Effect of the integration scheme on the rotation of non-spherical particles with the discrete element method
The discrete element method (DEM) is an emerging tool for the calculation of the behaviour of bulk materials. One of the key features of this method is the explicit integration of the motion equations. Explicit methods are rapid, at the cost of a limited time step to achieve numerical stability. Fir...
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| Vydáno v: | Computational particle mechanics Ročník 6; číslo 4; s. 545 - 559 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Springer International Publishing
01.10.2019
Springer Nature B.V |
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| ISSN: | 2196-4378, 2196-4386 |
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| Abstract | The discrete element method (DEM) is an emerging tool for the calculation of the behaviour of bulk materials. One of the key features of this method is the explicit integration of the motion equations. Explicit methods are rapid, at the cost of a limited time step to achieve numerical stability. First- or second-order integration schemes based on a Taylor series are frequently used in this framework and shown to be accurate for the translational and rotational motion of spherical particles. However, they may lead to relevant inaccuracies when non-spherical particles are used since the orientation implies a modification in the second-order inertia tensor in the inertial reference frame. Specific integration schemes for non-spherical particles have been proposed in the literature, such as the fourth-order Runge–Kutta scheme presented by Munjiza et al. and the predictor–corrector scheme developed by Zhao and van Wachem which applies the direct multiplication algorithm for integrating the orientation. In this work, both methods are adapted to be used together with a velocity Verlet scheme for the translational integration. The performance of the resulting schemes, as well as that of the direct integration method, is assessed, both in benchmark tests with analytical solution and in real-scale problems. The results suggest that the fourth-order Runge–Kutta and the Zhao and van Wachem schemes are clearly more accurate than the direct integration method without increasing the computational time. |
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| AbstractList | The discrete element method (DEM) is an emerging tool for the calculation of the behaviour of bulk materials. One of the key features of this method is the explicit integration of the motion equations. Explicit methods are rapid, at the cost of a limited time step to achieve numerical stability. First- or second-order integration schemes based on a Taylor series are frequently used in this framework and shown to be accurate for the translational and rotational motion of spherical particles. However, they may lead to relevant inaccuracies when non-spherical particles are used since the orientation implies a modification in the second-order inertia tensor in the inertial reference frame. Specific integration schemes for non-spherical particles have been proposed in the literature, such as the fourth-order Runge–Kutta scheme presented by Munjiza et al. and the predictor–corrector scheme developed by Zhao and van Wachem which applies the direct multiplication algorithm for integrating the orientation. In this work, both methods are adapted to be used together with a velocity Verlet scheme for the translational integration. The performance of the resulting schemes, as well as that of the direct integration method, is assessed, both in benchmark tests with analytical solution and in real-scale problems. The results suggest that the fourth-order Runge–Kutta and the Zhao and van Wachem schemes are clearly more accurate than the direct integration method without increasing the computational time. |
| Author | Santasusana, Miquel Irazábal, Joaquín Salazar, Fernando Oñate, Eugenio |
| Author_xml | – sequence: 1 givenname: Joaquín orcidid: 0000-0003-4966-4812 surname: Irazábal fullname: Irazábal, Joaquín email: jirazabal@cimne.upc.edu organization: International Centre for Numerical Methods in Engineering (CIMNE) – sequence: 2 givenname: Fernando surname: Salazar fullname: Salazar, Fernando organization: International Centre for Numerical Methods in Engineering (CIMNE) – sequence: 3 givenname: Miquel surname: Santasusana fullname: Santasusana, Miquel organization: International Centre for Numerical Methods in Engineering (CIMNE) – sequence: 4 givenname: Eugenio surname: Oñate fullname: Oñate, Eugenio organization: International Centre for Numerical Methods in Engineering (CIMNE), Polytechnic University of Catalonia |
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| CitedBy_id | crossref_primary_10_1016_j_powtec_2024_120528 crossref_primary_10_1007_s10948_020_05779_6 crossref_primary_10_3389_fbuil_2021_659382 crossref_primary_10_1016_j_conbuildmat_2019_05_102 crossref_primary_10_1186_s40323_022_00229_5 crossref_primary_10_1007_s40571_024_00780_5 crossref_primary_10_1007_s10035_025_01526_7 crossref_primary_10_1007_s40571_022_00550_1 crossref_primary_10_1007_s40571_023_00558_1 crossref_primary_10_1007_s40571_021_00415_z crossref_primary_10_1016_j_apt_2022_103887 crossref_primary_10_1007_s40571_020_00382_x crossref_primary_10_1063_1_5139988 crossref_primary_10_1007_s40571_024_00833_9 |
| Cites_doi | 10.1007/s11044-018-9620-0 10.1103/PhysRevE.81.061303 10.1007/s40571-016-0131-6 10.1142/S0219876204000204 10.1016/j.powtec.2011.01.003 10.1109/TRO.2007.914851 10.1016/j.ces.2008.08.006 10.1016/j.sandf.2013.12.001 10.1007/s40571-015-0044-9 10.1061/(ASCE)GM.1943-5622.0000149 10.1002/nag.2428 10.1007/s00707-013-0914-2 10.1016/j.powtec.2018.03.024 10.1007/s11044-010-9220-0 10.1097/00010694-194808000-00008 10.1007/s10035-017-0712-y 10.1061/(ASCE)MT.1943-5533.0000839 10.2174/1874129001307010103 10.1680/geot.1979.29.1.47 10.1016/j.geotexmem.2011.01.015 10.1209/0295-5075/83/14001 10.1016/0148-9062(88)92293-0 10.1061/(ASCE)0733-9410(1996)122:7(577) 10.1007/s10035-009-0139-1 10.1007/s40571-016-0109-4 10.1061/(ASCE)GM.1943-5622.0000264 10.1016/j.enggeo.2012.07.021 10.1680/geot.1997.47.2.255 10.1016/0148-9062(88)92294-2 10.1016/j.partic.2017.04.001 10.1016/j.powtec.2014.05.052 10.1002/nag.500 10.1002/nme.552 10.1108/02644400410519794 10.1016/j.proeng.2017.01.017 10.1016/j.compgeo.2016.12.034 10.1007/s00466-011-0617-2 10.1002/352760362X.ch13 |
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| Keywords | Non-spherical particles Discrete element method Granular material Clusters of spheres Explicit rotational integration |
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| SubjectTerms | Algorithms Classical and Continuum Physics Computational Science and Engineering Computing time Discrete element method Engineering Equations of motion Exact solutions Inertial reference systems Multiplication Numerical stability Rotating spheres Runge-Kutta method Taylor series Tensors Theoretical and Applied Mechanics |
| Title | Effect of the integration scheme on the rotation of non-spherical particles with the discrete element method |
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