Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
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IssuesArchive of Issues2019-4pp.491-501

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T.I. Belyankova, V.V. Kalinchuk, and D.N. Sheidakov, "Higher-Order Modules in the Equations of Dynamics of a Prestressed Elastic Solid," Mech. Solids. 54 (4), 491-501 (2019)
Year 2019 Volume 54 Number 4 Pages 491-501
DOI 10.3103/S0025654419040010
Title Higher-Order Modules in the Equations of Dynamics of a Prestressed Elastic Solid
Author(s) T.I. Belyankova (South Scienti fic Centre of the Russian Academy of Sciences, ul. Chekhova 41, Rostov-on-Don, 344006 Russia; South Federal University, pr. Stachki 200/1, Rostov-on-Don, 344090 Russia)
V.V. Kalinchuk (South Scienti fic Centre of the Russian Academy of Sciences, ul. Chekhova 41, Rostov-on-Don, 344006 Russia; South Federal University, pr. Stachki 200/1, Rostov-on-Don, 344090 Russia, kalin@ssc-ras.ru)
D.N. Sheidakov (South Scienti fic Centre of the Russian Academy of Sciences, ul. Chekhova 41, Rostov-on-Don, 344006 Russia)
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.
Keywords higher-order modules, prestressed medium, initial strain, algebraic invariants of the Cauchy-Green strain tensor
Received 28 August 2017
Link to Fulltext https://link.springer.com/article/10.3103/S0025654419040010
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