The Minkowski overlap and the energy‐conserving contact model for discrete element modeling of convex nonspherical particles
A unified contact overlap, termed the Minkowski overlap, between any two shapes is proposed in this article. 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...
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| Veröffentlicht in: | International journal for numerical methods in engineering Jg. 122; H. 22; S. 6476 - 6496 |
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| Sprache: | Englisch |
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Hoboken, USA
John Wiley & Sons, Inc
30.11.2021
Wiley Subscription Services, Inc |
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| ISSN: | 0029-5981, 1097-0207 |
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| Abstract | A unified contact overlap, termed the Minkowski overlap, between any two shapes is proposed in this article. 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. |
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| AbstractList | A unified contact overlap, termed the Minkowski overlap, between any two shapes is proposed in this article. 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. |
| Author | Tan, Yuanqiang Feng, Y. T. |
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| Cites_doi | 10.1063/1.474310 10.1007/978-981-15-3304-4 10.1016/0148-9062(88)92293-0 10.1007/s10035‐019‐0896‐4 10.1002/nme.6633 10.1109/ROBOT.1997.606761 10.1108/EC-03-2019-0124 10.1680/geot.1979.29.1.47 10.1108/02644400410519866 10.1016/j.cma.2021.113750 10.32604/cmes.2021.015913 10.1016/j.cma.2020.113454 10.1109/MCG.1981.1673799 10.1016/j.cma.2016.11.001 10.1016/j.powtec.2018.08.026 10.1201/b15791-3 10.1016/j.powtec.2021.05.037 10.1108/02644400810881374 10.1109/56.2083 10.1016/j.cma.2020.113493 |
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| References_xml | – start-page: 253 year: 2013 end-page: 269 – volume: 4 start-page: 193 issue: 2 year: 1988 end-page: 203 article-title: A fast procedure for computing the distance between complex objects in three‐dimensional space publication-title: IEEE Trans Robot Automat – volume: 107 start-page: 5831 issue: 15 year: 1997 end-page: 5851 article-title: Symplectic splitting methods for rigid body molecular dynamics publication-title: J Chem Phys – volume: 37 start-page: 54 year: 2020 end-page: 72 article-title: On Minkowski difference‐based contact detection in discrete/discontinuous modelling of convex polygons/polyhedra: algorithms and implementation publication-title: Eng Comput – volume: 127 start-page: 721 issue: 2 year: 2021 end-page: 735 article-title: Discrete element modelling of dynamic behaviour of rockfills for resisting high speed projectile penetration publication-title: Comput Model Eng Sci – volume: 379 year: 2021 article-title: An effective energy‐conserving contact modelling strategy for spherical harmonic particles represented by surface triangular meshes with automatic simplification publication-title: Comput Methods Appl Mech Eng – year: 1967 – year: 2001 – year: 2020 – year: 1997 – volume: 29 start-page: 47 issue: 1 year: 1979 end-page: 65 article-title: A discrete numerical model for granular assemblies publication-title: Geotechnique – volume: 21 year: 2019 article-title: Bond and fracture model in dilated polyhedral DEM and its application to simulate breakage of brittle materials publication-title: Granul Matter – volume: 373 year: 2021 article-title: An energy‐conserving contact theory for discrete element modelling of arbitrarily shaped particles: basic framework and general contact model publication-title: Comput Methods Appl Mech Eng – start-page: 1 year: 2021 end-page: 17 article-title: A generic energy‐conserving discrete element modelling strategy for concave particles represented by surface triangular meshes publication-title: Int J Numer Methods in Eng – volume: 25 start-page: 432 issue: 5 year: 2008 end-page: 442 article-title: A contact detection algorithm for superellipsoids based on the common‐normal concept publication-title: Eng Comput – volume: 315 start-page: 632 year: 2017 end-page: 651 article-title: A generic contact detection framework for cylindrical particles in discrete element modelling publication-title: Comput Methods Appl Mech Eng – volume: 21 start-page: 422 issue: 2/3/4 year: 2004 end-page: 430 article-title: Discrete element modeling with dilated particles publication-title: Eng Comput – volume: 339 start-page: 534 year: 2018 end-page: 549 article-title: Interaction between super‐quadric particles and triangular elements and its application to hopper discharge publication-title: Powder Technol – volume: 373 year: 2021 article-title: An energy‐conserving contact theory for discrete element modelling of arbitrarily shaped discrete elements: contact volume based model and computational issues publication-title: Comput Methods Appl Mech Eng – volume: 389 start-page: 376 year: 2021 end-page: 382 article-title: On the strain energy distribution of two elastic solids under smooth contact publication-title: Powder Technol – volume: 1 start-page: 11 issue: 1 year: 1981 end-page: 23 article-title: Superquadrics and angle‐preserving transformations publication-title: IEEE Comput Graph Appl – volume: 25 start-page: 107 year: 1988 end-page: 116 article-title: Formulation of a three‐dimensional distinct element model ‐ part I. a scheme to detect and represent contacts in a system composed of many polyhedral blocks publication-title: Int J Rock Mech Min Sci Geomech – year: 2013 – ident: e_1_2_9_23_1 doi: 10.1063/1.474310 – ident: e_1_2_9_3_1 doi: 10.1007/978-981-15-3304-4 – ident: e_1_2_9_4_1 doi: 10.1016/0148-9062(88)92293-0 – ident: e_1_2_9_9_1 doi: 10.1007/s10035‐019‐0896‐4 – ident: e_1_2_9_12_1 doi: 10.1002/nme.6633 – ident: e_1_2_9_20_1 doi: 10.1109/ROBOT.1997.606761 – ident: e_1_2_9_14_1 doi: 10.1108/EC-03-2019-0124 – ident: e_1_2_9_2_1 doi: 10.1680/geot.1979.29.1.47 – ident: e_1_2_9_8_1 doi: 10.1108/02644400410519866 – ident: e_1_2_9_13_1 doi: 10.1016/j.cma.2021.113750 – start-page: 253 volume-title: Proceedings of the 47th US Rock Mechanics/Geo‐mechanics Symposium year: 2013 ident: e_1_2_9_17_1 – ident: e_1_2_9_21_1 doi: 10.32604/cmes.2021.015913 – ident: e_1_2_9_10_1 doi: 10.1016/j.cma.2020.113454 – ident: e_1_2_9_24_1 doi: 10.1109/MCG.1981.1673799 – ident: e_1_2_9_5_1 doi: 10.1016/j.cma.2016.11.001 – ident: e_1_2_9_6_1 doi: 10.1016/j.powtec.2018.08.026 – ident: e_1_2_9_18_1 doi: 10.1201/b15791-3 – ident: e_1_2_9_19_1 doi: 10.1016/j.powtec.2021.05.037 – volume-title: Calculus. Volume 1: One‐variable Calculus with an Introduction to Linear Algebra year: 1967 ident: e_1_2_9_22_1 – ident: e_1_2_9_7_1 doi: 10.1108/02644400810881374 – ident: e_1_2_9_16_1 – ident: e_1_2_9_15_1 doi: 10.1109/56.2083 – ident: e_1_2_9_11_1 doi: 10.1016/j.cma.2020.113493 |
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| SubjectTerms | Algorithms convex nonspherical particles convex polyhedral particle Discrete element method energy conservation GJK and EPA algorithms Minkowski overlap Robustness (mathematics) |
| Title | The Minkowski overlap and the energy‐conserving contact model for discrete element modeling of convex nonspherical particles |
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