Journal of Elasticity

, Volume 133, Issue 2, pp 155–199 | Cite as

On the Use of the Continuum Mechanics Method for Describing Interactions in Discrete Systems with Rotational Degrees of Freedom

  • Elena A. IvanovaEmail author


Elastic interactions in a system of two body-points possessing both translational and rotational degrees of freedom are studied for the most general case of motion in 3D space. The continuum mechanics method is used as a theoretical foundation for describing the interactions. A definition of strain measures for the discrete system is given by analogy with that in continuum mechanics. Constitutive equations for force and moment vectors are derived based on the energy balance equation. Several new interaction potentials are suggested.


Discrete systems Constitutive equations Interaction potentials Rotational motion Moment interactions Continuum mechanics method Molecular dynamics Discrete element method Proppant packing 

Mathematics Subject Classification (2010)

70E17 70E55 70E99 70F99 70G99 74E15 74E40 74E99 74M25 



The author is deeply grateful to A.K. Belyaev and V.A. Kuzkin for useful discussions on the paper.

This work was supported by Ministry of Education and Science of the Russian Federation within the framework of the Federal Program “Research and development in priority areas for the development of the scientific and technological complex of Russia for 2014–2020” (activity 1.2), grant No. 14.575.21.0146 of September 26, 2017, unique identifier: RFMEFI57517X0146.


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Authors and Affiliations

  1. 1.Dept. of Theoretical MechanicsPeter the Great St. Petersburg Polytechnic UniversitySt. PetersburgRussia
  2. 2.Institute for Problems in Mechanical Engineering of Russian Academy of SciencesSt. PetersburgRussia

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