The problem of the compression of two electroelastic transversely isotropic half-spaces having different properties with a rigid flat inclusion of arbitrary shape between them is studied. When considering the problem, it is assumed that the surfaces of the half-spaces do not have electrode coatings. The regularities of contact interaction of two piezoelectric transversely isotropic half-spaces (with nonelectroded surfaces) with a flat inclusion of arbitrary shape under compression are determined on the basis of representation of the general solution of the system of static equations of electroelasticity for a transversely isotropic piezoelectric body using harmonic functions. A generalization of Gladwell’s result on the contact interaction of two isotropic elastic half-spaces with a rigid flat inclusion of arbitrary shape under compression is obtained for the case of interaction with an inclusion of two electroelastic transversely isotropic half-spaces. For a disk-shaped inclusion (the partial case of the problem), numerical studies have been carried out, and the effect of the electroelastic properties of half-spaces and the geometric dimensions of the inclusion on the parameters of contact interaction has been 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).
L. Dai, W. Guo, and X. Wang, “Stress concentration at an elliptic hole in transversely isotropic piezoelectric solids,” Int. J. Solids Struct., 43, No. 6, 1818–1831 (2006).
F. Dinzart and H. Sabar, “Electroelastic ellipsoidal inclusion with imperfect interface and its application to piezoelectric composite materials,” Int J. Solids Struct., 136–137, 241–249 (2018).
K. L. Johnson, Contact Mechanics, Cambridge University Press, Cambridge (1985).
J. El Ouafi, L. Azrar, and A. Al**aidi, “Analytical and semi-analytical modeling of effective moduli bounds: application to transversely isotropic piezoelectric materials,” J. Intel. Mat. Syst. Str., 27, No. 12, 1600–1623 (2016).
G. M. L. Gladwell, “On contact problems for a medium with rigid flat inclusions of arbitrary shape,” Int. J. Solids Struct., 32, Nos. 3–4, 383–389 (1995).
V. Govorukha and M. Kamlah, “Analysis of a mode III interface crack in a piezoelectric bimaterial based on the dielectric breakdown model,” Arch. Appl. Mech., 90, No. 5, 1201–1213 (2020).
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).
S. A. Kaloerov and A. A. Samodurov, “Problem of electromagnetoviscoelasticity for multiply connected plates,” Int. Appl. Mech., 51, No. 6, 623–639 (2015).
V. S. Kirilyuk, “The stress state of an elastic orthotropic medium with an ellipsoidal cavity,” Int. Appl. Mech., 41, No. 3, 302–308 (2005).
V. S. Kirilyuk, “Stress state of an elastic orthotropic medium with an elliptic crack under tension and shear,” Int. Appl. Mech., 41, No. 4, 358–366 (2005).
V. S. Kirilyuk, “On the relationship between the solutions of static contact problems of elasticity and electroelasticity for a half-space,” Int. Appl. Mech., 42, No. 11, 1256–1269 (2006).
V. S. Kirilyuk, “Elastic state of a transversely isotropic piezoelectric body with an arbitrarily oriented elliptic crack,” Int. Appl. Mech., 44, No. 2, 150–157 (2008).
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 contact interaction of two piezoelectric half-space, one of which contains a near-surface notch of elliptical cross-section,” Int. Appl. Mech., 58, No. 4, 436–444 (2022).
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. 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).
V. Loboda, A. Sheveleva, O. Komarov, and Y. Lapusta, “An interface crack with mixed electrical conditions at it faces in 1D quasicrystal with piezoelectric effect,” Mech. of Adv. Mat. and Struct., 29, No. 23, 3334–3344 (2021).
G. Martinez-Ayuso, M. I. Friswell, H. H. Khodaparast, J. I. Roscow, and C. R. Bowen, “Electric field distribution in porous piezoelectric materials during polarization,” Acta Mater., 173, 332–341 (2019).
Y. M. Pasternak, H. T. Sulym , and R. M. Pasternak, “Action of concentrated heat sources in a pyroelectric with cracks for constant temperature of their faces,” Mat. Sci., No. 3, 358–365 (2015).
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., 39, No. 2, 132–170 (2003).
A. P. S. Selvadurai, “A unilateral contact problem for a rigid disc inclusion embedded between two dissimilar elastic half-spaces,” Q. J. Mech. Appl. Math., No. 3, 493–509 (1994).
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., 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., 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 and Struct., 94–95, 50–59 (2016).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prykladna Mekhanika, Vol. 60, No. 1, pp. 79–88, January–February 2024.
This study was sponsored by the budget program “Support for Priority Areas of Scientific Research” (KPKVK 6541230).
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
Kyryliuk, V.S., Levchuk, O.I. Contact Interaction of Two Piezoelectric Transversely Isotropic Half-Spaces with Rigid Flat Inclusion of Arbitrary Shape Between Them. Int Appl Mech 60, 70–79 (2024). https://doi.org/10.1007/s10778-024-01263-z
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10778-024-01263-z