Modularity is a fundamental and intriguing property of fabrics. Given the same set of threads, one can construct different geometries and therefore physical behavior simply by changing how those ...threads are linked to each other. As a result, fabrics have been studied with great interest in engineering applications. However, most engineering applications model fabrics as composite structures reinforced with a secondary material that fills the gaps between thread elements.
In this work, we first show the existence of threads that are space-filling without the need for other materials. We then introduce a simple approach to construct such space-filling threads by using a single modular element that can be obtained by partitioning a cube into two yin-yang type identical pieces. These yin-yang type congruent tiles can directly be constructed by using a parametric approach. Another property of these tiles is that they are foldable, i.e., they can be constructed by folding planar materials. We show that there exist infinitely many such congruent tiles. We further demonstrate that any 2-way 2-fold woven structure can be constructed by translated and rotated versions of such congruent tiles.
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•We showed the existence of space-filling threads built with single modular element.•One element is obtained by partitioning cube into two yin-yang type identical pieces.•These yin-yang type parts can directly be constructed by using a parametric approach.•These tiles can be made foldable, i.e. can be constructed by folding planar material.•We show that there exist infinitely many such congruent tiles.
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Voronoi tessellation techniques are widely accepted methods for the generation of representative models of polycrystalline microstructures of metallurgic and ceramic materials. ...Contrary to most of the Voronoi-based tessellation methods developed, the Laguerre Voronoi technique provides control over the size and shape of the cells, therefore allowing to simulate accurately the grain structure of a wide range of materials. This paper presents a method for the generation of numerical models of 3D polycrystalline microstructures, based on the Laguerre-Voronoi tessellation technique. An innovative approach to define the additional parameters required by the Laguerre-Voronoi formulation for the generation of realistic 3D microstructures is presented, providing the algorithm with information on the given microstructure from a set of 2D micrographs easily obtainable experimentally. The method implemented efficiently avoids degenerated cells (affecting the quality of the final structure) and finds the most representative set of input values by comparing 2D sections of the numerical model against 2D imaging of real polished surfaces. In this paper, the capability of the method developed is verified by reproducing the microstructure of polycrystalline alumina with various ranges of grain sizes, deriving from different sintering procedures.
In this study, the Voronoi-based breakable block model (VBBM) based on the combined finite-discrete element method (FDEM) is used to investigate the failure mechanism of mine pillars and the ...rock-rockbolt interactions. The mechanical parameters of grout-rock and grout-bolt interfaces of a fully-grouted bolt are calibrated via numerical pull-out tests. Then, uniaxial compression tests are carried out on the reinforced pillars. The kinetic energy release rate (KERR) and crack aperture (CA) are used to evaluate the reinforcement effect. The results revealed that the VBBM can effectively characterize the damage failure mechanisms of spalling on the pillar surface and conjugate shear failure in the core zone of the pillar and reproduce the pre-peak nonlinear deformation and post-peak pseudo-ductile behaviors. The passive confining pressure generated by rockbolts is activated only when the rock mass produces sufficient deformation, and the constraints generated by different numbers of rockbolts can only affect the post-peak behavior of the pillar. There is a gradient feature in the internal deformation of the pillar from the shallow surface to the core. If the rockbolt density meets the strain demand, then rockbolts can delay the inward expansion of cracks by generating local constraints and can effectively fix the spalling rock blocks. With increasing support pressure, the CA and KERR exhibit a decreasing trend and strong power-exponential relationships with support pressure, indicating that there is a transition interval of support pressure and an optimal value for setting the rockbolt density.
•A novel numerical model (VBBM) is utilized to characterize the damage mechanisms of mine pillars.•The approach of combining the VBBM and the fully-grouted rockbolts is first used to explore the reinforcement effect.•The crack aperture and kinetic energy release rate are used to quantify the support effect.
So far, it is still controversial about how to divide the liquid-like and gas-like states boundary and Widom delta, since the deviation of boundaries determined by different thermodynamic criteria ...increases significantly when away from the critical point. For this reason, a superior method that does not rely on thermodynamic criteria to define the boundary line between liquid-like and gas-like states needs to be proposed urgently and the recent extensive use of deep neural networks in molecular dynamics simulation provides a feasible choice. The present work attempts to determine a novel phase state boundary and Widom delta of supercritical CO2 from extracting the microstructure features of subcritical vapor and liquid states in equilibrium by deep neural network coupled with molecular dynamics simulation. In addition, visualization of simulated systems containing distinct liquid-like molecule ratio πLL of supercritical CO2 is also presented as well as the radial distribution function at different states. The results show that the novel boundary is located in the middle of the Widom lines constructed by multiple thermodynamic criteria. The lower boundary T- of the novel Widom delta agrees well with the theoretical boundary constructed by pseudo-boiling theory when it is close to the critical point but starts to deviate when it is far away from the critical point, while the upper boundary T+ of that is opposite. More importantly, the novel boundary and Widom delta constructed have no pressure upper limit compared to those constructed by thermodynamic criteria, only depending on πLL, which means that the novel boundary and Widom delta can extend to the supercritical deep region. Further, the visualization and radial distribution function of simulated systems of supercritical CO2 at different states provide the persistence of a liquid-like and a gas-like transition. The work conducted here can present novel microscopic insight into supercritical phase transition and provide another available alternative to define the Widom line.
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•Novel boundary identified by DNN is located in middle of Widom lines.•Novel boundary and Widom delta gained from DNN have no upper pressure limit.•Structure feature of LL-GL transition is disappearance of second peak of RDF.
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•Model can be used to analyze the effect of coefficient of variation on real foams.•The distribution of foam-cell volumes is dependent on sphere volumes distribution.•The statistical ...data of modeled foams is very close to that of real materials.•The average number of faces varies from 13.56 to 14.43 for different CVs.•Porosity decreases with ds/E(d), while surface area increases with ds/E(d).
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).
We conduct carrier-phase direct numerical simulations (CP-DNS) to investigate the ignition of iron particles in homogeneous isotropic turbulence, and characterize the connection between particle ...clustering and particle ignition. A pseudo-spectral reacting multiphase flow solver using a low Mach number approximation is employed. It features an established point-particle sub-model for reacting iron particles and describes the mass, heat and momentum transfer across the particle boundary layers in a two-way coupled regime. Within this setup, we perform a series of simulations covering a broad range of Reynolds and Stokes numbers. The results confirm the well-known observation from incompressible dispersed multiphase flows that particle clustering is most pronounced for particle clouds with Stokes numbers of order one. Here, strong particle clustering additionally facilitates the earlier ignition of heterogeneously burning iron particles. This is because groups of neighboring particles locally deposit more heat per volume than a single isolated particle, thus more strongly increasing the local fluid temperature and shifting particle reactions from kinetically-limited to diffusion-limited particle conversion. A Voronoi tessellation analysis shows that the particles packed together in clusters tend to ignite first, even for small Stokes numbers, at which clustering is less prominent. An increase in Reynolds number reduces the ignition delay times, especially for high Stokes numbers, since particles with higher inertia are more sensitive to the larger scales of the turbulent motion. The present findings are of practical importance for the design and flame stabilization mechanisms in future iron combustion burners.
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.
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Adjustment of the mechanical properties (apparent elastic modulus and compressive strength) in porous scaffolds is important for artificial implants and bone tissue engineering. In this study, a ...top-down design method based on Voronoi-Tessellation was proposed. This method was successful in obtaining the porous structures with specified and functionally graded porosity. The porous specimens were prepared by selective laser melting technology. Quasi-static compressive tests were conducted as well. The experiment results revealed that the mechanical properties were affected by both porosity and irregularity. The irregularity coefficient proposed in this study can achieve good accommodation and balance of “irregularity” and “controllability”. The method proposed in this study provides an efficient approach for the bionic design and topological optimization of scaffolds.
Voronoi tessellation theory is applied to model the cells and ligaments in the open aluminum foam material. The cores of the cells are first generated by packing random spheres into the specified ...spatial domain. Weighted Voronoi tessellation is then applied to make the cellular structure of the foam material. For the open cell foam, the ligaments are created from the edges in the multiple polyhedron geometry.
Hypervelocity impact simulation is conducted with the smoothed particle hydrodynamics method in LS-dyna. The finite element reconstruction technique is applied based on the particle output for the fragmentation analysis. The modeling and simulation techniques are verified by comparing the simulation results with testing results. The failure shown in the numerical prediction is consistent to the test result.
The stress wave propagation in the foam material, which is extracted from the simulation output, is very different from that in the homogeneous material. The stress wave can only propagate inside the ligaments, and is diffused by the cellular structure. The important tensile failure pattern in the homogeneous material, which is generated by the reflection of the compressive wave on the free surface, is not observed in the foam material. The diffusion of the stress wave spreads the impact effect to a large area, leading to the enhanced dissipation of the impact energy, which increases the ballistic limit of the foam panel.
We propose finite-time measures to compute the divergence, the curl and the velocity gradient tensor of the point particle velocity for two- and three-dimensional moving particle clouds. For this ...purpose, a tessellation of the particle positions is performed to assign a volume to each particle. We introduce a modified Voronoi tessellation which overcomes some drawbacks of the classical construction. Instead of the circumcenter we use the center of gravity of the Delaunay cell for defining the vertices. Considering then two subsequent time instants, the dynamics of the volume can be assessed. Determining the volume change of tessellation cells yields the divergence of the particle velocity. Reorganizing the various velocity coefficients allows computing the curl and even the velocity gradient tensor. The helicity of particle velocity can be likewise computed and swirling motion of particle clouds can be quantified. First we assess the numerical accuracy for randomly distributed particles. We find a strong Pearson correlation between the divergence computed with the the modified tessellation, and the exact value. Moreover, we show that the proposed method converges with first order in space and time in two and three dimensions. Then we consider particles advected with random velocity fields with imposed power-law energy spectra. We study the number of particles necessary to guarantee a given precision. Finally, applications to fluid particles advected in three-dimensional fully developed isotropic turbulence show the utility of the approach for real world applications to quantify self-organization in particle clouds and their vortical or even swirling motion.
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