The effects of regularity on the geometrical properties of Voronoi tessellations

Zhu, Hanxing; Zhang, P.; Balint, D.; Thorpe, S. M.; Elliott, James A.; Windle, A. H.; Lin, Jixing

doi:10.1016/j.physa.2014.03.012

Cited by 36 publications

(16 citation statements)

References 42 publications

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“…The RVE is divided into 100 polyhedral grains with random size, shape and orientation. This cubic FEM model is a representation of a real grain structure and can be regarded as the product of the isotropic growth process from a spatial distribution of grain nuclei (Zhu et al, 2014). These grain nuclei are randomly generated one by one, and the subsequent ones are accepted only if they are located no nearer than an allowed distance from all others, thus the distance between two neighbor grains will not too close.…”

Section: Modeling the Materials As Statistically Representative Volumementioning

confidence: 99%

Micromechanics based fatigue life prediction of a polycrystalline metal applying crystal plasticity

Zhang

et al. 2015

Mechanics of Materials

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Section: Modeling the Materials As Statistically Representative Volumementioning

confidence: 99%

Micromechanics based fatigue life prediction of a polycrystalline metal applying crystal plasticity

Zhang

et al. 2015

Mechanics of Materials

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“…Voronoi tessellation have been traditionally used to generate a random structure which is representative of polycrystalline materials in metallurgy [6]. A lot of research have been carried out to in the past to produce numerical microstructure using Voronoi tessellation [7], [8], [9], [10], . The Voronoi tessellation divides a region into convex polygons, or cells, that fill space without overlap.…”

Section: Generation Of Synthetic Microstructurementioning

confidence: 99%

Heat Diffusion in Polycrystalline Rolled Steel - A Microstructure Based Material Model

Unnikrishnakurup¹,

Krishnamurthy²,

Balasubramaniam³

2015

Proceedings of the 2015 Asia International Conference on Quantitative InfraRed Thermography

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A two-dimensional Voronoi tessellation based material model has been introduced to study the heat diffusion phenomena in polycrystalline materials consisting of a distribution of grain sizes and shapes. A method to control Voronoi cell-size distributions is presented. As the main focus of the numerical investigation is to study the role of anisotropy of the thermal conductivities in each grain of the polycrystalline material, the thermal conductivity tensor of each cell is chosen to correspond to a random crystallographic orientation. A finite element analysis of heat transport from a centrally spot-heated sample is carried out on the Voronoi tessellated domain for a fixed cell size distribution and a set of randomly oriented cells. The simulations are carried out for various sets of cell orientations. Time-Temperature profiles are generated at two orthogonally placed probes for each trial. Three inter-cell boundary conditions are examined to account for the heat transport across grains. The observed trends of the time-temperature profiles in the context of effective thermal conductivity of a polycrystalline material are discussed.

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“…Numerical microstructural approaches for closed cell foams can be categorized in three groups: (i) space filling polyhedron models [13,14,15,16,17,18], (ii) image based models [19,12,20] and (iii) tessellation based models [21,22,23,24,25,26,27,28,29]. Space filling polyhedron models can be easily constructed and then be analyzed using shell finite element because they radically simplify the foam geometry.…”

Section: Introductionmentioning

confidence: 99%

“…Many researchers used tessellation-based models for closed cell foams to consider probabilistic geometrical features in combination with shell-based finite element analysis on the microstructural scale [22,25,27,26,30,24]. For instance, [27] studied the effect of cell size variation on the elastic stiffness of closed foams and observed that the foam stiffness is decreased by increasing the cell size variation.…”

Section: Introductionmentioning

confidence: 99%

Efficient computational modelling of closed cell metallic foams using a morphologically controlled shell geometry

Ghazi

Tiago

Sonon

et al. 2020

International Journal of Mechanical Sciences

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This contribution addresses the finite element modelling of closed cell metallic foams using Representative Volume Elements (RVEs) based on shell geometries directly extracted from implicitly defined 3D geometries. 3D RVEs of closed cell foam materials are produced by means of a generation strategy allowing a close morphological control reproducing fine scale geometrical features incorporating cell size, cell wall thickness and cell wall curvature distributions. The strategy is built on three computational ingredients: (i) a random packing algorithm based on random sequential addition assisted by neighbour distance control, (ii) a distance field-based shape tessellation (morphing) that allows incorporating cell wall curvatures and varying cell wall thicknesses and (iii) a close control on the shape of the cells. In order to decrease the computational cost of a full 3D finite element model, an original approach is proposed to produce a shell-based geometry directly from 3D information. Extracting the shell geometry from the implicitly defined 3D geometry based on the zero level of distance fields that would represent the cell walls is computationally impossible. Therefore, a novel robust procedure is proposed using careful cutting operations on distance fields for this purpose. The effect of the different microstructural geometrical features of interest on the average mechanical behaviour of the foam is investigated using shell-based finite element analyses. The computational cost and the accuracy of the proposed shell models are then assessed by comparing their results to full 3D simulations. The macroscopic behaviour of the generated shell-based model under compressive loading is then assessed up to the densification stage (including contact), and compared qualitatively with experiments from the literature. The macroscopic behaviour of the shell-based model is explained by linking it to cell/wall level deformation mechanisms.

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The effects of regularity on the geometrical properties of Voronoi tessellations

Cited by 36 publications

References 42 publications

Micromechanics based fatigue life prediction of a polycrystalline metal applying crystal plasticity

Micromechanics based fatigue life prediction of a polycrystalline metal applying crystal plasticity

Heat Diffusion in Polycrystalline Rolled Steel - A Microstructure Based Material Model

Efficient computational modelling of closed cell metallic foams using a morphologically controlled shell geometry

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