Optimisation of Size-controllable Centroidal Voronoi Tessellation for FEM Simulation of Micro Forming Processes

Luo, Liang; Jiang, Zhengyi; Lu, Haina; Wei, Dongbin; Linghu, Kezhi; Xi-nan, Zhao; Wu, Di

doi:10.1016/j.proeng.2014.10.342

Cited by 17 publications

(10 citation statements)

References 5 publications

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“…Different strategies exist for vertex sets with varying density: Surazhsky et al (2003] insert vertices at places with high curvature and then use Uoyd's method for moving points to reach a smooth mesh. Luo et al (2014] create mesh vertices for FEM tests by using Lloyd' s method, then perform a Delaunay triangulation, splitting triangles according to the needed density and use the updated set for their simulations. Tournois et aL (2009] interleave Delauney refinement and Optimal Delauney Triangulation, which is a variant ofCVT.…”

Section: Related Workmentioning

confidence: 99%

Weighted linde-buzo-gray stippling

2017

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Fig. 1. Starting from a single random point, our dynamic illustration method creates high-quality stipple drawings with a small number of iterations (left to right: 12, 14, and 18 iterations). In the example shown above we end up with 36k points of constant size.We propose an adaptive version of Lloyd's optimization method that distributes points based on Voronoi diagrams. Our inspiration is the LindeBuzo-Gray-Algorithm in vector quantization, which dynamically splits Voronoi cells until a desired number of representative vectors is reached. We reformulate this algorithm by splitting and merging Voronoi cells based on their size, greyscale level, or variance of an underlying input image. The proposed method automatically adapts to various constraints and, in contrast to previous work, requires no good initial point distribution or prior knowledge about the final number of points. Compared to weighted Voronoi stippling the convergence rate is much higher and the spectral and spatial properties are superior. Further, because points are created based on local operations, coherent stipple animations can be produced. Our method is also able to produce good quality point sets in other fields, such as remeshing of geometry, based on local geometric features such as curvature.

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Section: Related Workmentioning

confidence: 99%

Weighted linde-buzo-gray stippling

2017

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“…The grains with various sizes, orientations and shapes are distributed in the specimen nonuniformly, giving a rise to inhomogeneous material behaviour and the scatter of experiment results [13,14]. Consequently in the finite element simulation of microforming process, Voronoi tessellation has been widely applied to model the microstructure of grain aggregate, and then the material heterogeneity caused by different grain properties can be reflected via assigning a certain property to each Voronoi polyhedron [15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Analysis of micro flexible rolling with consideration of material heterogeneity

Jiang

2016

International Journal of Mechanical Sciences

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This paper establishes a finite element model to numerically study the springback in thickness direction during micro flexible rolling process, in which 3D Voronoi tessellation has been applied to describe grain boundary and generation process of grain in the workpiece. To reflect material heterogeneity, nine kinds of mechanical properties defined by nine types of heterogeneity coefficients are selected and assigned to Voronoi polyhedrons as per the statistical distribution of hardness of grains identified by micro hardness testing. Initial workpiece thicknesses of 100, 250 and 500 μm with reduction changing from 20% to 50% are respectively considered in the numerical simulation of micro flexible rolling process, and the effects of front and back tensions on the average springback have been discussed. With average grain sizes of 1, 10, 50, 100 and 250 μm respectively employed in the workpieces with the aforesaid initial thicknesses, the scatter of springback in thickness direction has been determined, and a model for springback has also been developed based on the simulation results. Analysis of micro flexible rolling with consideration of material heterogeneityAbstract: This paper establishes a finite element model to numerically study the springback in thickness direction during micro flexible rolling process, in which 3D Voronoi tessellation has been applied to describe grain boundary and generation process of grain in the blankworkpiece. To reflect material heterogeneity, nine kinds of mechanical properties defined by nine types of heterogeneity coefficients are selected and assigned to Voronoi polyhedrons as per the statistical distribution of hardness of grains identified by micro hardness testing. Initial blank thicknesses of 100, 250 and 500 m with reductions changingof from 20 toand 50% respectively are respectively considered in the numerical simulation of micro flexible rolling process. With grain sizes of 1, 10, 50, 100 and 250 m respectively employed in the workpieceblank, the scatter of springback in thickness direction has been determined, and a model for springback has also been developed based on the simulation results.

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“…However, all the aforementioned models cannot explain the increasing data scatter from experiments and the localised deformation behaviour caused by the individual grain. To further reveal the size effects, the Voronoi models were developed [8][9][10]. The sample was divided into small subareas according to the Voronoi structures and the small subareas were assigned different mechanical properties.…”

Section: Introductionmentioning

confidence: 99%

A new micro scale FE model of crystalline materials in micro forming process

et al. 2016

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Abstract. Micro forming of metals has drawn global attention due to the increasing requirement of micro metal products. However, the size effects become significant in micro forming processes and affect the application of finite element (FE) simulation of micro forming processes. Dividing samples into small areas according to their microstructures and assigning individual properties to each small area are a possible access to micro forming simulation considering material size effects. In this study, a new model that includes both grains and their boundaries was developed based on the observed microstructures of samples. The divided subareas in the model have exact shapes and sizes with real crystals on the sample, and each grain and grain boundaries have their own properties. Moreover, two modelling methods using different information from the microstructural images were introduced in detail. The two modelling methods largely increase the availability of various microstructural images. The new model provides accurate results which present the size effects well.

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Optimisation of Size-controllable Centroidal Voronoi Tessellation for FEM Simulation of Micro Forming Processes

Cited by 17 publications

References 5 publications

Weighted linde-buzo-gray stippling

Weighted linde-buzo-gray stippling

Analysis of micro flexible rolling with consideration of material heterogeneity

A new micro scale FE model of crystalline materials in micro forming process

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