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Hertzian and adhesive plane models of contact of two inhomogeneous elastic bodies

Part of: Special kinds of problems

Published online by Cambridge University Press:  25 July 2022

Y. A. ANTIPOV Open the ORCID record for Y. A. ANTIPOV [Opens in a new window]  and
S. M. MKHITARYAN
Y. A. ANTIPOV
Affiliation:
Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA email: yantipov@lsu.edu
S. M. MKHITARYAN
Affiliation:
Department of Mechanics of Elastic and Viscoelastic Bodies, National Academy of Sciences of Armenia, Yerevan 0019, Armenia email: smkhitaryan@mechins.sci.am Department of Mathematics and Physics, National University of Architecture and Construction, Yerevan 0009, Armenia
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Abstract

Previous study of contact of power-law graded materials concerned the contact of a rigid body (punch) with an elastic inhomogeneous foundation whose inhomogeneity is characterised by the Young modulus varying with depth as a power function. This paper models Hertzian and adhesive contact of two elastic inhomogeneous power-law graded bodies with different exponents. The problem is governed by an integral equation with two different power kernels. A nonstandard method of Gegenbauer orthogonal polynomials for its solution is proposed. It leads to an infinite system of linear algebraic equations of a special structure. The integral representations of the system coefficients are evaluated, and the properties of the system are studied. It is shown that if the exponents coincide, the infinite system admits a simple exact solution that corresponds to the case when the Young moduli are different but the exponents are the same. Formulas for the length of the contact zone, the pressure distribution and the surface normal displacements of the contacting bodies are obtained in the form convenient for computations. Effects of the mismatch in the Young moduli exponents are studied. A comparative analysis of the Hertzian and adhesive contact models clarifies the effects of the surface energy density on the contact pressure, the contact zone size and the profile of the contacting bodies outside the contact area.

Keywords

Integral equation with two power-law kernelsgegenbauer polynomialshertzian and adhezive plane contactpower-law graded materials

MSC classification

Primary: 74M15: Contact
Secondary: 45H05: Miscellaneous special kernels
Type
Papers
Information
European Journal of Applied Mathematics , Volume 34 , Issue 4 , August 2023 , pp. 667 - 700
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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