A new algorithm for dense ellipse packing and polygonal structures generation in context of FEM or DEM

Ilin, Dmitrii Nikolaevich; Bernacki, Marc

doi:10.1051/matecconf/20168002004

Cited by 9 publications

(4 citation statements)

References 25 publications

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“…To determine the typical value of the packing fraction of the randomly jammed ellipsoidal particles, computer modeling was performed using a FORTRAN program based on a nonlinear mathematical programming model . It should be emphasized that in the last decade, several theoretical works have been carried out to study the packing behavior of nonspherical objects. ,,,,− The work based on mathematical modeling reported by Birgin et al deals with the 3D packing of a given set of nonoverlapping identical ellipsoids inside a sphere of minimum possible volume. The algorithm of the numerical model consists of the following steps: Generation of “ m ” number of identical ellipsoids with predefined semimajor and semiminor axis inside a container (a sphere in this case). The center of the ellipsoids should be distributed in such a way that the interiors of the ellipsoids are mutually disjoint to ensure the nonoverlapping of the ellipsoids. All the ellipsoids must be inside the container at any given point of time. All the translation and rotational motions of the ellipsoids should satisfy the criteria of (ii) and (iii). Finally, the container volume with respect to the motion of the ellipsoids should be minimized. …”

Section: Resultsmentioning

confidence: 99%

Jamming of Nano-Ellipsoids in a Microsphere: A Quantitative Analysis of Packing Fraction by Small-Angle Scattering

et al. 2022

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The packing of particles is ubiquitous, and it is of fundamental importance, particularly in materials science in the nanometric length scale. It becomes more intriguing when constituent particles deviate from spherical symmetry owing to the inherent complexity in quantifying their positional and rotational correlation. For quantitative estimation of packing fraction, it requires a thorough analysis of the positional correlation of jammed particles. This article adopts a novel approach for determination of the packing fraction of strongly correlated nano-ellipsoids in a microsphere using small-angle scattering. The method has been elucidated through a quantitative analysis of structural correlation of nano-hematite ellipsoids in 3D micrometric granules, which are realized using rapid evaporative assembly. Owing to the deviation from spherical symmetry, the conventional analysis of scattering data fails to interpret the actual packing fraction of the anisotropic particles. The structural correlation gets smeared out because of orientation distribution among the packed anisotropic particles, which leads to an anomaly in the estimation of packing fraction using the conventional analysis approach. It is illustrated that consideration of an interparticle distance distribution function of the correlated nano-ellipsoids becomes indispensable in determining their packing fraction.

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Section: Resultsmentioning

confidence: 99%

Jamming of Nano-Ellipsoids in a Microsphere: A Quantitative Analysis of Packing Fraction by Small-Angle Scattering

et al. 2022

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“…First, it is to provide examples where one can observe the significant differences Fig. 25 The location of the contact points x c is the same for both the MDP and MPP pairs c associated with the MDP belongs to the intersection of both ellipses. However, the MPP produces a reasonable contact point y c inside the intersection between both ellipses E i ∩ E j .…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Given our intended applications, this study will omit discussing contact detection between particles not defined analytically by an ellipse and will also ignore contact detection for rapidly moving pairs of ellipses. In particular, we are not interested by the contact detection problem when the ellipse is approximated by segments of circles [ 25 , 28 , 37 , 49 ], by grid or polar representation of particles [ 24 ], by the four arc approximation of ellipses [ 28 , 49 ], as a polyhedral surface [ 17 ], or in the most general form as a combination of NURBS [ 30 , 48 ]. The analysis is also limited to soft particles, that is to pairs of ellipses for which an accurate estimate of the separation/penetration distance is required, usually to compute forces between particles.…”

Section: Introductionmentioning

confidence: 99%

A mathematical framework for the analysis and comparison of contact detection methods for ellipses and ellipsoids

2022

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The purpose of this research is to provide a framework for the analysis and comparison of contact detection algorithms for pairs of ellipses and ellipsoids. This work focuses primarily on the category of algorithms that are the most computationally efficient and can produce estimates of the separation and the penetration distance between ellipses and ellipsoids. Specifically, only analytic representations of the ellipses and ellipsoids are considered and contact detection for moving pairs of ellipsoids is not treated. The first contribution is a mathematical framework for the study of these algorithms, most notably with existence and uniqueness proofs for classes of contact detection algorithms, formal descriptions of the asymptotics of pairs of ellipses in close contact (or overlap), and a global analysis of constraints on the normals. The framework highlights the key role played by the different definitions of contact found in the literature, independent of the numerical strategies deployed to estimate the separation/penetration distance. Specifically, it is shown that all the studied algorithms can be expressed as minimization problems, with or without non-binding constraints on the normal(s) at the contact point(s), and that the constraints can be used to identify the global minima among the critical points in the minimization problem. Another contribution of this research, based on the mathematical framework introduced, is a better classification of the known algorithms. These algorithms are compared on established test problems, and their strengths and weaknesses are highlighted and explained in terms of their classification. Furthermore, this research provides comparisons in speed and stability between the most efficient algorithms in each category over a large sample size of test problems. Among the other contributions, this research describes inexpensive but effective initial estimates of the contact to be used in iterative algorithms. Finally, the usefulness of the new framework is illustrated with the introduction of a fast algorithm combining some new and old ideas.

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“…This class of methods can be primarily divided into dynamic and constructive solutions. In the dynamic approaches, the spheres change their position or their size during the packing process, which is controlled by a shrinking algorithm (Tory & Jodrey, 1986;Torquato & Jiao, 2010;He et al, 2018), compression forces algorithm (Khirevich, et al, 2013;Baranau & Tallarek, 2014) or gravitational algorithm (Shi & Zhang, 2008;Hitti & Bernacki, 2013;Sahu, 2009;Ilina & Bernacki, 2016). In the case of constructive approaches, sphere parameters like size or position are preserved during the packing process, so they are less costly but have difficulties in achieving high-density packing (Evans, 1993;Cui & O'Sullivan, 2003;Kazakov et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

Sphere packing algorithm for the generation of digital models of polycrystalline microstructures with heterogeneous grain sizes

Hajder¹,

Madej²

2020

cmms

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Development of the cellular automata (CA) sphere packing algorithm dedicated to the generation of two-and threedimensional digital, synthetic microstructure models with heterogenous grain size distribution is presented within the paper. The synthetic microstructure model is generated in four major steps: generation of 2D/3D cellular automata computational domain, generation of circles/spheres with a required size distribution, close-packed filling of the computational domain with generated circles/spheres, growth of the circles/spheres according to the unconstrained CA growth algorithm. As a result, synthetic microstructure models with prescribed, e.g. uni-or bimodal, grain size distribution are obtained. To reduce the computational complexity and decrease execution time, the rotation of the circles/spheres during the packing stage is based on the vector accounting for the distance from computational domain borders and other spheres. The CA grain growth algorithm is also implemented using threads mechanism, allowing parallel execution of computations to increase its efficiency. The developed algorithm, along with the implementation details as well as a set of exemplary results, are presented within the paper.

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A new algorithm for dense ellipse packing and polygonal structures generation in context of FEM or DEM

Cited by 9 publications

References 25 publications

Jamming of Nano-Ellipsoids in a Microsphere: A Quantitative Analysis of Packing Fraction by Small-Angle Scattering

Jamming of Nano-Ellipsoids in a Microsphere: A Quantitative Analysis of Packing Fraction by Small-Angle Scattering

A mathematical framework for the analysis and comparison of contact detection methods for ellipses and ellipsoids

Sphere packing algorithm for the generation of digital models of polycrystalline microstructures with heterogeneous grain sizes

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