 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| << 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 2020 | Revised |
13 April 2020 | Accepted |
23 May 2020 |
| Link to Fulltext |
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