{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T17:57:57Z","timestamp":1770832677783,"version":"3.50.1"},"reference-count":30,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,1,28]],"date-time":"2021-01-28T00:00:00Z","timestamp":1611792000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012190","name":"Ministry of Science and Higher Education of the Russian Federation","doi-asserted-by":"publisher","award":["075-15-2020-799"],"award-info":[{"award-number":["075-15-2020-799"]}],"id":[{"id":"10.13039\/501100012190","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A multiscale approach to discrete element modeling is presented. A distinctive feature of the method is that each macroscopic discrete element has an associated atomic sample representing the material\u2019s atomic structure. The dynamics of the elements on macro and micro levels are described by systems of ordinary differential equations, which are solved in a self-consistent manner. A full cycle of multiscale simulations is applied to polycrystalline silicon. Macroscale elastic properties of silicon were obtained only using data extracted from the quantum mechanical properties. The results of computational experiments correspond well to the reference data.<\/jats:p>","DOI":"10.3390\/sym13020219","type":"journal-article","created":{"date-parts":[[2021,1,28]],"date-time":"2021-01-28T22:02:01Z","timestamp":1611871321000},"page":"219","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Multiscale Discrete Element Modeling"],"prefix":"10.3390","volume":"13","author":[{"given":"Andrew A.","family":"Zhuravlev","sequence":"first","affiliation":[{"name":"Federal Research Centre \u201cComputer Science and Control\u201d of the Russian Academy of Sciences, Vavilov st. 44, 119333 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Karine K.","family":"Abgaryan","sequence":"additional","affiliation":[{"name":"Federal Research Centre \u201cComputer Science and Control\u201d of the Russian Academy of Sciences, Vavilov st. 44, 119333 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dmitry L.","family":"Reviznikov","sequence":"additional","affiliation":[{"name":"Federal Research Centre \u201cComputer Science and Control\u201d of the Russian Academy of Sciences, Vavilov st. 44, 119333 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,28]]},"reference":[{"key":"ref_1","unstructured":"Tadmor, E.B., and Miller, R.E. (2014). Modeling Materials. Continuum, Atomistic and Multiscale Techniques, Cambridge University Press."},{"key":"ref_2","unstructured":"Abgaryan, K.K. (2017). Mnogomashtabnoe Modelirovanie v Zadachah Strukturnogo Materialovedeniya [Multiscale Modeling in Material Science Problems], MAKS Press. (In Russian)."},{"key":"ref_3","unstructured":"Steinhauser, M.O. (2008). Computational Multiscale Modeling of Fluids and Solids: Theory and Applications, Springer."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"751","DOI":"10.3390\/polym5020751","article-title":"Challenges in multiscale modeling of polymer dynamics","volume":"5","author":"Li","year":"2013","journal-title":"Polymers"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"937","DOI":"10.20537\/2076-7633-2017-9-6-937-944","article-title":"High-speed penetration. Discrete-element simulation and experiments","volume":"9","author":"Abgaryan","year":"2017","journal-title":"Comput. Res. Model."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1740009","DOI":"10.1142\/S0219876217400096","article-title":"Discrete Particle Methods for Simulating Quasi-Static Load and Hypervelocity Impact Phenomena","volume":"16","author":"Steinhauser","year":"2019","journal-title":"Int. J. Comput. Methods"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1029","DOI":"10.1016\/j.jeurceramsoc.2008.07.060","article-title":"Discrete element method (DEM) modeling of fracture and damage in the machining process of polycrystalline SiC","volume":"29","author":"Tan","year":"2009","journal-title":"J. Eur. Ceram. Soc."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"5955","DOI":"10.1021\/acsomega.9b00144","article-title":"Development of Coarse-Grained Models for Polymers by Trajectory Matching","volume":"4","author":"Kempfer","year":"2019","journal-title":"ACS Omega"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"244114","DOI":"10.1063\/1.2938860","article-title":"The multiscale coarse-graining method. I. A rigorous bridge between atomistic and coarse-grained models","volume":"128","author":"Noid","year":"2008","journal-title":"J. Chem. Phys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2469","DOI":"10.1021\/jp044629q","article-title":"A multiscale coarse-graining method for biomolecular systems","volume":"109","author":"Izvekov","year":"2005","journal-title":"J. Phys. Chem. B"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"164107","DOI":"10.1063\/1.3394863","article-title":"The multiscale coarse-graining method. VI: Implementation of three-body coarse-grained potentials","volume":"132","author":"Larini","year":"2010","journal-title":"J. Chem. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"035002:1","DOI":"10.1088\/0965-0393\/17\/3\/035002","article-title":"Coarse-grained simulations of single-crystal silicon","volume":"17","author":"Xiong","year":"2009","journal-title":"Model. Simul. Mater. Sci. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1448","DOI":"10.1016\/j.ijsolstr.2008.11.012","article-title":"Multiscale modeling and simulation of single-crystal MgO through an atomistic field theory","volume":"46","author":"Xiong","year":"2009","journal-title":"Int. J. Solids Struct."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1337","DOI":"10.1016\/j.ijengsci.2011.03.018","article-title":"Assessment of atomistic coarse-graining methods","volume":"49","author":"Chen","year":"2011","journal-title":"Int. J. Eng. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1002\/nme.5732","article-title":"FEM\u00d7DEM multiscale modeling: Model performance enhancement from Newton strategy to element loop parallelization","volume":"114","author":"Argilaga","year":"2018","journal-title":"Int. J. Numer. Methods Eng."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Ferretti, E. (2020). DECM: A Discrete Element for Multiscale Modelingof Composite Materials Using the Cell Method. Materials, 13.","DOI":"10.20944\/preprints201912.0014.v3"},{"key":"ref_17","first-page":"114","article-title":"Multiscale Modeling of Composite Materials with DECM Approach: Shape Effect of Inclusions","volume":"13","author":"Ferretti","year":"2019","journal-title":"Int. J. Mech."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"4423","DOI":"10.1063\/1.474784","article-title":"Dissipative particle dynamics: Bridging the gap between atomistic and mesoscopic simulation","volume":"107","author":"Groot","year":"1997","journal-title":"J. Chem. Phys."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"737","DOI":"10.1142\/S1758825109000381","article-title":"Dissipative particle dynamics: Introduction, methodology and complex fluidapplications\u2014A review","volume":"1","author":"Moeendarbary","year":"2009","journal-title":"Int. J. Appl. Mech."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.ijsolstr.2017.05.018","article-title":"Discrete element method to simulate the elastic behavior of 3D heterogeneous continuous media","volume":"121","author":"Leclerc","year":"2017","journal-title":"Int. J. Solids Struct."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1016\/j.ijsolstr.2016.11.015","article-title":"On the suitability of a Discrete Element Method to simulate cracks initiation and propagation in heterogeneous media","volume":"108","author":"Leclerc","year":"2017","journal-title":"Int. J. Solids Struct."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"26","DOI":"10.3221\/IGF-ESIS.24.04","article-title":"Development of a formalism of movable cellular automaton method for numerical modeling of fracture of heterogeneous elastic-plastic materials","volume":"24","author":"Psakhie","year":"2013","journal-title":"Frat. Integrita Strutt."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1007\/978-981-15-2600-8_17","article-title":"Discrete element method adopting microstructure information","volume":"Volume 173","author":"Jain","year":"2020","journal-title":"Advances in Theory and Practice of Computational Mechanics: Proceedings of the 21st International Conference on Computational Mechanics and Modern Applied Software Systems"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"6991","DOI":"10.1103\/PhysRevB.37.6991","article-title":"New empirical approach for the structure and energy of covalent systems","volume":"37","author":"Tersoff","year":"1988","journal-title":"Phys. Rev. B"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1016\/j.commatsci.2006.07.013","article-title":"Development of bond-order potentials that can reproduce the elastic constants and melting point of silicon for classical molecular dynamics simulation","volume":"39","author":"Kumagai","year":"2007","journal-title":"Comput. Mater. Sci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1929","DOI":"10.1134\/S0965542514120021","article-title":"Optimization methods as applied to parametric identification of interatomic potentials","volume":"54","author":"Abgaryan","year":"2014","journal-title":"Comput. Math. Math. Phys."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1007\/978-981-15-2600-8_19","article-title":"Parametric Identification of Tersoff Potential for Two-Component Materials","volume":"Volume 173","author":"Jain","year":"2020","journal-title":"Advances in Theory and Practice of Computational Mechanics: Proceedings of the 21st International Conference on Computational Mechanics and Modern Applied Software Systems"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/S0377-0427(00)00422-2","article-title":"Automatic differentiation of algorithms","volume":"124","author":"Brown","year":"2000","journal-title":"J. Comput. Appl. Math."},{"key":"ref_29","unstructured":"Powell, D. (2006). Elasticity, Lattice Dynamics and Parameterisation Techniques for the Tersoff Potential Applied to Elemental and Type III-V Semiconductors. [Diploma Thesis, The University of Sheffield]."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1109\/JMEMS.2009.2039697","article-title":"What is the Young\u2019s Modulus of Silicon?","volume":"19","author":"Hopcroft","year":"2010","journal-title":"J. Microelectromech. 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