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Exact solution of one problem of imposition of large deformations in a compound slab with pre-deformed layers of incompressible nonlinear elastic micropolar material

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Abstract

An exact solution is obtained for a new class of problems on the imposition of large deformations in nonlinear elastic micropolar bodies. The problem of determining the stress state in a compound slab having the shape of a rectangular parallelepiped, composed of pre-deformed layers and subjected to biaxial tension or compression is solved. The layers are made of isotropic incompressible nonlinear elastic micropolar materials. The layers are preliminarily deformed by straightening of circular cylindrical sectors. The solution is based on a class of universal deformations for isotropic incompressible nonlinear elastic micropolar materials. Numerical studies were carried out. The dependencies of stresses, resulting forces and moments on the parameters of initial and additional deformations are presented. Significant nonlinear effects are revealed. The influence of micropolar effects on the stress state has been studied. The solution can be used to verify software designed to numerically solve problems on the imposition of large deformations in bodies made of nonlinear elastic micropolar materials.

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Acknowledgements

The research for this article was performed in Lomonosov Moscow State University and was financially supported by the Ministry of Science and Higher Education of the Russian Federation as part of the program of the Mathematical Center for Fundamental and Applied Mathematics under the agreement No. 075-15-2022-284 (Sects. 1–4), and by Russian Scientific Foundation (project No. 22-11-00110, Sects. 5–7).

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russian Federation

    V. A. Levin

  2. Department of Applied Mathematics and Cybernetics, Tver State University, Tver, Russian Federation

    K. M. Zingerman

  3. Division of Nuclear Physics and Technologies, National Research Nuclear University MEPhI, Moscow, Russian Federation

    K. M. Zingerman

  4. Institute of Applied Mathematics and Computer Science, Tula State University, Tula, Russian Federation

    A. E. Belkin

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  1. V. A. Levin
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  3. A. E. Belkin
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Levin, V.A., Zingerman, K.M. & Belkin, A.E. Exact solution of one problem of imposition of large deformations in a compound slab with pre-deformed layers of incompressible nonlinear elastic micropolar material. Continuum Mech. Thermodyn. (2024). https://doi.org/10.1007/s00161-024-01294-4

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