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Three-Dimensional Model of a Structured Linearly Elastic Body

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Abstract

The classical theory of elasticity implies the validity of Hooke’s law and the existence of partial spatial derivatives of displacements. A weakening of the latter assumption yields models with internal structure. Here we develop a three-dimensional elastic model with two structural levels. Microscopic elements of the medium experience local bending. Consideration is given to the contribution of the local bends to macroscopic deformation and rotation, the kinematic compatibility conditions, and the formulation of boundary value problems that ensure a unique solution.

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Funding

The work was carried out within the projects funded by the Russian Foundation for Basic Research (No. 20-05-00184) and Fundamental Research Program (State Reg. No. 121052500138-4).

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Authors and Affiliations

  1. Chinakal Institute of Mining, Siberian Branch, Russian Academy of Sciences, 630091, Novosibirsk, Russia

    A. F. Revuzhenko

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  1. A. F. Revuzhenko
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Correspondence to A. F. Revuzhenko.

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Translated from Fizicheskaya Mezomekhanika, 2021, Vol. 24, No. 3, pp. 26–35.

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Revuzhenko, A.F. Three-Dimensional Model of a Structured Linearly Elastic Body. Phys Mesomech 25, 33–41 (2022). https://doi.org/10.1134/S1029959922010052

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