Conclusions
The simplest mechanical block model of a medium, whose behavior is determined by Hooke's generalized law of elasticity for small deformations, and by classical laws of plasticity for more significant deformations, is constructed.
It is shown that conversion from a mechanical block model of a medium, which has finite block dimensions, to an idealized model consisting of blocks of zero dimensions (a plane with a thickness equal to zero), occurs with retention of the directions of simple shears and simple elongations, or the directions of the slip planes (a slip plane is a plane, along the normal to which simple elongation occurs; two simple shears occur in two mutually orthogonal directions falling in the plane).
Symmetry of simple shears does not follow from the symmetry of the strain tensor. The components of the vector {ie306-1} are referenced from states of pure shear.
Dynamic manifestations of the model under consideration for a medium will be discussed in the next part of the study.
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Mining Institute. Siberian Branch of the Russian Academy of Sciences, Novosibirsk. Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 4, pp. 26–35, July–August, 1998.
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Chanyshev, A.I. Phenomenological mechanical block model of an element of a deformable medium. Part 1: Definition and basic properties. J Min Sci 34, 300–307 (1998). https://doi.org/10.1007/BF02803689
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DOI: https://doi.org/10.1007/BF02803689