Based on a rigorous mathematical statement that takes into account the coupling of the mechanical and electric fields, the problem of the compression of two electroelastic transversely isotropic half-spaces is solved. One of the half-spaces contains an inclined near-surface notch of elliptical cross-section. The analytical solution of the problem is found by representing the solution of the static equations of electroelasticity in terms of harmonic functions and by reducing the boundary-value problem to an integro-differential equation with an unknown domain of integration. As a partial case, the parameters of the contact of two elastic transversely isotropic half-spaces (if one of them has a notch of elliptical cross-section), as well as the parameters of the contact interaction of two electroelastic half-spaces, one of which contains a an axisymmetric notch, are obtained from the analytical expressions. Numerical results are obtained. The effect of the electroelastic properties of the half-spaces, the geometrical parameters of the notch, and loading on the contact interaction as well as the closure of the gap between the bodies is studied.
Similar content being viewed by others
References
V. T. Grinchenko, A. F. Ulitko, and N. A. Shul’ga, Electroelasticity, Vol. 5 of the five-volume series Mechanics of Coupled Fields in Structural Members [in Russian], Naukova Dumka, Kyiv (1989).
H. S. Kit and R. M. Martyniak, “Spatial contact problems for an elastic half-space and a rigid foundation with surface notches,” Mat. Met. Fiz.-Mekh. Polya, 42, No. 6, 7–11 (1999).
B. E. Monastyrskyi, “Axisymmetric contact problem for half-spaces with geometric surface perturbation,” Fiz.-Khim. Mekh. Mat., No. 6, 22–26 (1999).
M. V. Khai, Two-Dimensional Integral Equations of the Newtonian Potential and Their Applications [in Russian], Naukova Dumka, Kyiv (1993).
G. M. L. Gladwell, “On inclusions at a bi-material elastic interface,” J. Elast., 54, No. 1, 27–41 (1999).
V. Govorukha, M. Kamlah, and A. Sheveleva, “Influence of concentrated loading on opening of an interface crack between piezoelectric materials in a compressive field,” Acta Mech., 226, No. 7, 2379–2391 (2015).
V. Govorukha, A. Sheveleva, and M. Kamlah, “A crack along a part of an interface electrode in a piezoelectric bimaterial under anti-plane mechanical and in-plane electric loadings,” Acta Mech., 230, No. 6, 1999–2012 (2019).
S. A. Kaloerov, “Determining the intensity factors for stresses, electric-flux density, and electric-field strength in multiply connected electroelastic anisotropic media,” Int. Appl. Mech., 43, No. 6, 631–637 (2007).
V. S. Kirilyuk, “Thermostressed state of a piezoelectric body with a plane crack under symmetric thermal load,” Int. Appl. Mech., 44, No. 3, 320–330 (2008).
V. S. Kirilyuk, “Stress state of a piezoceramic body with a plane crack opened by a rigid inclusion,” Int. Appl. Mech., 44, No. 7, 757–768 (2008).
V. S. Kirilyuk and O. I. Levchuk, “Stress state of an orthotropic piezoelectric body with a triaxial ellipsoidal inclusion subject to tension,” Int. Appl. Mech., 55, No. 3, 305–310 (2019).
A. Kotousov, L. B. Neto, and A. Khanna, “On a rigid inclusion pressed between two elastic half spaces,” Mech. of Mat., 68, No. 1, 38–44 (2014).
V. S. Kyryliuk and O. I. Levchuk, “Stress state of an orthotropic electroelastic medium with an arbitrarily oriented elliptic crack under uniaxial tension,” Int. Appl. Mech., 57, No. 1, 53–62 (2021).
V. V. Loboda, A. G. Kryvoruchko, and A. Y. Sheveleva, “Electrically plane and mechanically antiplane problem for an inclusion with stepwise rigidity between piezoelectric materials,” Adv. Struct. Mat., No. 94, 463–481 (2019).
Yu. N. Podil’chuk, “Representation of the general solution of statics equations of the electroelasticity of a transversally isotropic piezoceramic body in terms of harmonic functions,” Int. Appl. Mech., 34, No. 7, 623–628 (1998).
Yu. N. Podil’chuk, “Exact analytical solutions of static electroelastic and thermoelectroelastic problems for a transversely isotropic body in curvilinear coordinate systems,” Int. Appl. Mech., 394, No. 2, 132–170 (2003).
Y. J. Wang, C. F. Gao, and H. P. Song, “The anti-plane solution for the edge cracks originating from an arbitrary hole in a piezoelectric material,” Mech. Res. Com., No. 65, 17–23 (2015).
Z. K. Wang and B. L. Zheng, “The general solution of three-dimension problems in piezoelectric media,” Int. J. Solids Struct., 32, No. 1, 105–115 (1995).
M. H. Zhao, Y. Li, Y. Yan, and C. Y. Fan, “Singularity analysis of planar cracks in three-dimensional piezoelectric semiconductors via extended displacement discontinuity boundary integral equation method,” Eng. Anal. Bound. Elem., No. 67, 115–125 (2016).
M. H. Zhao, Y. B. Pan, C. Y. Fan, and G. T. Xu, “Extended displacement discontinuity method for analysis of cracks in 2D piezoelectric semiconductors,” Int. J. Solids Struct., No. 94–95, 50–59 (2016).
Author information
Authors and Affiliations
Corresponding author
Additional information
*This study was sponsored by the budget program “Support for Priority Areas of Scientific Research” (KPKVK 6541230).
Translated from Prykladna Mekhanika, Vol. 58, No. 4, pp. 75–84, July–August 2022.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Kirilyuk, V.S., Levchuk, O.I. Contact Interaction of Two Piezoelectric Half-Spaces, One of Which Contains a Near-Surface Notch of Elliptical Cross-Section*. Int Appl Mech 58, 436–444 (2022). https://doi.org/10.1007/s10778-022-01168-9
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10778-022-01168-9