Experimental fretting fatigue lives exhibit large degree of scatter. One of the aspects behind this is the microstructural inhomogeneity which affects the stresses in the material. Variance in stress ...values can greatly impact crack initiation speed, leading to changes in fretting fatigue lifetimes, as well as the crack propagation behaviour. This research aims to study this issue in more detail and recreate the experimentally observed scatter using numerical modelling. In this work, Voronoi tessellation is used to simulate microstructural topologies of low carbon steel, where each grain is assigned elasto-plastic properties at random, from a predetermined range. In total, 60 finite element models are created and the effect of microstructural inhomogeneity on fretting fatigue lifetime dispersion is evaluated using a Continuum Damage Mechanics approach. Additionally, crack propagation is studied with XFEM combined with Smith-Watson-Topper fatigue parameter to determine crack path under multiaxial, non-proportional loading conditions. For both crack initiation and propagation investigation, the Theory of Critical Distances is applied to overcome the effect of high stress gradients. Simulation results show that microstructural inhomogeneity has significant impact on the contact stress distributions and subsurface stress and strain fields. Scatter observed in the predicted lifetimes matches well with that observed in practical experiments and is used to propose a design curve for the studied material. The applied crack path prediction approach captures the variance in crack paths originating from microstructural inhomogeneity and shows good correlation with reference experimental results at low bulk stress levels.
•Developing 2.5D CVT grids and refinement with unstructured vertical discretization.•Curve-fitting matches Voronoi cell edges with geological traces in horizontal projection.•Centroidal Voronoi grids ...in MODFLOW 6 for complex groundwater modeling.•Linking multiple unstructured-grid models in MODFLOW 6.
An unstructured grid is a powerful data structure for a proper depiction of various geological features such as faults and pinch-outs and for groundwater simulation in a complex aquifer system. This study presents a mesh generation methodology based on 2.5D centroidal Voronoi tessellations (CVTs), which provides a great flexibility in specifying grid connections in 3D, matching irregular geometries, and adding high levels of refinement in areas of interest. Lloyd relaxation approximation is introduced to effectively guarantee the generation of centroidal Voronoi grids. A curve-fitting Voronoi gridding approach is developed to construct Voronoi cell edges conforming to intricated geological traces in the horizontal 2D projection with unstructured vertical discretization. A controlled refinement in spatial grid resolution has been demonstrated to prevent adverse impacts on groundwater flow simulations. The methodology is applied to the Southern Hills aquifer system in the Capital Area of Louisiana, USA. Significant groundwater depletion has occurred due to continuous and excessive withdrawals over decades for public supplies and industries. The Baton Rouge fault and the Denham-Springs Scotlandville fault are leaky barriers and have a significant influence on groundwater flow. A curve-fitting centroidal Voronoi grid is developed to simulate the effects of the two faults as leaky barriers. CVT-based high-fidelity unstructured multi-model groundwater modeling is conducted using MODFLOW 6 to allow more flexibility in model design. Complex groundwater flow in the Southern Hills aquifer system was revealed through the centroidal Voronoi unstructured grid.
Interacting particle assemblies embedded on a surface are often used to model biophysical systems and to study new colloidal materials. The configurations resulting from the particles interacting ...with each other and with their substrate affect the system's physical properties, which depend on local symmetries and defects. It is therefore important to identify the nature and location of defects in the particle assembly. This task is often achieved using either the Voronoi tessellation algorithm or order parameters. Although very useful, they present limitations, especially when the particle assemblies are embedded on irregular or highly deformed 3D surfaces. In this work, we present a novel algorithm to generate the tessellation of particle assemblies on 3D surfaces of arbitrary geometry. The algorithm is based on the particles' physical interactions and does not require a priori information on the surface geometry. The resulting cells in the tessellation represent each particle's interactions with its first ring of neighboring particles. The algorithm is tested using 2D and 3D surfaces, with or without periodic boundary conditions, with holes or fully covered by particles, of regular geometry or highly deformed shape, and in the presence of positive, zero, and negative Gaussian curvature. In all cases, the presented algorithm is capable of generating a tessellation representing the particle interactions and highlighting the location and nature of the assembly defects. Finally, the proposed algorithm is compared with both Voronoi and hexatic order parameters in several representative cases to highlight similarities with existing methods as well as the advantages of the newly proposed algorithm.
•A novel algorithm is presented to tessellate particle assemblies on surfaces.•The generated tessellations represent particle interactions with first neighbors.•The algorithm does not require a priori information on the surface geometry.•The algorithm offers an alternative to Voronoi tessellation and order parameters.•Valid tessellations are created on complex surfaces and in assemblies with holes.
Bone tissue engineering plays an extremely important role in the clinical treatment of bone defects. Porous scaffold is one of the three essential factors of bone tissue engineering, and its ...structural design has attracted more and more attention . At present, most of the design methods of porous scaffolds focus on uniform porous scaffolds with periodic and regular pore structures. However, periodic and regular pore structure cannot comprehensively and accurately simulate the microstructures and mechanical properties of natural bone. To address this problem, based on bone slice images and VT (Voronoi‐Tessellation) method, this article proposed a design method of HPS (Heterogeneous Porous Scaffolds) with bionic pore structure and controllable porosity. The FDM (fused deposition modeling) printing technology was applied to fabricate HPS with different porosities, and the mechanical properties of the HPS were analyzed by experiments. The research results illustrate that the HPS constructed by the design method proposed in this article have good controllability, and their internal pore structures are highly similar to those of natural bone, which have biomimetic characteristics. The mechanical property analysis illustrate that the stiffness and compressive strength of HPS decrease with the increase of porosity, in addition, the heterogeneous pore distribution makes HPS have the characteristics of non‐concentrated and discontinuous damage distribution. This study provides a new idea for the design of porous scaffolds and a theoretical basis for the bionic design of HPS.
In this article, VT (Voronoi‐Tessellation) was used to simulate the pore contour of biological bone, and a bionic scaffold design method based on the medical information of bone slice images was proposed. Furthermore, combined with CAD software and computer program, HPS (Heterogeneous Porous Scaffolds) with irregular pore shape, heterogeneous internal pore distribution and controllable porosity were designed. And the mechanical properties of the HPS were analyzed by mechanical compression tests and finite‐element simulation experiments.
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•A more effective method is proposed to build the meso-scale model of concrete.•The inherent defects of traditional voronoi models have been well solved.•The computational efficiency ...of generating the meso-scale model of concrete is improved.•Reinforcements are introduced into the concrete model with graded aggregates.•Perforation processes of projectile penetrating into RC slabs are simulated well.
An effective numerical method is proposed in this paper to generate a meso-scale composite model of reinforcement concrete (RC) which contains aggregates with random size and shape based on Voronoi tessellation method. Besides the randomly distributed aggregates, the present model takes into account the reinforcement, compared with other conventional methods in finite element modeling of concrete. The shrinking algorithm with random shrinking factors is employed to generate graded aggregates. A simple and effective intersection detection is used for aggregate-reinforcement to prevent the aggregates from overlapping with preset reinforcements, but it is unnecessary for aggregate-aggregate due to the characteristic of Voronoi technique. The artificial layer with random offset distance is adopted to simulate the minimum gap between two adjacent aggregates, and the high-volume fraction model is obtained by the sinking process. In order to verify the reliability of the RC model, the numerical results of penetration are compared with the referenced experimental data, and good agreements are obtained. It is indicated that the proposed model can simulate and explain qualitatively the effects of the meso-scale structural properties on the macroscopic dynamic response of RC. Furthermore, this method has great significance in performance analysis, structural optimization and material design for RC composites.
The use of irregular porous structures in bone tissue engineering (BTE) has attracted increasing attention. An irregular porous structure is similar to that of human bone tissue and is more suitable ...for bone tissue growth than a regular porous structure.
In this study, we propose a top-down design method for constructing irregular porous structures based on Voronoi tessellation. The model constructed with this method was fabricated by selective laser melting (SLM) and industrial computed tomography (CT) was used to measure the morphological characteristics; the mechanical properties were obtained by quasi-static compressive test. The experimental results showed that the samples had a porosity ranging from 50% to 85%, an average pore diameter ranging from 512 to 998 μm, an apparent elastic modulus ranging from 2.13 to 3.97 Gpa, and a compressive strength ranging from 78.99 to 130.5 Mpa and met the artificial implant requirements. Three regression equations were established between the three design parameters and the porosity, apparent elastic modulus, and compressive strength using a response surface methodology (RSM). The equations allow for better control of the irregular porous structure and the prediction of the properties.
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•Irregular porous scaffolds were constructed and samples were obtained by SLM.•Irregular porous structure met needs of bone tissue engineering.•Relationship between structural design parameters and porosity, mechanical properties were concluded.
A two-fold approach is considered to study hydrogen (H) diffusion characteristics in martensitic steels. Initially, a multi-trap stress coupled H diffusion finite element model was developed to ...investigate the role of various trap states on effective H trapping during a four point bend test. The calculations show that high angle boundaries are more influential in controlling H diffusion in presence of low initial (bulk) H concentrations, while dislocations can have more pronounced impact, when the bulk H concentration is higher. A microstructural model comprising of prior austenite grains and packets was further developed. The study highlights the importance of packet boundaries (PBs) moderating H diffusion in martensite microstructure. The presence of retained austenite content affecting H diffusion paths was also studied. Overall, this parametric study presents complementary techniques in numerical modeling, as well as implications on the role of various microstructural entities affecting H diffusion.
•A multitrap stress-coupled H diffusion FEA model is developed.•Role of various trap states affecting H distribution is presented.•Microstructural model of martensite with two fold hierarchy is developed.•Influence of packet boundaries and retained austenite on H transport is demonstrated.
•VHCF studied with crystal plasticity theory.•Pores have more signification effect on shortening fatigue life than inclusions.•Fatigue highly depends on microstructure, especially inclusions and ...pores.•Residual stress near inclusion is harmful to the fatigue life.
The high-cycle and very-high-cycle fatigue (VHCF) behaviors of AlSi10Mg alloy produced by additive manufacturing (AM) were studied. A crystal plasticity finite element model (CPFEM) with Voronoi tessellation was developed to simulate the cyclic plastic deformation considering defect effects. Morrow’s model and Smith-Watson-Topper (SWT) model were used to predict the fatigue life and the SWT model was in good agreement with the experimental life between 105 and 109. CPFEM simulation indicated that the accumulated cyclic plastic strain is significantly increased near a pore than that of an inclusion. The residual stress near an inclusion led to large plastic strain localization, which is harmful to fatigue performance.
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.
•A new methodology for representing the microstructure of pearlitic steel is proposed.•Plastic deformation is introduced in the representation by geometric modification.•The proposed mesh combined with the DEM method represents a sound basis for modeling the FCG in pearlitic steel.
In unresolved flow CFD-DEM simulations, the porosity values for each CFD cell are determined using a coarse-graining algorithm. While this approach enables coupled simulations of representative ...numbers of particles, the influence of the porosity local to the particles on the fluid-particle interaction force is not captured. This contribution considers a two-grid coarse-graining method that determines a local porosity for each particle using a radical Voronoi tessellation of the system. A relatively fine, regular point cloud is used to map these local porosity data to the CFD cells. The method is evaluated using two different cases considering both disperse and tightly packed particles. The data show that the method conserves porosity data, is reasonably grid-independent and can generate a relatively smooth porosity field. The new method can more accurately predict the fluid-particle interactive force for polydisperse particle system than alternative methods that have been implemented in unresolved CFD-DEM codes.
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•A two-grid coarse-graining method by the radical Voronoi tessellation is proposed.•A regular point cloud is used to map the local porosity of particle to CFD cells.•Validation cases with both disperse and tightly packed particles are used.•The drag force for polydisperse particle system is accurately predicted.
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