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The Minkowski overlap and the energy‐conserving contact model for discrete element modeling of convex nonspherical particles

Yuntian Feng Orcid Logo, Yuanqiang Tan

International Journal for Numerical Methods in Engineering, Volume: 122, Issue: 22, Pages: 6476 - 6496

Swansea University Author: Yuntian Feng Orcid Logo

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DOI (Published version): 10.1002/nme.6800

Abstract

A unified contact overlap, termed the Minkowski overlap, between any two shapes is proposed in this paper. This overlap is based on the concept of the Minkowski difference of two shapes, and particularly on the equivalence between the contact state of the two shapes and the location of the origin re...

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Published in: International Journal for Numerical Methods in Engineering
ISSN: 0029-5981 1097-0207
Published: Wiley 2021
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URI: https://cronfa.swan.ac.uk/Record/cronfa57480
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first_indexed 2021-07-30T09:12:52Z
last_indexed 2021-11-17T04:24:32Z
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spelling 2021-11-16T11:03:58.8569706 v2 57480 2021-07-30 The Minkowski overlap and the energy‐conserving contact model for discrete element modeling of convex nonspherical particles d66794f9c1357969a5badf654f960275 0000-0002-6396-8698 Yuntian Feng Yuntian Feng true false 2021-07-30 CIVL A unified contact overlap, termed the Minkowski overlap, between any two shapes is proposed in this paper. This overlap is based on the concept of the Minkowski difference of two shapes, and particularly on the equivalence between the contact state of the two shapes and the location of the origin relative to their Minkowski difference. The Minkowski contact features of a contact, including the overlap, normal direction and contact points, are also defined for convex shapes. In particular, an important property of the Minkowski overlap is introduced which lays the solid theoretical foundation for proposing a Minkowski overlap based energy‐conserving contact model in the current work. The energy‐conserving property for cases where the contact normal direction and point may be subject to discrete changes is also rigorously proved. For convex particles, the computational procedures combining both GJK and EPA algorithms are outlined, and uniqueness and ambiguity issues associated with some special cases are clarified and resolved. The elastic energy conservation of the proposed contact model for convex shapes in elastic impact is further verified using two numerical examples, and two more examples involving more convex particles with different sizes and shapes are also conducted to demonstrate the robustness and applicability of the proposed Minkowski overlap contact model and the computational procedures. Journal Article International Journal for Numerical Methods in Engineering 122 22 6476 6496 Wiley 0029-5981 1097-0207 convex nonspherical particles; convex polyhedral particle; energy conservation; GJK and EPA algorithms; Minkowski overlap 30 11 2021 2021-11-30 10.1002/nme.6800 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University National Natural Science Foundation of China. Grant Number: 11772135; National Natural Science Foundation of China. Grant Number: 12072217 2021-11-16T11:03:58.8569706 2021-07-30T10:10:19.9259531 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Yuntian Feng 0000-0002-6396-8698 1 Yuanqiang Tan 2 57480__20491__19fe3f40eed041c49796d36137e01c8d.pdf 57480.pdf 2021-07-30T10:11:56.5005022 Output 13119726 application/pdf Accepted Manuscript true 2022-08-01T00:00:00.0000000 true eng https://creativecommons.org/licenses/by-nc-nd/2.0/
title The Minkowski overlap and the energy‐conserving contact model for discrete element modeling of convex nonspherical particles
spellingShingle The Minkowski overlap and the energy‐conserving contact model for discrete element modeling of convex nonspherical particles
Yuntian Feng
title_short The Minkowski overlap and the energy‐conserving contact model for discrete element modeling of convex nonspherical particles
title_full The Minkowski overlap and the energy‐conserving contact model for discrete element modeling of convex nonspherical particles
title_fullStr The Minkowski overlap and the energy‐conserving contact model for discrete element modeling of convex nonspherical particles
title_full_unstemmed The Minkowski overlap and the energy‐conserving contact model for discrete element modeling of convex nonspherical particles
title_sort The Minkowski overlap and the energy‐conserving contact model for discrete element modeling of convex nonspherical particles
author_id_str_mv d66794f9c1357969a5badf654f960275
author_id_fullname_str_mv d66794f9c1357969a5badf654f960275_***_Yuntian Feng
author Yuntian Feng
author2 Yuntian Feng
Yuanqiang Tan
format Journal article
container_title International Journal for Numerical Methods in Engineering
container_volume 122
container_issue 22
container_start_page 6476
publishDate 2021
institution Swansea University
issn 0029-5981
1097-0207
doi_str_mv 10.1002/nme.6800
publisher Wiley
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering
document_store_str 1
active_str 0
description A unified contact overlap, termed the Minkowski overlap, between any two shapes is proposed in this paper. This overlap is based on the concept of the Minkowski difference of two shapes, and particularly on the equivalence between the contact state of the two shapes and the location of the origin relative to their Minkowski difference. The Minkowski contact features of a contact, including the overlap, normal direction and contact points, are also defined for convex shapes. In particular, an important property of the Minkowski overlap is introduced which lays the solid theoretical foundation for proposing a Minkowski overlap based energy‐conserving contact model in the current work. The energy‐conserving property for cases where the contact normal direction and point may be subject to discrete changes is also rigorously proved. For convex particles, the computational procedures combining both GJK and EPA algorithms are outlined, and uniqueness and ambiguity issues associated with some special cases are clarified and resolved. The elastic energy conservation of the proposed contact model for convex shapes in elastic impact is further verified using two numerical examples, and two more examples involving more convex particles with different sizes and shapes are also conducted to demonstrate the robustness and applicability of the proposed Minkowski overlap contact model and the computational procedures.
published_date 2021-11-30T04:13:15Z
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score 11.013148

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