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Journal articles on the topic 'Voronoi Cell Finite Element Method'

Author: Grafiati

Published: 4 June 2021

Last updated: 12 February 2022

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1

Zhang, Rui, and Ran Guo. "Voronoi Cell Finite Element Method for Fluid-Filled Materials." Transport in Porous Media 120, no. 1 (2017): 23–35. http://dx.doi.org/10.1007/s11242-017-0898-9.

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2

Xu, Jia Li, Ran Guo, and Wen Hai Gai. "VCFEM Method Mixed with Finite Element Method Calculation of Numerical Simulation." Applied Mechanics and Materials 444-445 (October 2013): 103–9. http://dx.doi.org/10.4028/www.scientific.net/amm.444-445.103.

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As a new type of composite material, particle reinforced composite materials, which has good mechanical properties and secondary machining, have been widely used in mechanical, biological, aerospace, military, motor and other important industrial areas. With the development of science and technology lots of research and numerical simulation have been carried on at home and aboard. Because of the reinforcements, the overall mechanical properties have been significantly improved. At the same time, fracture properties and fatigue characteristics are lower. This paper, based on the VCFEM, lead in

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3

Liu, Yuan Yuan, Ran Guo, and Wen Hai Gai. "The Analysis of Interfacial Debonding Using Voronoi Cell Finite Element Method." Applied Mechanics and Materials 644-650 (September 2014): 4922–26. http://dx.doi.org/10.4028/www.scientific.net/amm.644-650.4922.

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This paper bases on the principle of the stress hybrid element, using voronoi cell finite element method to analysis the interfacial debonding phenomenon of a particle reinforced composite materials, then it contrasts by the commercial finite element software MARC in the same conditions of numerical simulation. Research results show that: In the interfacial debonding, especially at the crack tip stress, Stress is the biggest. Particles and matrix interface delamination is the important cause of material damage, at the same time, it has a great impact on the service life of components.

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4

Guo, Jun, Ran Guo, and Wen Hai Gai. "Simulation of Particle Reinforced Composite Materials in Macro- and Meso-Scales." Applied Mechanics and Materials 444-445 (October 2013): 37–44. http://dx.doi.org/10.4028/www.scientific.net/amm.444-445.37.

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A simulation method of macro-and meso-scales is developed for particle reinforce composite materials. The two-scale modeling based on homogenization theory enables to formulate the macro scale problem with Finite Element Method (FEM), while the meso-scale one with Voronoi Cell Finite Element Method (VCFEM). Dangerous regions are identified in macro scale computing period, which lately be meshed into Voronoi Cells in meso-scale period to get a more accurate solution. Representative numerical examples are presented to demonstrate the capability of the proposed two-scale analysis method of partic

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5

Zhang, Guangjie, and Ran Guo. "Interfacial cracks analysis of functionally graded materials using Voronoi cell finite element method." Procedia Engineering 31 (2012): 1125–30. http://dx.doi.org/10.1016/j.proeng.2012.01.1152.

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6

Li, Huan, Ran Guo, and Heming Cheng. "Extended Voronoi cell finite element method for multiple crack propagation in brittle materials." Theoretical and Applied Fracture Mechanics 109 (October 2020): 102741. http://dx.doi.org/10.1016/j.tafmec.2020.102741.

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7

Guo, Ran, Wenyan Zhang, Tao Tan, and Benning Qu. "Modeling of fatigue crack in particle reinforced composites with Voronoi cell finite element method." Procedia Engineering 31 (2012): 288–96. http://dx.doi.org/10.1016/j.proeng.2012.01.1026.

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8

Ghosh, Somnath, and Suresh Moorthy. "Elastic-plastic analysis of arbitrary heterogeneous materials with the Voronoi Cell finite element method." Computer Methods in Applied Mechanics and Engineering 121, no. 1-4 (1995): 373–409. http://dx.doi.org/10.1016/0045-7825(94)00687-i.

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9

Zhang, H. W., H. Wang, B. S. Chen, and Z. Q. Xie. "Analysis of Cosserat materials with Voronoi cell finite element method and parametric variational principle." Computer Methods in Applied Mechanics and Engineering 197, no. 6-8 (2008): 741–55. http://dx.doi.org/10.1016/j.cma.2007.09.003.

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10

Yang, Jie, Shi Long Wang, Zhi Jun Zheng, and Ji Lin Yu. "Impact Resistance of Graded Cellular Metals Using Cell-Based Finite Element Models." Key Engineering Materials 703 (August 2016): 400–405. http://dx.doi.org/10.4028/www.scientific.net/kem.703.400.

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A varying cell-size method based on Voronoi technique is extended to construct 3D graded cellular models. The dynamic behaviors of graded cellular structures with different density gradients are then investigated with finite element code ABAQUS/Explicit. Results show that graded cellular materials have better performance as energy absorbers. Graded cellular structures with large density near the distal end can protect strikers, and those with low density near the distal end can protect structures at the distal end. It is concluded that graded cellular materials with suitable design may have ex

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11

Gai, Wen Hai, R. Guo, and Jun Guo. "Molecular Dynamics Approach and its Application in the Analysis of Multi-Scale." Applied Mechanics and Materials 444-445 (October 2013): 1364–69. http://dx.doi.org/10.4028/www.scientific.net/amm.444-445.1364.

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Numerical simulation of the behavior of materials can be used as a versatile, efficient and low cost tool for developing an understanding of material behavior [. The numerical simulation methods include quantum mechanics, molecular dynamics, Voronoi cell finite element method and finite element method et al. These methods themselves are not sufficient for many fundamental problems in computational mechanics, and the deficiencies lead to the thrust of multiple-scale methods. The multi-scale method to model micro-scale systems by coupled continuum mechanics and molecular dynamics was introduced.

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12

Grujicic, M., and Y. Zhang. "Determination of effective elastic properties of functionally graded materials using Voronoi cell finite element method." Materials Science and Engineering: A 251, no. 1-2 (1998): 64–76. http://dx.doi.org/10.1016/s0921-5093(98)00647-9.

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13

Guo, R., H. J. Shi, and Z. H. Yao. "Modeling of interfacial debonding crack in particle reinforced composites using Voronoi cell finite element method." Computational Mechanics 32, no. 1-2 (2003): 52–59. http://dx.doi.org/10.1007/s00466-003-0461-0.

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14

Shen, Liu-Lei, Zhi-Bin Shen, Hai-Yang Li, and Ze-Yuan Zhang. "A Voronoi cell finite element method for estimating effective mechanical properties of composite solid propellants." Journal of Mechanical Science and Technology 31, no. 11 (2017): 5377–85. http://dx.doi.org/10.1007/s12206-017-1032-1.

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15

Tiwary, Abhijeet, Chao Hu, and Somnath Ghosh. "Numerical conformal mapping method based Voronoi cell finite element model for analyzing microstructures with irregular heterogeneities." Finite Elements in Analysis and Design 43, no. 6-7 (2007): 504–20. http://dx.doi.org/10.1016/j.finel.2006.12.005.

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16

Ghosh, Somnath, Kyunghoon Lee, and Suresh Moorthy. "Multiple scale analysis of heterogeneous elastic structures using homogenization theory and voronoi cell finite element method." International Journal of Solids and Structures 32, no. 1 (1995): 27–62. http://dx.doi.org/10.1016/0020-7683(94)00097-g.

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17

Shi, Hui Ji, Ya-Xiong Zheng, Ran Guo, and Gerard Mesmacque. "Characterization of High Temperature Thermomechanical Fatigue Properties for Particle Reinforced Composites." Key Engineering Materials 297-300 (November 2005): 1495–502. http://dx.doi.org/10.4028/www.scientific.net/kem.297-300.1495.

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Voronoi cell finite element method (VCFEM) is introduced in this paper to describe the elastic-plastic-creep behavior of particle reinforced composites. The interfacial damage is simulated by partly debonding between Matrix and inclusion. A validation of the nonlinear behavior of the cell element has been carry out by comparing VCFEM results with those calculated by the general finite element package MARC and ABAQUS, and good agreements are found. A microstructure with five inclusions is taken as an example to describe the cyclic stress-strain behavior under different particulate orientation c

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18

Li, Huan, Ran Guo, and Heming Cheng. "Modelling interfacial cracking and matrix cracking in particle reinforced composites using the extended Voronoi cell finite element method." Composite Structures 255 (January 2021): 112991. http://dx.doi.org/10.1016/j.compstruct.2020.112991.

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19

Shen, Liu-Lei, Zhi-Bin Shen, Yan Xie, and Hai-Yang Li. "Effective Mechanical Property Estimation of Composite Solid Propellants Based on VCFEM." International Journal of Aerospace Engineering 2018 (2018): 1–9. http://dx.doi.org/10.1155/2018/2050876.

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A solid rocket motor is one of the critical components of solid missiles, and its life and reliability mostly depend on the mechanical behavior of a composite solid propellant (CSP). Effective mechanical properties are critical material constants to analyze the structural integrity of propellant grain. They are estimated by a numerical method that combines the Voronoi cell finite element method (VCFEM) and the homogenization method in the present paper. The correctness of this combined method has been validated by comparing with a standard finite element method and conventional theoretical mod

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20

Zhang, H. W., H. Wang, and J. B. Wang. "Parametric variational principle based elastic–plastic analysis of materials with polygonal and Voronoi cell finite element methods." Finite Elements in Analysis and Design 43, no. 3 (2007): 206–17. http://dx.doi.org/10.1016/j.finel.2006.09.001.

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21

Skibinski, Jakub, Karol Cwieka, Samih Haj Ibrahim, and Tomasz Wejrzanowski. "Influence of Pore Size Variation on Thermal Conductivity of Open-Porous Foams." Materials 12, no. 12 (2019): 2017. http://dx.doi.org/10.3390/ma12122017.

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This study addresses the influence of pore size variation on the effective thermal conductivity of open-cell foam structures. Numerical design procedure which renders it possible to control chosen structural parameters has been developed based on characterization of commercially available open-cell copper foams. Open-porous materials with various pore size distribution were numerically designed using the Laguerre–Voronoi Tessellations procedure. Heat transfer through an isolated structure was simulated with the finite element method. The results reveal that thermal conductivity is strongly rel

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22

Li, Huan, Ran Guo, and Heming Cheng. "Calculation of stress intensity factors of matrix crack tip in particle reinforced composites using the singular Voronoi cell finite element method." Theoretical and Applied Fracture Mechanics 101 (June 2019): 269–78. http://dx.doi.org/10.1016/j.tafmec.2019.03.008.

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23

Zhang, Xiaoyang, Liqun Tang, Zhenyu Jiang, Zejia Liu, Yiping Liu, and Daining Fang. "Effects of Meso Shape Irregularity of Metal Foam on Yield Features under Triaxial Loading." International Journal of Structural Stability and Dynamics 15, no. 07 (2015): 1540014. http://dx.doi.org/10.1142/s0219455415400143.

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Metallic foam is a typical porous material with heterogeneous meso structures that affect the metallic foam's mechanical properties, in which shape irregularity of meso structures (porous cells) is the key. Shape irregularity of a porous cell reflects the deviation the cell shape from a sphere having the same volume. This paper examines the effects of meso shape irregularity of metallic foam on yield features based on three-dimensional (3D) Voronoi model and the finite element (FE) method. Three cubic foams designed by 3D Voronoi technique were constructed to furnish different statistics of sh

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24

Wang, Xiao Kai, Zhi Jun Zheng, Ji Lin Yu, and Chang Feng Wang. "Impact Resistance and Energy Absorption of Functionally Graded Cellular Structures." Applied Mechanics and Materials 69 (July 2011): 73–78. http://dx.doi.org/10.4028/www.scientific.net/amm.69.73.

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The dynamic response of functionally graded cellular structures subjected to impact of a finite mass was investigated in this paper. Compared to a cellular structure with a uniform cell size, the one with gradually changing cell sizes may improve many properties. Based on the two-dimensional random Voronoi technique, a two-dimensional topological configuration of cellular structures with a linear density-gradient in one direction was constructed by changing the cell sizes. The finite element method using ABAQUS/Explicit code was employed to investigate the energy absorption and the influence o

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25

Tateyama, Kohei, and Keiko Watanabe. "Effect of microstructure on dynamic compressive behavior of cellular materials." EPJ Web of Conferences 250 (2021): 02026. http://dx.doi.org/10.1051/epjconf/202125002026.

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It is known that the microstructure of cellular materials has a significant impact on their compressive properties. To study these phenomena, a hierarchical Poisson disk sampling algorithm and Voronoi partitioning were used to create a 3D numerical analysis model of cellular materials. In this study, we prepared random, periodic, and ellipsoidal cell models to investigate the effects of cell shape randomness and oblateness. Numerical experiments were performed using the finite element method solver RADIOSS. In the numerical analysis, an object collided with the cellular materials at a velocity

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26

Jahandari, Hormoz, and Colin G. Farquharson. "Forward modeling of gravity data using finite-volume and finite-element methods on unstructured grids." GEOPHYSICS 78, no. 3 (2013): G69—G80. http://dx.doi.org/10.1190/geo2012-0246.1.

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Minimum-structure inversion is one of the most effective tools for the inversion of gravity data. However, the standard Gauss-Newton algorithms that are commonly used for the minimization procedure and that employ forward solvers based on analytic formulas require large memory storage for the formation and inversion of the involved matrices. An alternative to the analytical solvers are numerical ones that result in sparse matrices. This sparsity suits gradient-based minimization methods that avoid the explicit formation of the inversion matrices and that solve the system of equations using mem

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27

Yu, Ji Lin, Shen Fei Liao, Zhi Jun Zheng, and Chang Feng Wang. "Dynamic Crushing of Voronoi Honeycombs: Local Stress-Strain States." Applied Mechanics and Materials 566 (June 2014): 563–68. http://dx.doi.org/10.4028/www.scientific.net/amm.566.563.

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Dynamic stress-strain states in Voronoi honeycombs are investigated by using cell-based finite element models. Two different loading scenarios are considered: the high-constant-velocity compression and the direct impact. The 2D local engineering strain fields are calculated. According to the feature of shock front propagation, the 1D distribution of local engineering strain in the loading direction is deduced from the 2D strain fields, which provide evidences of the existence of discontinuities at shock front in cellular materials and thus enhance the basis of the continuum-based shock models.

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28

Ćwieka, K., T. Wejrzanowski, and K. J. Kurzydłowski. "Incorporation of the Pore Size Variation to Modeling of the Elastic Behavior of Metallic Open-Cell Foams." Archives of Metallurgy and Materials 62, no. 1 (2017): 259–62. http://dx.doi.org/10.1515/amm-2017-0039.

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Abstract In the present paper we present the approach for modeling of the elastic behavior of open-cell metallic foams concerning non-uniform pore size distribution. This approach combines design of foam structures and numerical simulations of compression tests using finite element method (FEM). In the design stage, Laguerre-Voronoi tessellations (LVT) were performed on several sets of packed spheres with defined variation of radii, bringing about a set of foam structures with porosity ranging from 74 to 98% and different pore size variation quantified by the coefficient of pore volume variati

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29

Yang, B., Z. J. Liu, L. Q. Tang, Z. Y. Jiang, and Y. P. Liu. "Mechanism of the Strain Rate Effect of Metal Foams with Numerical Simulations of 3D Voronoi Foams during the Split Hopkinson Pressure Bar Tests." International Journal of Computational Methods 12, no. 04 (2015): 1540010. http://dx.doi.org/10.1142/s0219876215400101.

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With the demand of lightweight structure, more and more metal foams were employed as impact protection and efficient energy absorption materials in engineering fields. But, results from different impact experiments showed that the strain rate sensitivity of metal foams were different or even controversial. In order to explore the true hiding behind the controversial experimental data about the strain rate sensitivity of metal foams, numerical simulations of split Hopkinson pressure bar (SHPB) tests of the metal foams were carried out by finite element methods. In the analysis, cell structures

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30

Huang, Yunqing, Hengfeng Qin, Desheng Wang, and Qiang Du. "Convergent Adaptive Finite Element Method Based on Centroidal Voronoi Tessellations and Superconvergence." Communications in Computational Physics 10, no. 2 (2011): 339–70. http://dx.doi.org/10.4208/cicp.030210.051110a.

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AbstractWe present a novel adaptive finite element method (AFEM) for elliptic equations which is based upon the Centroidal Voronoi Tessellation (CVT) and superconvergent gradient recovery. The constructions of CVT and its dual Centroidal Voronoi Delaunay Triangulation (CVDT) are facilitated by a localized Lloyd iteration to produce almost equilateral two dimensional meshes. Working with finite element solutions on such high quality triangulations, superconvergent recovery methods become particularly effective so that asymptotically exact a posteriori error estimations can be obtained. Through

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31

Zhou, Qibin, Hongxiang Yang, Xin Huang, Manyu Wang, and Xin Ren. "Numerical modelling of MOV with Voronoi network and finite element method." High Voltage 6, no. 4 (2021): 711–17. http://dx.doi.org/10.1049/hve2.12072.

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32

Moorthy, Suresh, Somnath Ghosh, and Yunshan Liu. "Voronoi Cell Finite Element Model for Thermoelastoplastic Deformation in Random Heterogeneous Media." Applied Mechanics Reviews 47, no. 1S (1994): S207—S220. http://dx.doi.org/10.1115/1.3122815.

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A finite element model has been developed for analysis of heterogeneous media, in which second phase inclusions are arbitrarily dispersed within a matrix. A mesh generator based on Dirichlet tessellation, discretizes the heterogeneous domain, accounting for the arbitrariness in location, shape and size of the second phase. This results in a network of convex “Voronoi” polygons which form the elements in a finite element mesh. An assumed stress hybrid formulation has been implemented for accommodating arbitrary multi-sided elements in the finite element model. Composite element formulations hav

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33

Tu, Yuhui, Seán B. Leen, and Noel M. Harrison. "A high-fidelity crystal-plasticity finite element methodology for low-cycle fatigue using automatic electron backscatter diffraction scan conversion: Application to hot-rolled cobalt–chromium alloy." Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 235, no. 8 (2021): 1901–24. http://dx.doi.org/10.1177/14644207211010836.

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The common approach to crystal-plasticity finite element modeling for load-bearing prediction of metallic structures involves the simulation of simplified grain morphology and substructure detail. This paper details a methodology for predicting the structure–property effect of as-manufactured microstructure, including true grain morphology and orientation, on cyclic plasticity, and fatigue crack initiation in biomedical-grade CoCr alloy. The methodology generates high-fidelity crystal-plasticity finite element models, by directly converting measured electron backscatter diffraction metal micro

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34

Ghosh, S., and S. Moorthy. "Three dimensional Voronoi cell finite element model for microstructures with ellipsoidal heterogeneties." Computational Mechanics 34, no. 6 (2004): 510–31. http://dx.doi.org/10.1007/s00466-004-0598-5.

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35

Zhang, Rui, and Ran Guo. "Voronoi cell finite element model to simulate crack propagation in porous materials." Theoretical and Applied Fracture Mechanics 115 (October 2021): 103045. http://dx.doi.org/10.1016/j.tafmec.2021.103045.

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36

Gafarova, Yu A. "Numerical implementation of finite-element method of control volume using irregular mesh." Proceedings of the Mavlyutov Institute of Mechanics 7 (2010): 98–108. http://dx.doi.org/10.21662/uim2010.1.008.

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To solve problems with complex geometry it is considered the possibility of application of irregular mesh and the use of various numerical methods using them. Discrete analogues of the Beltrami-Mitchell equations are obtained by the control volume method using the rectangular grid and the finite element method of control volume using the Delaunay triangulation. The efficiency of using the Delaunay triangulation, Voronoi diagrams and the finite element method of control volume in a test case is demonstrated.

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37

Moorthy, S., and S. Ghosh. "Particle cracking in discretely reinforced materials with the voronoi cell finite element model." International Journal of Plasticity 14, no. 8 (1998): 805–27. http://dx.doi.org/10.1016/s0749-6419(98)00024-2.

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38

Vena, P., and D. Gastaldi. "A Voronoi cell finite element model for the indentation of graded ceramic composites." Composites Part B: Engineering 36, no. 2 (2005): 115–26. http://dx.doi.org/10.1016/j.compositesb.2004.05.003.

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39

Wang, Zhiyong, and Peifeng Li. "Voronoi cell finite element modelling of the intergranular fracture mechanism in polycrystalline alumina." Ceramics International 43, no. 9 (2017): 6967–75. http://dx.doi.org/10.1016/j.ceramint.2017.02.121.

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40

Deng, Da Zhao, and Ji Xiang Luo. "Study of the Crack Propagation for Particles Reinforced Composite Materials with Different Inclusion Distribution." Advanced Materials Research 461 (February 2012): 338–42. http://dx.doi.org/10.4028/www.scientific.net/amr.461.338.

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Based on the Voronoi cell finite element can also reflect fiber reinforced composites interface to take off the layer and matrix crack propagation of the new cell (X-VCFEM cell)[1]. Combined with the re-mesh strategy and grid dynamic technology, Simulated analysis in different inclusion distribution, interface crack propagation for fiber reinforced composites, the results show that for the model with multiple Voronoi cell, The horizontal tension was the largest; For only a Voronoi cell, The size of the horizontal tension was little change.The result was very important reference value for manuf

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41

Yu, Hai Bin, Chuan Zhen Huang, Han Lian Liu, Bin Zou, Hong Tao Zhu, and Jun Wang. "A 3D Cohesive Element Model for Fracture Behavior Analysis of Ceramic Tool Materials Microstructure." Materials Science Forum 723 (June 2012): 119–23. http://dx.doi.org/10.4028/www.scientific.net/msf.723.119.

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A 3D finite element polycrystalline microstructure model of ceramic tool materials is presented. Quasi-static crack propagation is modeled using the cohesive finite element method (CFEM) and the microstructure is represented by 3D Voronoi tessellation. The influences of cohesive parameters, the ratios of maximum traction of grain boundary to maximum traction of grain on the crack patterns of Al2O3 have been discussed. This study has demonstrated the capability of modeling 3D crack propagation of ceramic microstructure with CFEM and Voronoi tessellation model. It is found that the fracture mode

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42

Tanaka, Kazuto, Kohji Minoshima, and Takehiro Imoto. "Young’s Modulus of Polysilicon Thin Film Evaluated by Finite Element Analysis." Key Engineering Materials 353-358 (September 2007): 2227–30. http://dx.doi.org/10.4028/www.scientific.net/kem.353-358.2227.

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To analyze the effect of the crystal orientations and the grain size on the Young's modulus of thin polysilicon microelements, two-dimensional finite element models in plain strain condition were developed using a Voronoi structure. The number of grains in a model of a 10 μm square area was changed from 23 to 1200. The grain size and the crystal orientation of the film were analyzed by means of an electron back-scattering diffraction pattern (EBSP) method. The average grain size of the front surface of the thin film was about 0.69 μm, which is almost equal to the grain size of the Voronoi mode

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43

Luo, Ji Xiang. "Simulation of the Cracking Behavior for Fiber Reinforced Composite Materials with Different Inclusion Quantity." Advanced Materials Research 568 (September 2012): 238–41. http://dx.doi.org/10.4028/www.scientific.net/amr.568.238.

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Based on the Voronoi cell finite element can also reflect fiber reinforced composites interface to take off the layer and matrix crack propagation of the new cell (X-VCFEM cell)[1]. Combined with the re-mesh strategy and grid dynamic technology, Simulated analysis in different inclusion quantity, interface crack propagation for fiber reinforced composites, the results show that for the model with four,nine,sisteen,twenty-five and thirty-six voronoi cell, The horizontal tension was not the largest; For only a Voronoi cell, The size of the horizontal tension was the largest.The result was very i

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44

Song, Chongmin, and John P. Wolf. "The scaled boundary finite-element method—alias consistent infinitesimal finite-element cell method—for elastodynamics." Computer Methods in Applied Mechanics and Engineering 147, no. 3-4 (1997): 329–55. http://dx.doi.org/10.1016/s0045-7825(97)00021-2.

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45

Song, Chongmin, and John P. Wolf. "The scaled boundary finite element method?alias consistent infinitesimal finite element cell method?for diffusion." International Journal for Numerical Methods in Engineering 45, no. 10 (1999): 1403–31. http://dx.doi.org/10.1002/(sici)1097-0207(19990810)45:10<1403::aid-nme636>3.0.co;2-e.

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46

Darbani, Mohsen. "The Meshfree Finite Element Method for Fluids with Large Deformations." Defect and Diffusion Forum 326-328 (April 2012): 176–80. http://dx.doi.org/10.4028/www.scientific.net/ddf.326-328.176.

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The shallow water equations (SWE) is often simulated by using Eulerian descriptions. These phenomena may give rise to strong gradients and lead to large distortion of grids meshes. Hence classical finite elements methods may fall in simulating such problems. In this paper we present a meshless method, based on the natural element nethod (NEM). In a geometrical domain of a cloud of nodes, NEM uses the Voronoi cells and then its dual, namely Delaunay triangulation. Its main advantage lies in shape function of the natural neighbour interpolation, such that the position of natural neighbours is en

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47

Moorthy, Suresh, and Somnath Ghosh. "Adaptivity and convergence in the Voronoi cell finite element model for analyzing heterogeneous materials." Computer Methods in Applied Mechanics and Engineering 185, no. 1 (2000): 37–74. http://dx.doi.org/10.1016/s0045-7825(99)00349-7.

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48

Moorthy, Suresh, and Somnath Ghosh. "A Voronoi Cell finite element model for particle cracking in elastic-plastic composite materials." Computer Methods in Applied Mechanics and Engineering 151, no. 3-4 (1998): 377–400. http://dx.doi.org/10.1016/s0045-7825(97)00160-6.

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49

Ghosh, Somnath, and Yunshan Liu. "Voronoi cell finite element model based on micropolar theory of thermoelasticity for heterogeneous materials." International Journal for Numerical Methods in Engineering 38, no. 8 (1995): 1361–98. http://dx.doi.org/10.1002/nme.1620380808.

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Li, Shanhu, and Somnath Ghosh. "Extended Voronoi cell finite element model for multiple cohesive crack propagation in brittle materials." International Journal for Numerical Methods in Engineering 65, no. 7 (2006): 1028–67. http://dx.doi.org/10.1002/nme.1472.

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