The problem of the contact interaction of a rigid cylindrical ring punch and half-space with initial (residual) stresses is considered disregarding the friction forces in the case of unequal roots of the characteristic equation. The study is performed in common form for the theory of large (finite) initial deformations and two variants of the theory of small initial deformations within the framework of the linearized theory of elasticity for arbitrary elastic potential. The numerical results are presented in the form of graphs for Treloar’s potential.
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References
V. M. Aleksandrov and N. Kh. Arutyunyan, “Contact problems for prestressed deformable bodies,” Prikl. Mekh., 20, No. 3, 9–16 (1984).
I. Yu. Gabruseva and B. G. Shelestovskiy, “Contact interaction of a ring punch with a prestressed isotropic sphere,” Mat. Metod. Fiz.-Mekh. Polya, 54, No. 3, 138–146 (2011).
D. V. Frilitskii and Ya. M. Kizyma, Axisymmetric Contact Problems of Theory of Elasticity and Thermoelesticity [in Russian], Vyshcha Shkola, Lvov (1981).
A. N. Guz, S. Yu. Babych, and Yu. P. Glukhov, Mixed Problems for Elastic Foundation with Initial Stresses [in Russian], LAP LAMBERT Academic Publishing, Saarbrücken (2015).
A. N. Guz, S. Yu. Babych, and Yu. P. Glukhov, Staics and Dynamics of Elastic Foundations with Initial (Residual) Stresses [in Russian], Press-Line, Kremenchuk (2007).
A. N. Guz, S. Yu. Babich, and V. B. Rudnitskii, Contact Interaction of Elastic Bodies with Initial Stresses Tutorial [in Ukrainian], Vyshcha Shkola, Kiev (1995).
A. N. Guz and V. B. Rudnitskii, Fundamentals of the Theory of Contact Interaction of Elastic Bosied with Initial (Residual) Stresses [in Russian], PP Melnik, Khmelnitskii (2006).
L. A. Galin (ed.), Development of Contact Problems in USSR [in Russian], Nauka, Moscow (1976).
L. Gorelik and D. Mordehai, “Atomically informed continuum models for the elastic contact properties of hollow and coated rigid cylinders at the nanoscale,” J. Appl. Mech., 84, No. 3, 031009 (2017).
J. W. Hutchinson and J M. T. Thompson, “Nonlinear buckling interaction for spherical shells subject to pressure and probing forces,” J. Appl. Mech., 84, No. 6, 061001 (2017).
J. Long, Y. Ding, W. Yuan, W. Chen, and G. Wang, “General relations of indentations on solids with surface tension,” J. Appl. Mech., 84, No. 5, 051007 (2017).
M. O. Petinrin, A. A. Oyedele, and O. O. Ajide, “Numerical analysis of thermo-elastic contact problem of disc brakes for vehicle on gradient surfaces,” World J. Eng. Technol., 4, No. 1, 51–58 (2016).
V. B. Rudnitskii and N. N. Dikhtyaruk, “Interaction between an infinite stringer and two identical prestressed strips: contact problem,” Int. Appl. Mech., 53, No. 2, 149–155 (2017).
T. S. Vasu and T. K. Bhandakkar, “A study of the contact of an elastic layer–substrate system indented by a long rigid cylinder incorporating surface effects,” J. Appl. Mech., 83, No. 6, 061009 (2016).
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).
P. Zheng, A. H.-D. Cheng, and H. Li, “Dynamic Green’s functions and integral equations for a double-porosity dual-permeability poroelastic material,” J. Appl. Mech., 84, No. 6, 061009 (2017).
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Translated from Prikladnaya Mekhanika, Vol. 54, No. 5, pp. 55–60, September–October, 2018.
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Yaretskaya, N.F. Contact Problem for the Rigid Ring Stamp and the Half-Space with Initial (Residual) Stresses. Int Appl Mech 54, 539–543 (2018). https://doi.org/10.1007/s10778-018-0906-y
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DOI: https://doi.org/10.1007/s10778-018-0906-y