A Numerical Model of Random Packing of Spheres

Levine, M.M.; Chernick, J.

doi:10.1038/208068a0

Cited by 48 publications

(6 citation statements)

References 4 publications

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“…By computing the fraction contained by the four balls at the vertices, they were able to achieve an explanation for the density δ d (B) ≈ 0.6357. There are other mathematical verifications and explanations for this fact (see [24][25][26][27]). Nevertheless, a mathematical proof is still missing.…”

Section: Statistical Explanationsmentioning

confidence: 98%

A Mathematical Theory for Random Solid Packings

Zong

2014

Preprint

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Section: Statistical Explanationsmentioning

confidence: 98%

A Mathematical Theory for Random Solid Packings

Zong

2014

Preprint

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“…Laguerre geometry which is constructed based on random closed packing of spheres. 100 The spheres which are computed with an algorithm of random closed packing of spheres [101][102][103] are the input for the power tessellation. 91 Thus, the resulting cell size distribution is similar to the sphere size distribution obtained by the algorithm.…”

Section: As the Name Says This Type Of Tessellation Is Based On A Vormentioning

confidence: 99%

Overview and comparison of modelling methods for foams

Hössinger-Kalteis

Reiter

Jerabek

et al. 2020

Journal of Cellular Plastics

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Cellular materials, especially foams, are widely used in several applications because of their special mechanical, electrical and thermal properties. Their properties are determined by three factors: bulk material properties, cell topology and shape as well as relative density. The bulk material properties include the mechanical, thermal and electrical properties of the matrix. The cell topology determines if the foam exhibits stretch or bending dominated behaviour. The relative density corresponds to the foaming degree. It is defined by the cell edge length and cell wall thickness. Especially for the linear elastic properties there are many different modelling approaches. In general, these methods can be divided into two groups namely direct modelling, e.g. analytical and finite element models and constitutive modelling, e.g. models which are generated through homogenization methods. This paper presents an overview of the different modelling methods for foams. Furthermore, sensitivity studies are presented which enable the comparison of the models with regard to the estimation of the elastic properties, show the limits of those models and enable the investigation of the influence of the above mentioned factors on the elastic properties. Selected models are validated with experimental data of a low density foam regarding the Young’s modulus.

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“…cell size distribution and anisotropic cell shape). Cell size distributions can be implemented, for example, by using Voronoi diagrams with Laguerre geometry [20][21][22][23][24][25][26][27] and anisotropic cell shapes by using Set Voronoi diagrams. 28,29 In our previous research work, 1 a Voronoibased approach is presented, where microstructural features like cell size distribution, anisotropic cell shape, cell wall thickness distribution and open cell content are considered.…”

Section: Introductionmentioning

confidence: 99%

Application of computed tomography data–based modelling technique for polymeric low density foams, Part B: Characterization of the mechanical behaviour

Hössinger-Kalteis

Reiter

Jerabek

et al. 2022

Journal of Cellular Plastics

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The non-linear material behaviour of low density polypropylene foams is investigated under several quasi-static loading conditions with a combined modelling technique based on computed tomography data and Voronoi diagrams. A simulation methodology for determining the linear elastic properties is introduced in Hössinger-Kalteis et al. (2021). In this paper, the methodology is extended regarding the material model, where additionally the non-linear region is considered. The model takes into account property determining microstructural features like orientation-dependent cell wall thicknesses and anisotropic cell shapes. Thus, the anisotropic material behaviour under tension and compression load is estimated for extrusion foams with different densities utilizing the microstructural simulation model. Based on the characterized behaviour under tension and compression, constitutive models are generated. These are implemented in bending test simulations due to lower computational effort. The simulation results are validated with experimental results, which shows that the model gives satisfactory results.

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A Numerical Model of Random Packing of Spheres

Cited by 48 publications

References 4 publications

A Mathematical Theory for Random Solid Packings

A Mathematical Theory for Random Solid Packings

Overview and comparison of modelling methods for foams

Application of computed tomography data–based modelling technique for polymeric low density foams, Part B: Characterization of the mechanical behaviour

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