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Higher-Order Modules in the Equations of Dynamics of a Prestressed Elastic Solid

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Abstract

In terms of the reference configuration, the linearization of the equations of nonlinear mechanics of an initially isotropic elastic solid (IIES) is carried out in the vicinity of a. certain prestressed equilibrium state. In this case, we used a. special representation of the elastic potential in terms of algebraic invariants of the Cauchy-Green strain tensor containing moduli of higher orders. Linearized defining relations and equations of motion are constructed that take into account the nonlinear effect of the initial deformations on the properties of the IIES.

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Acknowledgments

This work was supported by the Russian Science Foundation (Grant 14-19-01676) and the Ministry of Science and Higher Education of the Russian Federation (project 01201354242).

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Authors and Affiliations

  1. South Scientific Centre of the Russian Academy of Sciences, ul. Chekhova 41, Rostov-on-Don, 344006, Russia

    T. I. Belyankova, V. V. Kalinchuk & D. N. Sheidakov

  2. South Federal University, pr. Stachki 200/1, Rostov-on-Don, 344090, Russia

    T. I. Belyankova & V. V. Kalinchuk

Authors
  1. T. I. Belyankova
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  2. V. V. Kalinchuk
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  3. D. N. Sheidakov
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Corresponding author

Correspondence to V. V. Kalinchuk.

Additional information

Russian Text © Author(s), 2019, published in Izvestiya Akademii Nauk, Mekhanika Tverdogo Tela, 2019, No. 3, pp. 3-15.

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Belyankova, T.I., Kalinchuk, V.V. & Sheidakov, D.N. Higher-Order Modules in the Equations of Dynamics of a Prestressed Elastic Solid. Mech. Solids 54, 491–501 (2019). https://doi.org/10.3103/S0025654419040010

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  • DOI: https://doi.org/10.3103/S0025654419040010

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