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ArticleName Mechanics of granular media under vibration action: the methods of description and mathematical modeling
DOI 10.17580/or.2015.04.05
ArticleAuthor Vaisberg L. А., Demidov I. V., Ivanov K. S.

Institute of Problems of Mechanical Engineering of the RAS (Russia):

Demidov I. V., Postgraduate


REC «Mekhanobr-tekhnika» (Russia):

Vaisberg L. А., Corresponding Member of the Russian Academy of Sciences (RAS), Doctor of Engineering Sciences, Professor, Company Scientific Advisor

Ivanov K. S., Ph. D. in Engineering Sciences, Researcher

E-mail (common):


The article presents a review of the modern methods of computational investigation and modeling of dynamics of granular media under vibration action. Attention is focused on typical states of granular material, realized depending on intensity of vibration action and mechanical characteristics of material. Three «physical states» are distinguished: «elastic-plastic» solid — if mutual arrangement of material particles is changed little, viscous «granular liquid» — if most particles are shifted without breaking contacts, and «granular gaseous» — when time of contact interaction between particles is small in comparison with their free time of flight. Also, three groups of approaches to modeling are distinguished: microscopical — considering material at the level of separate particles, statistical mechanics / kinetic theory — generalizing kinetic theory of gases with respect to inelastic interactions, phenomenological models and continuum mechanical models. A range of applicability and possibilities are specified for each group of models. Application of the described approaches is illustrated by a number of cases of specific behavior of granular materials: Leidenfrost granular effect, granular convection, oscillons, etc.

The work was performed under the Ministry of Education and Science of the Russian Federation grant No. 14.579.21.0023 from 05.06.2014.

keywords Granular media, vibration action, physical state of material, mathematical modeling, microscopical models, phenomenological models, continuum mechanical models

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