populations due to the typical paucity of available field outcrops of fallout deposits. To encompass this issue, we performed a sensitivity study on the assumption behind TGSD reconstructions and described TGSDs through analytical grain-size distributions that best fit the field TGSDs. Our main objective is a more robust estimation of the TGSDs associated with the different eruptive styles, which is crucial, together with the other eruption source parameters, for robustly predicting tephra loading and airborne ash dispersal of future eruptions at Somma-Vesuvius.