Voronoi Tessellation Method Research Articles

Investigation of failure analysis on fatigue crack initiation influenced by critical resolved shear stress in X10CrMoVNb9-1 steel

This study investigates the influences of the critical resolved shear stress (CRSS) values on calculating the number of cycles for the fatigue crack initiation cycle of X10CrMoVNb9-1 (P91) under cyclic loading conditions at room temperature while considering varied surface roughness on microstructure models. The micropillar compression test was utilized to calculate the CRSS values, incorporating the Schmid factor, the Frank–Read source together with the Hall–Petch effect, measuring the diameter of the micropillar after compression, and the Mlikota and Schmauder equation. Two primary microstructure surface roughness – plane surface roughness (PS) and surface roughness (SR) with an average of 1 µm – were generated using the Voronoi Tessellation (VT) method. Finite Element Method (FEM) simulations were conducted to identify different stress distributions across these artificial microstructures. These stress distributions were subsequently analyzed using the physics-based Tanaka-Mura model (TMM) to estimate the number of cycles for fatigue crack initiation at several stress amplitudes and six types of microstructure. The number of cycles varies significantly at lower stress amplitudes and convergence at higher stress amplitudes. The study of the CRSS of steel P91 offers a significant advancement in fatigue research, particularly with implications for power plants.

Numerical Assessment of Effective Elastic Properties of Needled Carbon/Carbon Composites Based on a Multiscale Method

Needled carbon/carbon composites contain complex microstructures such as irregular pores, anisotropic pyrolytic carbon, and interphases between fibers and pyrolytic carbon matrices. Additionally, these composites have hierarchical structures including weftless plies, short-cut fiber plies, and needled regions. To predict the effective elastic properties of needled carbon/carbon composites, this paper proposes a novel sequential multiscale method. At the microscale, representative volume element (RVE) models are established based on the microstructures of the weftless ply, short-cut fiber ply, and needled region, respectively. In the microscale RVE model, a modified Voronoi tessellation method is developed to characterize anisotropic pyrolytic carbon matrices. At the macroscale, an RVE model containing hierarchical structures is developed to predict the effective elastic properties of needled carbon/carbon composites. For the data interaction between scales, the homogenization results of microscale models are used as inputs for the macroscale model. By comparing these against the experimental results, the proposed multiscale model is validated. Furthermore, the effect of porosity on the effective elastic properties of needled carbon/carbon composites is investigated based on the multiscale model. The results show that the effective elastic properties of needled carbon/carbon composites decrease with the increase in porosity, but the extent of decrease is different in different directions.

Tough Cortical Bone-Inspired Tubular Architected Cement-Based Material with Disorder.

Cortical bone is a tough biological material composed of tube-like osteons embedded in the organic matrix surrounded by weak interfaces known as cement lines. The cement lines provide a microstructurally preferable crack path, hence triggering in-plane crack deflection around osteons due to cement line-crack interaction. Inspired by this toughening mechanism and facilitated by a hybrid (3D-printing/casting) process, the study engineers architected tubular cement-based materials with the stepwise cracking toughening mechanism, that enables a non-brittle fracture. Using experimental and theoretical approaches, the study demonstrates the competition between tube size and shape on stress intensity factor from which engineering stepwise cracking can emerge. Two competing mechanisms, both positively and negatively affected by the growing tube size, arise to significantly enhance the overall fracture toughness by up to 5.6-fold compared to the monolithic brittle counterpart without sacrificing the specific strength. This is enabled by crack-tube interaction and engineering the tube size, shape, and orientation, which promotes rising resistance-curves (R-curve). "Disorder" curves and statistical mechanics parameters are proposed for the first time to quantitatively characterize the degree of disorder for describing the representation of the architected arrangement of materials in lieu of otherwise inadequate "periodicity" classification and misperceiveddisorder parameters (perturbation and Voronoi tessellation methods).

Vibrational Spectra Simulations in Amino Acid-Based Imidazolium Ionic Liquids.

We present maximally localized Wannier functions and Voronoi tessellation to obtain dipole moment distributions for vibrational spectra in several important ionic liquids calculated by using ab initio molecular dynamics simulations. IR and Raman spectra of various imidazolium-based ionic liquids (ILs) paired with six amino acid anions are shown herein. For IR spectra, two approaches (Wannier and Voronoi) are in agreement with respect to the relative intensities and the overall shapes for the main peaks. Under Raman spectra, the polarizability of the covalent bonds is shown to affect the strength of the Raman scattering signal. The advantage of the Voronoi tessellation method, being that it does not have strong spikes in its time development, is demonstrated by the comparison of two theoretical methods (Wannier and Voronoi) with experimental data. We analyze the errors between theoretical and experimental spectroscopic data, with the Voronoi method shown to accurately reproduce experimental values. In addition, theoretical spectroscopy shows the ability to accurately separate components of a mixture. The combination of theoretical and experimental methods is utilized to understand the spectroscopic properties of amino acid-based imidazolium ILs.

Accelerating structure search using atomistic graph-based classifiers.

We introduce an atomistic classifier based on a combination of spectral graph theory and a Voronoi tessellation method. This classifier allows for the discrimination between structures from different minima of a potential energy surface, making it a useful tool for sorting through large datasets of atomic systems. We incorporate the classifier as a filtering method in the Global Optimization with First-principles Energy Expressions (GOFEE) algorithm. Here, it is used to filter out structures from exploited regions of the potential energy landscape, whereby the risk of stagnation during the searches is lowered. We demonstrate the usefulness of the classifier by solving the global optimization problem of two-dimensional pyroxene, three-dimensional olivine, Au12, and Lennard-Jones LJ55 and LJ75 nanoparticles.

Dental stem cells improve memory and reduce cell death in rat seizure model.

Epilepsy is a common neurological disorder that significantly affects the quality of life of patients. In this study, we aim to evaluate the effectiveness of dental pulp stem cell (DPSC) transplantation in decreasing inflammation and cell death in brain cells, thus reducing seizure damage. We induced seizures in rats using intraperitoneal injections of pentylenetetrazole (PTZ). In the PTZ + DPSC group, we conducted bilateral hippocampal transplantation of DPSCs in PTZ-lesioned rat models. After 1 month, we performed post-graft analysis and measured some behavioral factors, such as working memory and long-term memory, using a T-maze test and passive avoidance test, respectively. We investigated the immunohistopathology and distribution of astrocyte cells through light microscopy and Sholl analysis. Additionally, we employed the Voronoi tessellation method to estimate the spatial distribution of the cells in the hippocampus. Compared to the control group, we observed a reduction in astrogliosis, astrocyte process length, the number of branches, and intersections distal to the soma in the hippocampus of the PTZ + DPSC group. Further analysis indicated that the grafted DPSCs decreased the expression of caspase-3 in the hippocampus of rats with induced seizures. Moreover, the DPSCs transplant protected hippocampal pyramidal neurons against PTZ toxicity and improved the spatial distribution of the hippocampal neurons. Our findings suggest that DPSCs transplant can be an effective modifier of astrocyte reactivation and inflammatory responses.

Crystal plasticity modeling fatigue behavior in bimodal Ti–6Al–4V: Effects of microdefect and lamellar orientation

AbstractInvestigating fatigue failure in titanium alloys is crucial for material design and engineering. Fatigue behavior in dual‐phase titanium alloys is strongly correlated with microstructural features and microdefects. This work formulates an improved modeling method to investigate fatigue behavior of bimodal Ti–6Al–4V, emphasizing the effects of lamellar orientation and microdefects. Using an improved Voronoi tessellation method, we establish representative volume element (RVE) models with various grain size distributions. Crystal plasticity finite element modeling (CPFEM) is used to analyze fatigue deformation in bimodal Ti–6Al–4V, considering microdefects and lamellar orientation. Fatigue indicator parameters are then incorporated into CPFEM to predict fatigue life and verified with experimental data. Numerical results highlight the significant influence of lamellar orientation and microdefects on fatigue behavior, with predicted life within the 3‐error band. This method efficiently overcomes challenges in quantitatively characterizing microstructural lamellae that experiments are short of, paving the way for designing fatigue‐resistant alloy materials with similar microstructures.

Discrete element simulation study on effects of grain preferred orientation on micro-cracking and macro-mechanical behavior of crystalline rocks

Abstract Grain-preferred orientation significantly influences the brittle fracture mechanism and failure mode of crystalline rocks. However, current grain-based models (GBMs) based on particle flow code (PFC) software are mostly proposed on the basis of the Voronoi tessellation method for grain boundary generation, which is difficult to simulate the heterogeneity of microstructure such as shape and orientation of rock minerals. To study the effect of grain-preferred orientation on macroscopic mechanical properties and microscopic characteristics of crystalline rocks, a novel grain-based microstructure transformation method (MTM) is proposed. Based on the MTM, a GBM with a target aspect ratio and crystal orientation is obtained by transforming the Voronoi crystal geometry through a planar coordinate mapping. Specifically, embedded FISH language is used to control random mineral seed size and distribution pattern to generate Tyson polygons. A polygon geometry that satisfies the rock texture is obtained as a grain boundary by spatially transforming the vertex of the Tyson polygon. The transformed complex geometry is taken as the crystal structure of the GBM, and the Lac du Bonnet granite models with different aspect ratios and crystal orientations were developed in PFC2D. Finally, a series of unconfined compressive strength tests are performed in PFC2D to verify the proposed modeling methods for the geometric variation of the crystals and to study the effects of the preferred orientation of the grains on the macroscopic mechanical properties and microscopic fracture mechanisms of the crystalline rocks from different perspectives.

Representation of the microstructure of pearlitic steels for DEM simulations of fatigue

The fatigue behavior of pearlitic steels in wheel-rails is correlated to the microstructure. However, existing models do barely take this correlation into account. In this work, we propose a hierarchical meshing to describe the microstructure of pearlitic steels. The mesh includes grain and block/colony boundaries, lamellae orientations, and orientation perpendicular to lamellae. We use the Voronoi Tessellation method to generate elements with the specific area fraction distribution for pearlite colony areas. The colony and block information is obtained from SEM and EBSD measurements of R260 steel to construct the mesh that represents the microstructure. Finally, we obtained the deformed microstructure via simple geometrical shearing. This meshing method is the first step for modeling fatigue crack growth anisotropy due to plastic deformation.

Role of cluster structure on the deformation behavior of Zr58Cu36Al6 metallic glass

Molecular dynamics simulations were used to simulate the process of tensile and compressive deformation of Zr58Cu36Al6 metallic glass (MG), and the variations of various cluster structures during the deformation were analyzed by the Voronoi tessellation method. The prepared Zr58Cu36Al6 alloy was found to be amorphous and the glass transition temperature obtained was about 753 K. In the deformation processes, the icosahedral-like clusters with the biggest quantity percentage decreased significantly and eventually, the damaged icosahedral-like clusters tended to be destroyed into "fragmented" clusters. Icosahedral-like clusters were more stable due to their lower average strain and shear stress compared to other clusters. The higher strain and shear stress of the clusters led to an earlier stress drop of Zr58Cu36Al6 MG during compression. However, the higher connectivity of the icosahedral network remained in Zr58Cu36Al6 MG making the overshoot stress and flow stress larger but lower plasticity in compression than those in tension.

Additive manufactured trabecular-like Ti-6Al-4V scaffolds for promoting bone regeneration

The Voronoi-tessellation method is a promising technique for porous implant design as it mimics the irregular structure of bone trabeculae very well. However, the optimal pore size distribution of Voronoi-based trabecular-like scaffolds (VBTSs) remains unknown. In this study, three VBTSs with different pore size distributions were fabricated by Electron-beam melting (EBM), with a regular cubic scaffold as a control. Compression experiments showed that the elastic modulus of all the fabricated scaffolds was within the range of human bone. The biocompatibility of the porous scaffolds was evaluated by Cell Counting Kit-8, live/dead staining, phalloidin staining, and scanning electron microscope. The effects of scaffolds on osteogenic differentiation were evaluated by alkaline phosphatase (ALP) assay, Alizarin Red S (ARS) assay, and Real-time quantitative polymerase chain reaction (RT-qPCR). In vivo experiments were performed to evaluate the performance of bone regeneration in the scaffolds. The results showed that all scaffolds were nontoxic with good biosafety, and VBTSs were more conducive to promoting cell proliferation, osteogenic differentiation, and bone regeneration within the scaffolds. Among the 596–1044 μm range, the VBTS with an average pore size of 596 μm performed best. This study showed that bone regeneration could be regulated by controlling the porous structure and provided a reference for applying VBTSs in bone implants.

Non destructive control of permanent magnet rotors in a perspective of electric motor circularity

This work presents an innovative non destructive control process in order to guide for the end of life (re-use or recycling) of permanents magnets (PM) rotors of electric motors. The process is based on the measurement of the external field produced by the PM rotors. A Finite Element model of the rotor and its environment has been used to simulate a process of classification of the geometry of PM rotors, crucial information for the disassembling of the PM. Firstly, using a finite element model, we were able to investigate the field distribution outside the rotor of the magnetic flux density for different PM rotors designs. From this information, we can set up a classification methodology, based on the Central Voronoi Tessellation (CVT) method, which can help to identify how the PM are inserted within the rotor. This information can be very useful to choose PM disassembling process that should be applied.

Assessing Fatigue Life Cycles of Material X10CrMoVNb9-1 through a Combination of Experimental and Finite Element Analysis

This paper uses a two-scale material modeling approach to investigate fatigue crack initiation and propagation of the material X10CrMoVNb9-1 (P91) under cyclic loading at room temperature. The Voronoi tessellation method was implemented to generate an artificial microstructure model at the microstructure level, and then, the finite element (FE) method was applied to identify different stress distributions. The stress distributions for multiple artificial microstructures was analyzed by using the physically based Tanaka–Mura model to estimate the number of cycles for crack initiation. Considering the prediction of macro-scale and long-term crack formation, the Paris law was utilized in this research. Experimental work on fatigue life with this material was performed, and good agreement was found with the results obtained in FE modeling. The number of cycles for fatigue crack propagation attains up to a maximum of 40% of the final fatigue lifetime with a typical value of 15% in many cases. This physically based two-scale technique significantly advances fatigue research, particularly in power plants, and paves the way for rapid and low-cost virtual material analysis and fatigue resistance analysis in the context of environmental fatigue applications.

Pathways of hydrogen atom diffusion at fcc Cu: Σ9 and Σ5 grain boundaries vs single crystal

The diffusion of H-atoms is relevant for innumerous physical–chemical processes in metals. A detailed understanding of diffusion in a polycrystalline material requires the knowledge of the activation energies (ΔEa’s) for diffusion at different defects. Here, we report a study of the diffusion of H-atoms at the Σ9 and Σ5 grain boundaries (GBs) of fcc Cu that are relevant for practical applications of the material. The complete set of possible diffusion pathways was determined for each GB and we compared the ΔEa at bulk fcc Cu with the landscape of ΔEa’s at these defects. We found that while a number of diffusion pathways at the GBs have high tortuosity, there are also many paths with very low tortuosity because of specific structural features of the interstitial GB sites. These data show that the diffusion of H-atoms at these GBs is highly directional but can be fast because at certain paths the ΔEa can be as low as 0.05 eV. The lowest energy paths for diffusion of H-atoms through the whole GB models are ΔEa = 0.05 eV for the Σ9 and ΔEa = 0.20 eV at Σ5 which compare with ΔEa = 0.42 eV for the bulk fcc crystal. This shows that H-atoms will be able to diffuse very fast at these defects. With the Laguerre–Voronoi tessellation method, we studied how the local atomic structure of the interstitial sites of the GBs leads to different ΔEa’s for diffusion of H-atoms. We found that the volume expansions and the coordination numbers alone cannot account for the magnitude of the ΔEa’s. Hence, we developed a symmetry quantifying parameter that measures the deviation of symmetry of the GB sites from that of the bulk octahedral site and hence accounts for the distortion at the GB site. Only when this parameter is introduced together with the volume expansions and the coordination numbers, it is possible to correlate the local structure with the ΔEa’s and to obtain descriptors of diffusion. The complete set of data shows that the extrapolation of diffusion data for H-atoms between different types of GBs is non-trivial and should be done with care.

The elderberry diet protection against intrahippocampal Aβ-induced memory dysfunction; the abrogated apoptosis and neuroinflammation.

This study evaluates whether elderberry (EB) effectively decreases the inflammation and oxidative stress in the brain cells to reduce Aβ toxicity. In the Aβ+EB group, EB powder was added to rats' routine diet for eight consecutive weeks. Then, spatial memory, working memory, and long-term memory, were measured using the Morris water maze, T-maze, and passive avoidance test. Also, in this investigation immunohistopathology, distribution of hippocampal cells, and gene expression was carried out. Voronoi tessellation method was used to estimate the spatial distribution of the cells in the hippocampus. In addition to improving the memory functions of rats with Aβ toxicity, a reduction in astrogliosis and astrocytes process length and the number of branches and intersections distal to the soma was observed in their hippocampus compared to the control group. Further analysis indicated that the EB diet decreased the caspase-3 expression in the hippocampus of rats with Aβ toxicity. Also, EB protected hippocampal pyramidal neurons against Aβ toxicity and improved the spatial distribution of the hippocampal neurons. Moreover, EB decreased the expression of inflammatory and apoptotic genes. Overall, our study suggest that EB can be considered a potent modifier of astrocytes' reactivation and inflammatory responses.

Inverse design of dual-phase steel microstructures using generative machine learning model and Bayesian optimization

The design of optimal microstructures requires first, the identification of microstructural features that influence the material’s properties and, then, a search for a combination of these features that give rise to desired properties. For microstructures with complex morphologies, where the number of features is large, deriving these structure–property relationships is a challenging task. To address this challenge, we propose a generative machine learning model that can automatically identify low-dimensional descriptors of microstructural features that can be used to establish structure–property relationships. Based on this model, we present an integrated, data-driven framework for microstructure characterization, reconstruction, and design that is applicable to heterogeneous materials with polycrystalline microstructures. The proposed method is evaluated on a case study of designing dual-phase steel microstructures created with the multi-level Voronoi tessellation method. To this end, we train a variational autoencoder to identify the descriptors from these synthetic dual-phase steel microstructures. Subsequently, we employ Bayesian optimization to search for the optimal combination of the descriptors and generate microstructures with specific yield stress and low susceptibility for damage initiation. The presented results show how microstructure descriptors, determined by the variational autoencoder model, act as design variables for an optimization algorithm that identifies microstructures with desired properties.

A mechanistic computational framework to investigate the hemodynamic fingerprint of the blood oxygenation level-dependent signal.

Blood oxygenation level-dependent (BOLD) functional magnetic resonance imaging (fMRI) is one of the most used imaging techniques to map brain activity or to obtain clinical information about human cortical vasculature, in both healthy and disease conditions. Nevertheless, BOLD fMRI is an indirect measurement of brain functioning triggered by neurovascular coupling. The origin of the BOLD signal is quite complex, and the signal formation thus depends, among other factors, on the topology of the cortical vasculature and the associated hemodynamic changes. To understand the hemodynamic evolution of the BOLD signal response in humans, it is beneficial to have a computational framework available that virtually resembles the human cortical vasculature, and simulates hemodynamic changes and corresponding MRI signal changes via interactions of intrinsic biophysical and magnetic properties of the tissues. To this end, we have developed a mechanistic computational framework that simulates the hemodynamic fingerprint of the BOLD signal based on a statistically defined, three-dimensional, vascular model that approaches the human cortical vascular architecture. The microvasculature is approximated through a Voronoi tessellation method and the macrovasculature is adapted from two-photon microscopy mice data. Using this computational framework, we simulated hemodynamic changes-cerebral blood flow, cerebral blood volume, and blood oxygen saturation-induced by virtual arterial dilation. Then we computed local magnetic field disturbances generated by the vascular topology and the corresponding blood oxygen saturation changes. This mechanistic computational framework also considers the intrinsic biophysical and magnetic properties of nearby tissue, such as water diffusion and relaxation properties, resulting in a dynamic BOLD signal response. The proposed mechanistic computational framework provides an integrated biophysical model that can offer better insights regarding the spatial and temporal properties of the BOLD signal changes.

Estimation of multiple crack propagation pattern in concrete using Voronoi tessellation method

Estimation of multiple crack propagation pattern in concrete using Voronoi tessellation method

Effect of lattice orientation on compressive properties of selective laser sintered nylon lattice coupons

As AM lattices become more popular in medical devices, it is important to consider how lattice design parameters affect the mechanical integrity and performance of a device. This research investigated the effect of lattice orientation on the compressive mechanical response of five common lattice geometries: Hexagonal Honeycomb (Hex), Diamond, Voronoi Tessellation Method (VTM), sheet-based Gyroid, and Face-Centered-Cubic (FCC). Samples were tested at two relative densities and eight orientations, printed in Nylon 12 (PA2200) on an EOS P396. The mechanical response was compared to simulated finite element analysis (FEA) response for Hex and FCC lattices. Hex lattices displayed significant orientation dependance. Diamond lattices demonstrated some orientation dependance when at a lower relative density. Gyroid, FCC, and VTM all displayed minimal orientation dependance. Increasing lattice relative density appeared to reduce anisotropy among tested orientations of all lattice geometries except Hex. FEA simulations were able to produce a trend response that matched the mechanical response trends based on the investigated orientations. These results support the need for multi axial lattice mechanical test considerations. It also bolsters the need for lattice FEA models to have a sufficient comparator when identifying “worst-case” lattice test scenarios.

Computational Simulations of Fabrication of Aluminum-Based Josephson Junctions: Topological Aspects of the Barrier Structure

Although the performance of qubits has been improved in recent years, the differences in the microscopic atomic structure of the Josephson junctions, the core devices prepared under different preparation conditions, are still underexplored. In this paper, the effects of the oxygen temperature and upper aluminum deposition rate on the topology of the barrier layer in the aluminum-based Josephson junctions have been presented by classical molecular dynamics simulations. We apply a Voronoi tessellation method to characterize the topology of the interface and central regions of the barrier layers. We find that when the oxygen temperature is 573 K and the upper aluminum deposition rate is 4 Å/ps, the barrier has the fewest atomic voids and the most closely arranged atoms. However, if only the atomic arrangement of the central region is considered, the optimal rate of the aluminum deposition is 8 Å/ps. This work provides microscopic guidance for the experimental preparation of Josephson junctions, which helps to improve the performance of qubits and accelerate the practical application of quantum computers.