A fast contact detection method for ellipsoidal particles

Kheradmand, Elham; Prudhomme, Serge; Laforest, Marc

doi:10.1002/nag.3197

Cited by 4 publications

(11 citation statements)

References 27 publications

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“…4.3) is done in one of the normalized coordinate systems we introduce below. We remark that the estimation of the contact point is rarely addressed in the literature and, to the best of our knowledge, the focal point estimate was first presented by the authors in [29].…”

Section: Initializing the Positions Of Two Ellipses For Contact Detectionmentioning

confidence: 99%

“…The authors proposed a novel approach [29] for contact detection between pairs of ellipses and ellipsoids combining existing techniques and new features. The algorithm belongs to the class of geometrical potential methods and, more specifically, involves solving the constrained minimization problem (112) after applying the mapping of Sect.…”

Section: The Steered Geometric Potential Algorithm (S-gpa)mentioning

confidence: 99%

“…4.3, although generally accurate, is not guaranteed to be located inside the basin of attraction of t j , in which case the method will converge to another root of h(t). Among the roots of the function h(t), only t j satisfies n i (x(t j )) • n j (x(t j )) < 0 or, in an equivalent manner, ∇ f i (x(t j )) • ∇ f j (x(t j )) < 0; see [29] for a formal justification. This motivates us to introduce the function q(t), defined on [−π, π[, as…”

Section: The Steered Geometric Potential Algorithm (S-gpa)mentioning

confidence: 99%

“…These numerical experiments are carried out in Sect. 6, but the detailed algorithm used to generate random pairs of ellipses is detailed in a second paper by the authors [29].…”

Section: Introductionmentioning

confidence: 99%

“…This new CDA is only briefly explained in Sect. 5.4, but a complete description of the algorithm can be found in [29].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Initializing the Positions Of Two Ellipses For Contact Detectionmentioning

confidence: 99%

Section: The Steered Geometric Potential Algorithm (S-gpa)mentioning

confidence: 99%

Section: The Steered Geometric Potential Algorithm (S-gpa)mentioning

confidence: 99%

“…These numerical experiments are carried out in Sect. 6, but the detailed algorithm used to generate random pairs of ellipses is detailed in a second paper by the authors [29].…”

Section: Introductionmentioning

confidence: 99%

“…This new CDA is only briefly explained in Sect. 5.4, but a complete description of the algorithm can be found in [29].…”

Section: Introductionmentioning

confidence: 99%

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

2022

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A new cube movement test for verification of simulations of contact processes of blocks of different size in geological hazards

Wang,

Feng,

Lahayne

et al. 2024

Num Anal Meth Geomechanics

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In many geological hazards, such as landslides, a large number of irregular blocks start moving. Their interaction on the way down renders prediction of disaster scopes difficult. To study this process and to provide a novel method for validation and calibration of numerical tools for its simulation, a cube movement test is designed. The goal of this research is to obtain patterns of movement of cubes, starting from different initial stacking arrangements. Cubes of four sizes are inserted into a hollow cylinder. Their distribution after lifting the cylinder is determined. Three categories of tests refer to three different strategies of filling the cubes into the cylinder. In order to simulate cube movement tests, a numerical tool is developed in the framework of the continuum–discontinuum element method (CDEM). The contact between the individual cubes is modeled by the contact‐pairs‐based algorithm. Both the contact state and type are detected by determining the half‐space relation between contact pairs. The final positions of the cubes are strongly related to their initial arrangement. The latter is different in every test, even if the same strategy is used to fill the cubes into the cylinder. It is found that at least 20 experiments/simulations are required to obtain statistically representative results. The new test provides valuable data for validation of numerical tools used for the simulation of mass movement processes. The proposed numerical method captures the complicated movements of blocks.

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A machine learning-based particle-particle collision model for non-spherical particles with arbitrary shape

Hwang

Pan

Sunny

et al. 2022

Chemical Engineering Science

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A fast contact detection method for ellipsoidal particles

Cited by 4 publications

References 27 publications

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

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

A new cube movement test for verification of simulations of contact processes of blocks of different size in geological hazards

A machine learning-based particle-particle collision model for non-spherical particles with arbitrary shape

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