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IssuesArchive of Issues2020-6pp.857-864

Archive of Issues

Total articles in the database: 4918
In Russian (. . ): 2350
In English (Mech. Solids): 2568

<< Previous article | Volume 55, Issue 6 / 2020 | Next article >>
Kolosova E.M. and Chebakov M.I., "Analytical Solution of Axisymmetric Contact Problem for a Poroelastic Layer," Mech. Solids. 55 (6), 857-864 (2020)
Year 2020 Volume 55 Number 6 Pages 857-864
DOI 10.3103/S0025654420050118
Title Analytical Solution of Axisymmetric Contact Problem for a Poroelastic Layer
Author(s) Kolosova E.M. (Institute for Mathematics, Mechanics, and Computer Science named after I.I. Vorovich, Southern Federal University, Rostov-on-Don, 344058 Russia, a_lena_ch@mail.ru)
Chebakov M.I. (Institute for Mathematics, Mechanics, and Computer Science named after I.I. Vorovich, Southern Federal University, Rostov-on-Don, 344058 Russia, michebakov@yandex.ru)
Abstract In this article, we analyze axisymmetric contact problems on the interaction of a rigid stamp with a poroelastic layer using the equations of the Cowin-Nunziato theory of poroelastic bodies. It is assumed that the stamp base has a flat or parabolic shape and there is no friction in the contact zone. The posed problems are reduced to integral equations, the main kernel part of which is the delta function, by means of special function via which the contact stresses are expressed. Using a special approximation of the integral equation kernel transform, its asymptotic solution is constructed for the case of relatively large layer thicknesses. This approach to solving integral equations of contact problems was proposed by I.I. Vorovich and was further developed by his students. Expressions for the contact stresses and the contact area in the case of a parabolic stamp are obtained in a simple analytical form. Also, a relation between the force acting on the stamp and its displacement that is one of the main characteristics in determining the mechanical parameters of a material by the indentation method is found in terms of elementary expressions. A comparative analysis of the investigated quantities for various values of the parameters of porosity and layer thickness is carried out.
Keywords contact problem, porous materials, poroelasticity, Cowin-Nunziato model, axisymmetric problem, layer, asymptotic method, indentation
Received 30 March 2020Revised 13 April 2020Accepted 23 May 2020
Link to Fulltext https://link.springer.com/article/10.3103/S0025654420050118
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