Voro++ is a software library written in C++ for computing the Voronoi tessellation, a technique in computational geometry that is widely used for analyzing systems of particles. Voro++ was released ...in 2009 and is based on computing the Voronoi cell for each particle individually. Here, we take advantage of modern computer hardware, and extend the original serial version to allow for multithreaded computation of Voronoi cells via the OpenMP application programming interface. We test the performance of the code, and demonstrate that it can achieve parallel efficiencies greater than 95% in many cases. The multithreaded extension follows standard OpenMP programming paradigms, allowing it to be incorporated into other programs. We provide an example of this using the VoroTop software library, performing a multithreaded Voronoi cell topology analysis of up to 102.4 million particles.
Program title:Voro++
CPC Library link to program files:https://doi.org/10.17632/tddc4w4zkk.1
Developer's repository link:https://github.com/chr1shr/voro
Licensing provisions: BSD 3-clause (with LBNL modification)
Programming language: C++
External routines/libraries: OpenMP
Nature of problem: Multithreaded computation of the Voronoi tessellation in two and three dimensions
Solution method: The Voro++ library is built around several C++ classes that can be incorporated into other programs. The two largest components are the container... classes that spatially sort input particles into a grid-based data structure, allowing for efficient searches of nearby particles, and the voronoicell... classes that represent a single Voronoi cell as an arbitrary convex polygon or polyhedron. The Voronoi cell for each particle is built by considering a sequence of plane cuts based on neighboring particles, after which many different statistics (e.g. volume, centroid, number of vertices) can be computed. Since each Voronoi cell is calculated individually, the Voronoi cells can be computed using multithreading via OpenMP.
The Voronoi grain-based breakable block model (VGBBM) based on the combined finite-discrete element method (FDEM) was proposed to explicitly characterize the failure mechanism and predict the ...deformation behavior of hard-rock mine pillars. The influence of the microscopic parameters on the macroscopic mechanical behavior was investigated using laboratory-scale models. The field-scale pillar models (width-to-height, W/H=1, 2 and 3) were calibrated based on the empirically predicted stress-strain curves of Creighton mine pillars. The results indicated that as the W/H ratios increased, the VGBBM effectively predicted the transition from strain-softening to pseudo-ductile behavior in pillars, and explicitly captured the separated rock slabs and the V-shaped damage zones on both sides of pillars and conjugate shear bands in core zones of pillars. The volumetric strain field revealed significant compressional deformation in core zones of pillars. While the peak strains of W/H=1 and 2 pillars were relatively consistent, there were significant differences in the strain energy storage and release mechanism. W/H was the primary factor influencing the deformation and strain energy in the pillar core. The friction coefficient of the structural plane was also an important factor affecting the pillar strength and the weakest discontinuity angle. The fracture surface was controlled by the discontinuity angle and the friction coefficient. This study demonstrated the capability of the VGBBM in predicting the strengths and deformation behavior of hard-rock pillars in deep mine design.
Porous metal scaffolds play an important role in the orthopedic field, due to their wide applications in prostheses implantation. Some previous studies showed that the scaffolds with trabecular bone ...structure reconstructed via computed tomography had satisfactory biocompatibility. However, the reverse modeling scaffolds were inflexible for customized design. Therefore, a top-down designing biomimetic bone scaffold with favorable mechanical performances and cytocompatibility is urgently demanded for orthopedic implants. An emerging additive manufacturing technique, selective laser melting, was employed to fabricate the trabecular-like porous Ti-6Al-4 V scaffolds with varying irregularities (0.05-0.5) and porosities (48.83%–74.28%) designed through a novel Voronoi-Tessellation based method. Micro-computed tomography and scanning electron microscopy were used to characterize the scaffolds’ morphology. Quasi-static compression tests were performed to evaluate the scaffolds’ mechanical properties. The MG63 cells culture in vitro experiments, including adhesion, proliferation, and differentiation, were conducted to study the cytocompatibility of scaffolds. Compressive tests of scaffolds revealed an apparent elastic modulus range of 1.93–5.24 GPa and an ultimate strength ranging within 44.9–237.5 MPa, which were influenced by irregularity and porosity, and improved by heat treatment. Furthermore, the in vitro assay suggested that the original surface of the SLM-fabricated scaffolds was favorable for osteoblasts adhesion and migration because of micro scale pores and ravines. The trabecular-like porous scaffolds with full irregularity and higher porosity exhibited enhanced cells proliferation and osteoblast differentiation at earlier time, due to their preferable combination of small and large pores with various shapes. This study suggested that selective laser melting-derived Ti-6Al-4 V scaffold with the trabecular-like porous structure designed through Voronoi-Tessellation method, favorable mechanical performance, and good cytocompatibility was a potential biomaterial for orthopedic implants.
•A new approach is proposed for groundwater parameter structure identification.•Parameter structures are determined using the general form of the VT approach.•Minkowski distance is employed to assign ...the data points into the VT zones.•The heuristic SHALO approach is first applied to the solution of inverse problems.•Model identification performance has significantly enhanced.
A new simulation–optimization approach is proposed for solving the inverse parameter structure identification problems in groundwater systems. In the simulation part of the proposed approach, the numerical groundwater flow process is simulated by using MODFLOW. Parameter structures of the aquifer system are identified by partitioning the flow domain into a finite number of zones employing the general form of the Voronoi tessellation (VT). This MODFLOW and VT-based simulation model is then integrated into an optimization model where the SHuffled Ant Lion Optimization approach (SHALO) is used. This work is the first application of SHALO by considering the general form of the VT zonation approach for solving the inverse groundwater parameter structure identification problems. The applicability of the proposed simulation–optimization approach is evaluated on a hypothetical aquifer model in the literature. This evaluation is conducted by solving the same problem using Ant Lion Optimization (ALO) and its improved version, the self-adaptive ALO (saALO) for the same conditions. Furthermore, the identified results are compared with those obtained using harmony search (HS) and hybrid genetic algorithm (hybrid GA) based solution approaches in the literature. The obtained results indicated that the proposed approach provided better identification results than ALO, saALO, HS, and hybrid GA in terms of different evaluation metrics.
This paper is focused on the in-plane crushing of two-dimensional (2D) porous structures with a special attention on the effect of functionally graded (FG) porosities. The dynamic response and energy ...absorption of closed-cell metal foams with different porosity distributions are investigated by using finite element (FE) analysis. Two symmetric, two asymmetric and one uniform distributions of internal pores along the impact direction are constructed with Voronoi tessellation. The proposed porous structure is crushed under the impact of a rigid panel with a constant velocity. The deformation of cell walls is simulated using a plastic kinematic material model. The erosion criteria and hourglass control are applied to ensure the accuracy of numerical results, which are validated against the experimental data from open literature. The effects of varying parameters on the energy absorption, deformation pattern, and stress-strain curve of the FG porous structure are discussed. The dynamic response is found to be influenced by different random cell geometries, porosity gradients, cell wall thicknesses, internal pore numbers, and impact velocities. The effective way to improve the energy absorption capability of the porous structure under a constant-velocity impact is proposed, shedding new insights into the deformation mechanism of the FG porous structure for engineering design.
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•The porosity distribution of porous structures has a significant influence on the dynamic response.•The energy absorption under high-velocity impacting can be improved with the proposed graded porosity distribution.•The absorbed energy of porous structures increases with the increasing impact velocity.•The densification of cell walls tends to localize near the impact end under high impact velocities.
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•We propose an inverse design method for auxetic metamaterials using deep learning.•We designed novel 2D auxetic metamaterials based on Voronoi tessellation for the training ...dataset.•The trained neural network can generate 2D auxetic metamaterials with user-desired Young’s moduli and Poisson’s ratios.•The proposed method can easily be extended to the inverse design of other architected materials.
As typical mechanical metamaterials with negative Poisson’s ratios, auxetic metamaterials exhibit counterintuitive auxetic behaviors that are highly dependent on their geometric arrangements. The realization of the geometric arrangement required to achieve a negative Poisson’s ratio relies considerably on the experience of designers and trial-and-error approaches. This report proposes an inverse design method for auxetic metamaterials using deep learning, in which a batch of auxetic metamaterials with a user-defined Poisson’s ratio and Young’s modulus can be generated by a conditional generative adversarial network without prior knowledge. The network was trained based on supervised learning using a large number of geometrical patterns generated by Voronoi tessellation. The performance of the network was demonstrated by verifying the mechanical properties of the generated patterns using finite element method simulations and uniaxial compression tests. The successful realization of user-desired properties can potentially accelerate the inverse design and development of mechanical metamaterials.
The Voronoi tessellation is a fundamental geometric data structure which has numerous applications in various scientific and technological fields. For large particle datasets, computing Voronoi ...tessellations must be conducted in parallel on a distributed-memory supercomputer in order to satisfy time and memory-size constraints. However, due to load balance and communication, the parallelization of the Voronoi tessellation renders a challenge. In this paper, we present a scalable parallel algorithm for constructing 3D Voronoi tessellations, which evenly distributes the input particles between blocks through kd-tree decomposition. In order to construct the correct global Voronoi topology, we investigate both parametric and non-parametric methods for particle communication among the blocks of a spatial decomposition. The algorithm is implemented exploiting process-level and thread-level parallelization and can be used in a diverse architectural landscape. Using datasets containing up to 330 million particles, we show that our algorithm achieves parallel efficiency up to 57% using 4096 cores on a distributed-memory computer. Moreover, we compare our algorithm with previous attempts to parallelize Voronoi tessellations showing encouraging improvements in terms of computation time.
•A new parallel algorithm for computing 3D Voronoi based on kdtree decomposition.•Parametric and non-parametric methods for establish communication.•An evaluation of the algorithm, including parallel accuracy and scalability.•A publicly available library (named ParVoro++) implemented as a fork of Voro++.
This paper studies an adaptive area optimal coverage control method for multi-manipulator systems under the presence of both uncertain kinematics and dynamics. Initially, an objective cost function ...associating the voronoi tessellation is utilized to transform the optimal coverage control into the tracking control problem. Consequently, an adaptive area optimal coverage control strategy is designed by using the adaptive dynamic and kinematic programming. In this control strategy, the sliding mode control technology for each robot manipulator system is created to pursue control optimality and prescribed coverage performance simultaneously. The adaptive control algorithm using the parameter linearization properties is further deployed to directly cope with the influence caused by the parameter uncertainties of manipulator dynamics and kinematics. Theoretical analysis is given to guarantee the stability and convergence of the proposed optimal area converge controller, subject to optimal cost. Illustrative example is provided to validate the performance of the proposed framework.
•An area optimal coverage control strategy for manipulators is proposed.•This novel coverage control strategy is based on the voronoi tessellation.•The proposed method has great robustness and model generalization.
The current paper presents an overview of traditional and recent models for predicting the thermal properties of solid foams with open- and closed-cells. Their effective thermal conductivity has been ...determined analytically by empirical or thermal-resistance-network-based models. Radiative properties crucial to obtain the radiative conductivity have been determined analytically by models based on the independent scattering theory. Powerful models combine three-dimensional (3D) foam modelling (by X-ray tomography, Voronoi tessellation method, etc.) and numerical solution of transport equations. The finite-element method (FEM) has been used to compute thermal conductivity due to solid network for which the computation cost remains reasonable. The effective conductivity can be determined from FEM results combined with the conductivity due to the fluid, which can be accurately evaluated by a simple formula for air or weakly conducting gas. The finite volume method seems well appropriate for solving the thermal problem in both the solid and fluid phases. The ray-tracing Monte Carlo method constitutes the powerful model for radiative properties. Finally, 3D image analysis of foams is useful to determine topological information needed to feed analytical thermal and radiative properties models.
Cet article présente une vue globale des modèles traditionnels et récents de prédiction des propriétés thermiques et radiatives des mousses solides ayant des cellules ouvertes ou fermées. Leur conductivité thermique effective est déterminée par des modèles empiriques ou analytiques basés sur le réseau de résistances. Les propriétés radiatives nécessaires pour remonter à la conductivité radiative sont déterminées par des modèles analytiques basés sur la théorie de diffusion indépendante. Les approches robustes couplent la modélisation tridimensionnelle (3D) de mousses (par exemple, par la tomographie à rayons X, la mosaïque de Voronoï, etc.) et la résolution numérique des équations de transport. La conductivité thermique due à la phase solide est directement calculée par la méthode des éléments finis (EF), avec un coût de calcul raisonnable. La conductivité thermique effective, quant à elle, peut être déterminée à partir des calculs EF combinés avec la conductivité thermique due à la phase fluide. Cette dernière peut être évaluée de façon précise par des formules simples dans le cas de l'air ou d'un gaz faiblement conducteur thermique. Cependant, la méthode des volumes finis apparaît la mieux appropriée pour résoudre le problème thermique, à la fois dans la phase solide et la phase fluide. La méthode de Monte Carlo et de tracé de rayons constitue une approche solide pour calculer les propriétés radiatives. Enfin, la reconstruction d'image 3D des mousses est essentielle pour déterminer les informations topologiques nécessaires pour alimenter les modèles analytiques de conductivité thermique et de propriétés radiatives.
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