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On Compression of a Heavy Compressible Layer of an Elastoplastic or Elastoviscoplastic Medium

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Abstract

The problem of deformation of a horizontal plane layer of a compressible material is solved in the framework of the theory of small strains. The upper boundary of the layer is under the action of shear and compressing loads, and the no-slip condition is satisfied on the lower boundary of the layer. The loads increase in absolute value with time, then become constant, and then decrease to zero.Various plasticity conditions are consideredwith regard to the material compressibility, namely, the Coulomb–Mohr plasticity condition, the von Mises–Schleicher plasticity condition, and the same conditions with the viscous properties of the material taken into account. To solve the system of partial differential equations for the components of irreversible strains, a finite-difference scheme is developed for a spatial domain increasing with time. The laws of motion of elastoplastic boundaries are presented, the stresses, strains, rates of strain, and displacements are calculated, and the residual stresses and strains are found.

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Authors and Affiliations

  1. Institute for Automation and Control Processes of the Far East Branch of the Russian Academy of Sciences, ul. Radio 5, Vladivostok, 690041, Russia

    L. V. Kovtanyuk

  2. Institute ofMachinery and Metallurgy of the Far East Branch of the Russian Academy of Sciences, ul. Metallurgov 1, Komsomolsk-on-Amur, 681005, Russia

    G. L. Panchenko

  3. Vladivostok State University of Economics and Service, ul. Gogolya 41, Vladivostok, 690014, Russia

    G. L. Panchenko

Authors
  1. L. V. Kovtanyuk
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  2. G. L. Panchenko
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Correspondence to G. L. Panchenko.

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Original Russian Text © L.V. Kovtanyuk, G.L. Panchanko, 2017, published in Izvestiya Akademii Nauk, Mekhanika Tverdogo Tela, 2017, No. 6, pp. 71–82.

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Kovtanyuk, L.V., Panchenko, G.L. On Compression of a Heavy Compressible Layer of an Elastoplastic or Elastoviscoplastic Medium. Mech. Solids 52, 653–662 (2017). https://doi.org/10.3103/S002565441706005X

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  • DOI: https://doi.org/10.3103/S002565441706005X

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