The problem of contact interaction without friction between an elastic cylindrical ring punch and an elastic half-space with initial (residual) stresses under pressure in the case of unequal roots of the characteristic equation is considered. The research is presented in general form for the theory of large initial (final) strains and two variants of the theory of small initial strains within the framework of the linearized theory of elasticity for an arbitrary elastic potential. Numerical analysis is presented in the form of graphs for the Treloar potential.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. M. Aleksandrov and N. Kh. Arutyunyan, “Contact problems for prestressed deformable bodies,” Prikl. Mech., 20, No. 3, 9–16 (1984).
H. Bateman and A. Erdelyi, Higher Transcendental Functions, McGraw-Hill, New York (1953).
S. V. Bosakov, “Two contact problems on the indentation of a ring punch into an elastic half-space,” Nauka i Tekhnika, 17, No. 6, 458–464 (2018).
I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals of Sums, Series, and Products [in Russian], Fizmatlit, Moscow (1963).
D. V. Grilitskii and Ya. M. Kizima, Axisymmetric Contact Problems of the Theory of Elasticity and Thermoelasticity [in Russian], Vyshcha Shkola, Lviv, (1981).
A. N. Guz, “On contact problems for elastic compressible bodies with initial stresses,” Dokl. AN USSR. Ser. A, No. 6, 48–52 (1980).
A. Guz, S. Babich, and Yu. Glukhov, Mixed Problems for a Prestressed Elastic Foundation [in Russian], Lambert Academic Publishing (2015).
A. N. Guz, S. Yu. Babich, and Yu. P. Glukhov, Statics and Dynamics of Elastic Foundations with Initial (Residual) Stresses [in Russian], Press-line, Kremenchug (2007).
O. M. Guz, S. Yu. Babich, and V. B. Rudnitskii, Contact Interaction of Prestressed Bodies [in Ukrainian], Vyshcha Shkola, Kyiv (1995).
A. N. Guz and V. B. Rudnitskii, Basic Theory of Contact of Elastic Bodies with Initial (Residual) Stresses [in Russian], Mel’nik, Khmelnytskyi (2006).
L. M. Filippova, “Spatial contact problem for a prestressed elastic body,” Prikl. Mat. Mech., 42, No. 6, 1080–1084 (1978).
S. Yu. Babich and N. N. Dikhtyaruk, “Load transfer from an infinite inhomogeneous stringer to a prestressed elastic strip clamped at one edge,” Int. Appl. Mech., 56, No. 6, 708–716 (2020).
S. Yu. Babich, N. N. Dikhtyaruk, and S. V. Degtyar, “Contact problem for two identical strips reinforced by periodically arranged fasteners with initial stresses,” Int. Appl. Mech., 55, No. 6, 629–635 (2019).
R. S. Dhaliwal, B. M. Singh, and J. G. Rokne, “Axisymmetric contact and crack problems for an initially stressed Neo-Hooken elastic layer,” Int. J. Eng. Sci., 18, No. 1, 169–179 (1980).
A. N. Guz, “Nonclassical problems of fracture/failure mechanics: on the occasion of the 50th anniversary of the research (review) III,” Int. Appl. Mech., 55, No. 4, 343–415 (2019).
A. N. Guz, S. Yu. Babich, and V. B. Rudnitsky, “Contact problems for elastic bodies with initial (residual) stresses (Part I),” Problems of Tribology, No. 2, 34–51 (2002).
A. N. Guz, S. Yu. Babich, and V. B. Rudnitskiy, “Contact problems for elastic bodies with initial stresses: Focus on Ukrainian research,” Appl. Mech. Rev., 51, No. 5, 343–371 (1998).
A. N. Guz and A. M. Bagno, “Influence of prestresses on normal waves in an elastic compressible half-space interacting with a layer of a compressible ideal fluid,” Int. Appl. Mech., 55, No. 6, 585–595 (2019).
A. N. Guz and A. M. Bagno, “Influence of prestresses on quasi-lamb modes in hydroelastic waveguides,” Int. Appl. Mech., 56, No. 1, 1–12 (2020).
M. Kurashige, “Circular crack problem for initially stressed neo-Hookean solid,” ZAMM, 49, No. 8, 671–678 (1969).
H. M. MacDonald, “Note on the evaluation of the certain integral containing bessel’s functions,” Proc. London Math. Soc., S2–7, No. 1, 142–149 (1909).
N. P. Semenyuk and N. B. Zhukova, “Stability of a sandwich cylindrical shell with core subject to external pressure and pressure in the inner cylinder,” Int. Appl. Mech., 56, No. 1, 40–53 (2020).
N. A. Yaretskaya, “Three-dimensional contact problem for an elastic layer and a cylindrical punch with prestresses,” Int. Appl. Mech., 50, No. 4, 378–388 (2014).
N. A. Yaretskaya, “Contact problem for the rigid ring stamp and the half-space with initial (residual) stresses,” Int. Appl. Mech., 54, No. 5, 539–543 (2018).
Author information
Authors and Affiliations
Corresponding authors
Additional information
*This study was sponsored by the budget program “Support for Priority Areas of Scientific Research” (KPKVK 6541230).
Translated from Prikladnaya Mekhanika, Vol. 57, No. 3, pp. 52–61, May–June 2021.
Rights and permissions
About this article
Cite this article
Babych, S.Y., Yarets’ka, N.O. Contact Problem for an Elastic Ring Punch and a Half-Space with Initial (Residual) Stresses*. Int Appl Mech 57, 297–305 (2021). https://doi.org/10.1007/s10778-021-01081-7
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10778-021-01081-7