Voronoi Technique Research Articles

Anisotropic mechanics of cell-elongated structures: Finite element study based on a 3D cellular model

Cell-elongated structures present designable anisotropic behaviors by controlling the ratio and angle of elongation, but the relationship between geometric anisotropy and mechanical anisotropy remains poorly understood. In this study, a construction method based on the 3D Voronoi technique is employed to generate cell-elongated structures with different elongation ratios and angles, and their anisotropic compression behaviors are investigated using a 3D cellular model. The stress–strain curves can be categorized into four stages, including elasticity, initial collapse followed by strain-softening, plateau, and densification, which are accurately described by a statistical constitutive model. Our finding reveals that the mechanical properties and deformation modes of the cell-elongated structures are significantly influenced by the anisotropic angle. At an anisotropic angle of 0°, randomly distributed collapse bands due to shell buckling interact with each other during compression, enhancing the load-carrying and energy-absorbing capacities. Conversely, at 90°, the cells deform primarily through a stable bending mode, leading to reduced stress and a lower Poisson’s ratio. At 45°, collapse bands appear on both sides of the sample with rotation and buckling being the dominant deformation mode, resulting in a sandwich-like structure featuring an uncollapsed central zone due to a combined compression–shear stress state. Compared with the isotropic foam, the structure elongated in thickness direction exhibits a notable increase in impact resistance under a spherical bullet. This work demonstrates the potential to engineer anisotropic cellular materials with tailored mechanical properties and deformation modes through strategic geometric anisotropy design.

Effect of porosity and pore heterogeneity on heat transfer performance of polyimide aerogels

The effects of porosity and pore distribution on the heat transfer performance of polyimide (PI) aerogel under natural convection were investigated through a combination of experimental and numerical simulations. The governing equations of heat transfer were analyzed in detail. A novel heterogeneity factor (η) was introduced to quantify internal pore distribution. PI aerogels exhibiting a range of porosities and heterogeneity factors were synthesized and characterized. The natural convection heat transfer coefficient of PI aerogels was measured experimentally, providing empirical data. A porous model was developed by integrating Voronoi technique with a two-scale generation method, allowing for comprehensive numerical simulations of heat transfer. The numerical results demonstrated strong concordance with the experimental data, validating the model’s accuracy. The results revealed that the heat transfer performance of the aerogels diminished markedly with increasing porosity when heterogeneity was held constant. Conversely, with fixed porosity, the heat transfer performance improved significantly with greater heterogeneity. Numerical simulations further enabled the visualization of internal temperature and flow fields, elucidating that the effect of porosity and heterogeneity on natural convection heat transfer performance is predominantly driven by variations in internal permeability.

Blast-loading simulators: Multiscale design of graded cellular projectiles considering projectile–beam coupling effect

Graded cellular materials with a proper design may simulate blast loading and can be applied to test the anti-blast performance of protective structures. A multiscale design strategy is proposed to obtain the density distribution and mesostructure of graded cellular projectiles when taking a clamped beam as a protective structure and an exponential attenuation load as the simulation target. A projectile–target coupling model is developed for determining the projectile density distribution, and the dimensionless governing equations containing two kinds of dimensionless parameters, namely target-independent parameters and coupling parameters, are obtained. The closed-cell mesostructure of a graded cellular projectile is generated through the Voronoi technique, and the cell configuration parameters are optimized to achieve the designed density distribution while ensuring manufacturability. The graded cellular projectiles are prepared by using 3D printing technology, and their load simulation effects are verified through numerical simulations and impact tests. Case studies demonstrate the necessity of considering the projectile–target coupling effect in the density design. The applicable test condition and selection method of initial parameters of graded cellular projectiles are analyzed with dimensionless parameters. It is found that the initial momentum of the projectile mainly governs its effective simulation duration. With the increase of the initial momentum, the effective simulation duration increases, and the initial momentum should be less than the total impulse of the simulated blast load. The impact technique of well-designed graded cellular projectiles shows great potential in simulating various blast loadings and testing novel protective structures in a laboratory environment.

Investigations on the quasi-static/dynamic mechanical properties of 3D printed random honeycombs under in-plane compression

The aim of this study was to reveal the effects of inertia and base material strain rate on the mechanical properties of 3D-printed random honeycombs. First, random honeycombs were established with various meso-structural parameters based on the Voronoi technique and then manufactured by 3D printing. Quasi-static compression tests were performed using a universal test machine. The results indicated that the random honeycombs exhibited a more uniform deformation mode which led to a gentle stress–strain curve when compared with the regular honeycombs. Furthermore, the strain rate effect of the base material was determined by Split Hopkinson Pressure Bar (SHPB) tests. Finite element models considering the base material strain rate were verified by the quasi-static compression and drop weight impact tests. Dynamic simulations were carried out to determine the critical velocity between the deformation mode and clarify its mechanisms. The second critical velocities increase as the cell size and cell wall thickness increased or as the strain rate effect of the base material is considered. The effects of inertia and base material strain rate on the mechanical properties were discussed. The dynamic stress enhancement is dominated by the strain rate effect of the base material and the inertia effect in the random and shock modes, respectively. Finally, an empirical model that includes the inertia effect and strain rate effect of the base material was proposed based on the 1D shock wave theory and the Johnson–Cook material model.

A process-based hydrological model for continuous multi-year simulations of large-scale watersheds

Process-based hydrological models are useful tools to understand the mechanisms responsible for extreme floods and droughts and thus facilitate watershed management. This paper describes a watershed model, based on the coupled surface-subsurface distributed model Penn State Hydrologic Model (PIHM), to capture the hydrologic response of large watersheds over decades. Mathematical models for coupling surface-subsurface fluxes were developed to achieve mass conservation in multi-year simulations. A Voronoi technique was implemented to improve accuracy and computational efficiency. The model was used to simulate the Cedar River Watershed, IA from 2003 to 2018. Model predictions were compared against streamflow observations at four gauging stations. Results show good model performance with average Nash–Sutcliffe efficiency values greater than 0.70. The model results helped to identify the main hydrologic processes that contributed to the historic 2008 flood in the Cedar River Watershed. In addition to heavy storms, several other factors played an important role, including snowmelt and rainstorms in the spring, as well as low evapotranspiration values associated with traditional row crop agriculture in the first half of the year.

A note on the modelling of foams using Voronoi technique

Previous researchers have used Voronoi honeycombs to represent and predict the responses of random foams. Often, a two-dimensional Voronoi honeycomb model is used and the results are regarded as being identical to those of actual foams, which are in fact three-dimensional. The present study focuses on possible performance difference and the intrinsic relationship between Voronoi honeycombs and foams. Geometrical models of Voronoi honeycombs and foams with different cell irregularities are generated. Their relative densities are first calculated and compared. Based on the geometric models and an idealised elastic perfectly plastic property for the parent material, finite element (FE) analysis is carried out, respectively, for the block of the cellular material under quasi-static compression between two rigid platens. Consequently, stress–strain relationships are obtained, and it is shown that a two-dimensional Voronoi model cannot always be adopted to represent a three-dimensional foam in studying the behaviour of cellular solids.

Study on the effect of the size irregularity gradient of metal foams on macroscopic compressive properties

Size irregularity gradient and cell wall gradient, combined as the density gradient in previous studies, affect the macroscopic mechanical properties of the gradient metal foam. More and more complex mesostructures are designed and applied in metal foams, and the density gradient becomes insufficient to describe the difference in mesostructures. To explore the effect of mesostructures carefully, this study focuses on the effect of the size irregularity gradient on the macroscopic compressive properties of metal foams. A series of metal foam models were developed using the 3D Voronoi technique. These models have the same average relative densities, the same average diameters and different size irregularity gradients. Simulation results indicated that the macroscopic mechanical properties of cell wall gradient metal foams are significantly different from those of size irregularity gradient metal foams, though these models have the same relative density gradient. To explore the effect of size irregularity gradient, a theoretical model was developed to characterize the compression process from the first cell-collapse to full condensation. Theoretical results showed a linear relationship between the nominal stress and the current relative density. These findings can provide efficient guidance for the design and applications of gradient metal foams.

Research on Blast Resistance of the Cylinder with Aluminium Foam under Internal Explosive Load

Aluminium foam has an excellent performance in terms of impact resistance and energy absorption. The experimental and numerical investigations on the blast resistance of the cylinder with aluminium foam under internal explosive load are carried out in this thesis and the factors influencing the blast resistance are analyzed. First, experiments were carried out under internal explosive load with different relative densities and explosion loads, and the defections of inner and outer layers were obtained. Second, based on the voronoi technique, a 2D finite element model of sandwich cylinders with a core of aluminium foam was constructed, the effectiveness of the model was then confirmed by conflicting results from simulations and experiments. Finally, the finite element model was used to analyze the effects of characteristic cell size and explosive load, which were reflected in the energy absorption and deflection of the outer layer. The test results show that the simulation results agree well with the experimental results. The characteristic cell size has little influence on energy absorption. In the case of homogeneous cores, the energy absorption per unit of mass decreases linearly with increasing relative density and the deflections of outer layers increase slightly.

Mesoscale investigation on failure behavior of reinforced concrete slab subjected to projectile impact

The mesoscale components of concrete have a great influence on its mechanical performance, and thus the mesoscale investigation on failure behavior of reinforced concrete slab subjected to projectile impact has an important significance to accurately predict the impact resistance of structures. In this paper, a fast and parallel modeling method based on the Voronoi technique is proposed to establish the 3D mesoscale model of reinforced concrete, including the arranging nuclei method and adding reinforcement method, and the efficiency and success rate of arranging nuclei are analyzed. Then, the erosion criterion considering the coupling of damage and maximum principle strain is introduced to capture the tensile failure behavior of concrete, and the perforation simulations under impact velocities ranging from 434.0m/s to 1058.0m/s are conducted to verify the accuracy and reliability of the proposed model. The numerical results show good agreements with the experimental and theoretical results, which demonstrates that the mesoscale model of reinforced concrete combined with this erosion criterion can more precisely and visually predict the cratering, scabbing and cracking phenomena. Furthermore, the effects of mortar strength, aggregate strength and failure strength of tiebreak contact on the impact resistance of reinforced concrete are obtained.

Experimental and mesoscale numerical investigation on the failure behavior of reinforced concrete under projectile-impact loading

<p indent=0mm>Reinforced concrete is widely used and plays important roles in civil engineering and national defense. It also suffers from an obvious scale effect. Conducting a large-scale penetration experiment is necessary to study the dynamic response of reinforced-concrete under impact loading. In this study, experiments were conducted for a 100-mm large-caliber ovoid projectile to penetrate reinforced-concrete targets at high speed. The damage mode, penetration depth, and crater diameter of the target were analyzed in detail. Owing to the reinforcement, concrete exhibits more complex heterogeneity and anisotropy, and the deformation, damage, and interaction of each component indicate an important effect on the mechanical properties of concrete. A fast and parallel modeling method of 3D mesoscale reinforced-concrete model based on the Voronoi technique was proposed, which solved the problems of large-scale arranged aggregates and intersection detections between the reinforcement and aggregates. The mesoscale numerical simulations were conducted in combination with the K&C model, and the effects of the projectile hitting and not hitting the reinforcements on the penetration depth, crater diameter, and ballistic trajectory were analyzed. The damage mode of the slabs and reinforcements, penetration depth of the projectile, and trajectory deflection were obtained. The numerical results show good agreement with the experimental results, which indicate that the mesoscale model can effectively and accurately predict the failure behavior of reinforced-concrete.

Accurate determination of grain properties using three-dimensional synchrotron X-ray diffraction: A comparison with EBSD

The characterization of elastic strain and stress at the grain level is becoming an important route for validating meso- and nano-scale numerical models. The response of a grain to a mechanical load depends not only on the elastic and plastic properties of the single crystal, but also on the interaction of the grain with its local neighborhood. In this paper, an in-situ three-dimensional synchrotron X-ray diffraction experiment is conducted on a polycrystalline zirconium specimen. The data obtained from the experiment are used to develop methods to reconstruct three-dimensional grain maps by adding the grain layers measured by a planar X-ray beam, and to track individual grains across loading steps. The measured center-of-the-mass and volume of each grain are subsequently used to reconstruct 3D grain boundaries using the weighted Voronoi technique, and to determine grain neighborhoods. The results from the developed post-processing methods are compared against those measured using electron backscatter diffraction (EBSD) technique. It is shown that with the use of the developed methods, both small and big grains are accurately determined with 3D-XRD. It is further shown that the accuracy of the implemented Voronoi technique in determining the right grain neighborhood is more than 80%.

An Efficient Batch K-Fold Cross-Validation Voronoi Adaptive Sampling Technique for Global Surrogate Modeling

Abstract Surrogate models can be used to approximate complex systems at a reduced cost and are widely used when data generation is expensive or time consuming. The accuracy of these models is dependent on the samples used to create them. Therefore, proper sample selection within the parameter space is paramount. Numerous design of experiments (DOE) methodologies have been developed with the aim of identifying the optimal sample set to capture the system of interest. Adaptive sampling techniques are a subclass of DOE methods that identify optimal locations for new samples by leveraging response information from existing samples. By exploiting knowledge of the system, adaptive sampling methods have been demonstrated to significantly reduce the number of samples required to build a surrogate model of a given accuracy. However, utilizing the response information of the previous samples adds a computational cost associated with determining the ideal sample locations. Additionally, this cost typically grows with the sample count. This article presents techniques to reduce the cost associated with the adaptive sampling procedure so that the cost savings provided by adaptive sampling are maximized. A new K-fold cross-validation (KFCV)-Voronoi adaptive sampling technique is proposed to reduce the sample selection costs by adding a global KFCV filter to the cross-validation (CV)-Voronoi technique. The costs are further reduced through an innovative Voronoi batch sampling technique that is demonstrated to outperform naïve batch sampling. The proposed adaptive sampling acceleration techniques are evaluated using benchmark functions of increasing dimension and aerodynamic loading data.

Dynamic Compressive Behaviors of Two-Layer Graded Aluminum Foams under Blast Loading.

Experimental and numerical analyses were carried out to reveal the behaviors of two-layer graded aluminum foam materials for their dynamic compaction under blast loading. Blast experiments were conducted to investigate the deformation and densification wave formation of two-layer graded foams with positive and negative gradients. The shape of the stress waveform changed during the propagation process, and the time of edge rising was extended. Finite element models of two-layer graded aluminum foam were developed using the periodic Voronoi technique. Numerical analysis was performed to simulate deformation, energy absorption, and transmitted impulse of the two-layer graded aluminum foams by the software ABAQUS/Explicit. The deformation patterns were presented to provide insights into the influences of the foam gradient on compaction wave mechanisms. Results showed that the densification wave occurred at the blast end and then gradually propagated to the distal end for the positive gradient; however, compaction waves simultaneously formed in both layers and propagated to the distal end in the same direction for the negative gradient. The energy absorption and impulse transfer were examined to capture the effect of the blast pressure and the material gradient. The greater the foam gradient, the more energy dissipated and the more impulse transmitted. The absorbed energy and transferred impulse are conflicting objectives for the blast resistance capability of aluminum foam materials with different gradient distributions. The results could help in understanding the performance and mechanisms of two-layer graded aluminum foam materials under blast loading and provide a guideline for effective design of energy-absorbing materials and structures.

Revisiting the Deshpande-Fleck Foam Model

The self-similar isotropic hardening model developed by Deshpande and Fleck has been widely used. An important issue in this model is to determine the value of ellipticity. The ellipticity was treated as a constant in the subsequent yield, but different values were suggested in the literature. In this paper a cell-based finite element model based on the 3D Voronoi technique is used to verify the Deshpande-Fleck foam model. It is found that the ellipticity determined from uniaxial and hydrostatic compressions varies with the equivalent plastic strain.

Compaction Wave Propagation in Layered Cellular Materials Under Air-Blast

The propagation of compaction waves in layered cellular material subjected to air-blast is analyzed to examine the mechanism of compaction wave and reveal the phenomena that develop at the interface between the cellular layers. Similar to the previous studies of cellular materials under dynamic loading, the topology of cellular materials is neglected and homogeneous properties are assumed. The rigid-perfectly plastic-locking (R-PP-L) material idealization and the simple shock theory are employed to analyze the compaction situations. Analytical solutions for compaction wave propagation of double-layer cellular materials with two gradient-arrangements under air-blast loading have been worked out. The densification wave occurs at the blast end and then gradually propagates to the distal end for layers’ densities increase in the propagation direction (positive gradient). While compaction waves simultaneously form in both layers and propagate to the distal end in the same direction for the negative gradient. The finite element (FE) models using the Voronoi technique are carried out with practical aluminum foam to verify the predictions of the theoretical analysis. The potential of layered cellular materials to design efficient structural components under air-blast load is discussed, which would outperform their corresponding single counterpart with equal mass.

Impact Resistance and Design of Graded Cellular Cladding

One-dimensional impact response of graded cellular rods with monotonously increasing density distribution, which benefits in buffering the impact object in proximal end, is investigated by using shock models and cell-based finite element models. Based on the rigid–plastic hardening (R-PH) idealization, a theoretical model of the shock front propagation behavior in graded cellular rods subjected by impact is developed and solved numerically with a fourth-order Runge–Kutta scheme. Finite element analysis is performed using 2D random Voronoi technique, and the comparisons illustrate that the theoretical predictions and finite element results are in good agreement. The anti-impact responses of graded cellular materials with different gradient parameters are carried out, and it is demonstrated that the design indicators, including support stress, critical length and maximum deceleration of the object, are highly related to the gradient parameters of graded cellular materials. A design strategy for the impact alleviation of graded cellular materials is proposed. Thus, the gradient parameters can be finally determined to meet the requirement of the actual design indicators and it can also offer an optimal critical length for final graded cellular materials.

Crushing and densification of rapid prototyping polylactide foam: Meso-structural effect and a statistical constitutive model

The deformation characteristics and mechanical behavior of closed-cell polylactide (PLA) foams under quasi-static uniaxial compression are investigated. The PLA foam specimens are constructed numerically with 3D Voronoi technique and prepared with fused deposition modeling (FDM). The effects of meso‑structure, layer deposition strategy and relative density on the crushing and densification behaviors of PLA foams are analyzed. The experimental results indicate that PLA foams with regular meso‑structures are more likely to induce local collapse during compression, and those with random meso‑structures show good performances, such as high specific energy absorption, low stress fluctuation and stable deformation process. The experimental results further reveal that random PLA foams with the deposition layers perpendicular to the loading direction have higher strength and smaller lateral expansion than those with other orientations. The quasi-static compression stress-strain curves of random PLA foams exhibit three typical stages, namely linear elastic stage, plastic collapse stage and densification stage. A stress drop after reaching the initial peak stress is observed. To characterize these features, we propose a statistical constitutive model which takes into account the meso‑structural characteristics and deformation mechanism at the cell scale. This constitutive model contains six parameters and fits the experimental results very well. In particular, it can capture the peak stress at the onset of plastic collapse and the subsequent stress drop of cellular materials. Finally, the dependence of the six parameters in the constitutive model on the relative density is analyzed and the corresponding quantitative statistical relationships are determined.

Blast response of continuous-density graded cellular material based on the 3D Voronoi model

Abstract One-dimensional blast response of continuous-density graded cellular rods was investigated theoretically and numerically. Analytical model based on the rigid-plastic hardening (R-PH) model was used to predict the blast response of density-graded cellular rods. Finite element (FE) analysis was performed using a new model based on the 3D Voronoi technique. The FE results have a good agreement with the analytical predictions. The blast response and energy absorption of cellular rods with the same mass but different density distributions were examined under different blast loading. As a blast resistance structure, cellular materials with high energy absorption and low impulse transmit is attractive. However, high energy absorption and low impulse transmit cannot be achieved at the same time by changing the density distribution. The energy absorption capacity increases with the initial blast pressure and characteristic time of the exponentially decaying blast loading. By contract, when the blast loading exceeds the resistance capacity of cellular material, the transmitted stress will be enhanced which is detrimental to the structure being protected.

A Voronoi element based-numerical manifold method (VE-NMM) for investigating micro/macro-mechanical properties of intact rocks

In this study, a two-dimensional Voronoi element based-numerical manifold method (VE-NMM) was developed as a new approach to investigate the micro- and macro- mechanical properties of intact rocks. The Voronoi technique was used to generate a polygonal grain assemblage to approximate the microstructure of sandstone samples from Gubei colliery of Huainan mining area in China. A modified contact model incorporating cohesion and tensile strength was adopted to interpret the interactions between rock grains. A series of laboratory tests, i.e. scanning electron microscope tests, uniaxial compression and Brazilian tests were carried out to obtain the microstructural information and macro-mechanical properties of the sandstone samples. To verify the proposed VE-NMM, simulations of Brazilian tensile splitting and uniaxial compressive tests were carried out and the results, in terms of strength, elastic constant and crack distribution, were compared to those of the laboratory tests. To investigate the effects of grain size on the micro-mechanical parameters and the representative elementary volume (REV) size, numerical uniaxial compression tests with different grain sizes (2mm, 3 mm and 4 mm) were conducted using the developed VE-NMM approach. Simulation results indicate that both the micro-mechanical parameters and the representative elementary volume size are heavily dependent on grain size.

Generation of 3D polycrystalline microstructures with a conditioned Laguerre-Voronoi tessellation technique

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.