Laguerre approximation of random foams

Liebscher, André

doi:10.1080/14786435.2015.1078511

Cited by 17 publications

(17 citation statements)

References 50 publications

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“…Unlike the linear programming approach, the dimensionality of the optimization problem grows only linearly in the number of grains (and does not depend on the number of voxels). Thus, [35] avoids problem (iii) and, to a lesser extent, problem (i). However, the gradient-descent methods used there become stuck in local minima.…”

Section: Minimizing the Discrepancymentioning

confidence: 97%

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Fitting Laguerre tessellation approximations to tomographic image data

Spettl

Brereton

Duan

et al. 2016

Philosophical Magazine

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The analysis of polycrystalline materials benefits greatly from accurate quantitative descriptions of their grain structures. Laguerre tessellations approximate such grain structures very well. However, it is a quite challenging problem to fit a Laguerre tessellation to tomographic data, as a high-dimensional optimization problem with many local minima must be solved. In this paper, we formulate a version of this optimization problem that can be solved quickly using the cross-entropy method, a robust stochastic optimization technique that can avoid becoming trapped in local minima. We demonstrate the effectiveness of our approach by applying it to both artificially generated and experimentally produced tomographic data.Comment: 27 pages, 10 figures, 2 table

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Section: Minimizing the Discrepancymentioning

confidence: 97%

“…In [35], gradient-descent methods are used to obtain Laguerre approximations (with a relatively low number of evaluations of the discrepancy). Unlike the linear programming approach, the dimensionality of the optimization problem grows only linearly in the number of grains (and does not depend on the number of voxels).…”

Section: Minimizing the Discrepancymentioning

confidence: 99%

Fitting Laguerre tessellation approximations to tomographic image data

Spettl

Brereton

Duan

et al. 2016

Philosophical Magazine

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“…Voronoi diagrams and their generalisations are often used to represent the microstructure of polycrystalline metals and foams, e.g. [1][2][3][4][5][6][7][8][9][10][11][12][13][14], with individual Voronoi cells representing grains in metals and pores or bubbles in foams. They can be used to generate complex microstructures quickly using a relatively small number of parameters, and they are often used as representative volume elements (RVEs) for computational homogenisation, e.g.…”

Section: State Of the Artmentioning

confidence: 99%

“…where λ is a damping parameter between 0 and 1. The choice l = 1 corresponds to the Lloyd step (6). The closer l is to 0, the closer…”

Section: Choice Of the Initial Guessmentioning

confidence: 99%

Laguerre tessellations and polycrystalline microstructures: a fast algorithm for generating grains of given volumes

Bourne

Kok

Roper

et al. 2020

Philosophical Magazine

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We present a fast algorithm for generating Laguerre diagrams with cells of given volumes, which can be used for creating RVEs of polycrystalline materials for computational homogenisation, or for fitting Laguerre diagrams to EBSD or XRD measurements of metals. Given a list of desired cell volumes, we solve a convex optimisation problem to find a Laguerre diagram with cells of these volumes, up to any prescribed tolerance. The algorithm is built on tools from computational geometry and optimal transport theory which, as far as we are aware, have not been applied to microstructure modelling before. We illustrate the speed and accuracy of the algorithm by generating RVEs with user-defined volume distributions with up to 20,000 grains in 3D. We can achieve volume percentage errors of less than 1% in the order of minutes on a standard desktop PC. We also give examples of polydisperse microstructures with bands, clusters and size gradients, and of fitting a Laguerre diagram to 3D EBSD measurements of an IF steel.

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“…This requires a further material volume correction at the nodes of the ligaments to account for excess material due to beam overlap. It was shown that extracting the seed points of a possible Laguerre tessellation based on the intersection nodes of a given foam sample produces tessellations that are similar in terms of morphological properties with those of simulated foams generated using Surface Evolver [62]. The use of these seed points in the DN-RSA algorithm directly instead of a distribution of radius to generate an open foam RVE would be an interesting further development.…”

Section: Conclusion On the Statistical Distribution Of Rve Propertiesmentioning

confidence: 99%

Computational generation of open-foam representative volume elements with morphological control using distance fields

Kilingar

Kamel

Sonon

et al. 2019

European Journal of Mechanics - A/Solids

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This paper presents an automated approach to build computationally Representative Volume Elements (RVE) of open-foam cellular materials, enabling the study of the effects of the microstructural features on their macroscopic behavior. The approach strongly relies on the use of distance and level set functions. The methodology is based on the extraction of random tessellations from inclusion packings following predetermined statistical packing distribution criteria. With the help of simple recombination operations on the distance fields, the tessellations are made to degenerate in Laguerre tessellations. Predetermined morphological characteristics like strut cross-section variation based on commercially available materials are applied on the RVE to ensure the extraction of closely matching models using simple surface extraction tools, and a detailed morphology quantification of the resulting RVEs is provided by comparing them with experimental observations. The extracted RVE surface is then treated with smoothening criteria before obtaining a 3D tetrahedralized model. This model can then be exported for multi-scale simulations to assess the effects of microstructural features by an upscaling methodology. The approach is illustrated by the simulation of a compression test on an RVE incorporating plasticity with geometrically non-linear behavior.

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Laguerre approximation of random foams

Cited by 17 publications

References 50 publications

Fitting Laguerre tessellation approximations to tomographic image data

Fitting Laguerre tessellation approximations to tomographic image data

Laguerre tessellations and polycrystalline microstructures: a fast algorithm for generating grains of given volumes

Computational generation of open-foam representative volume elements with morphological control using distance fields

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