# Mathematical modeling of contact interaction of two electroelastic half-spaces (without electrode coating of surfaces) in the presence of a hard disk-like inclusion between them and pressure in the area of separation

## DOI:

https://doi.org/10.20535/SRIT.2308-8893.2021.3.10## Keywords:

mathematical model, piezoelectric material, electroelastic half-space, hard disk-shaped inclusions, pressure in the delamination region, contact parameters## Abstract

Based on the use of a rigorous mathematical model that takes into account the connectivity of force and electric fields in electroelastic bodies, the contact interaction of two piezoelectric transversely isotropic half-spaces with different properties under compression (in the presence of a hard disk-shaped inclusion between them and pressure in the material separation region) was studied. The solution to the problem is obtained by representing the general solution of the static equations of the electroelasticity for a transversely isotropic body in terms of harmonic functions, followed by the construction of the boundary value problem of the electroelasticity to the consideration of the integral equation and the expansion of the desired function in a small parameter. As a special case from the constructed analytical expressions, the main parameters of the contact for two elastic transversely isotropic and isotropic half-spaces (with the inclusion between them and pressure in the separation region) are implied. Numerical results were obtained. The influence was studied of the electroelastic properties of half-spaces, the geometric dimensions of the inclusion, and loads on the parameters of the contact interaction of electroelastic bodies.

## References

V.S. Kirilyuk, Levchuk O.I., O.V. Gavrilenko, and M.B. Viter, “Simulation of contact interaction of a heated flat rigid elliptical stamp with a transversely isotropic half-space”, System research and information technologies, no. 3, pp. 138 –148, 2020. doi: 10.20535/SRIT.2308-8893.2020.3.10

V.S. Kirilyuk and O.I. Levchuk, “Simulation of the contact interaction of two transversely isotropic spring half-spaces for the presence of a hard disk-like inclusion between them and pressure on the stratification area”, System research and information technologies, no. 1, pp. 107–119, 2020. doi: 10.20535/SRIT.2308-8893.2020.1.10.

Yu.N. Podil’chuk, Boundary value problems of statics of elastic bodies. Kyiv: Nauk. dumka, 1984, 304 p.

Yu.N. Podil’chuk, “Exact analytical solutions of spatial boundary value problems of statics of a transversely isotropic body of canonical form (Review)”, Int. Appl. Mech., 33, no. 10, pp. 3–30, 1997.

Y.S. Chai and I.I. Argatov, “Local tangential contact of elastically similar, transversely isotropic elastic bodies”, Meccanica, 53, no. 11–12, pp. 3137–3143, 2018.

W.Q. Chen, J. Zhu, and X.Y. Li, “General solutions for elasticity of transversely isotropic materials with thermal and other effects: A review”, J. Thermal Stresses, 42, no. 1, pp. 90–106, 2019.

V.I. Fabrikant, “Contact problem for an arbitrarily oriented transversely isotropic half-space”, Acta Mechanca, 228, no. 4, pp. 1541–1560, 2017.

V.T. Grinchenko, A.F. Ulitko, and N.A. Shulga, Electroelasticity. Kyiv: Nauk. dumka, 1989, 279 p.

Yu.N. Podil’chuk, “Representation of the general solution of the equations of statics of electroelasticity of a transversely isotropic piezoceramic body in terms of harmonic functions”, Int. Appl. Mech., 34, no. 7, pp. 20–26, 1998.

Yu.N. Podil’chuk, “Exact analytical solutions of static problems of electroelasticity and thermoelectroelasticity for a transversely isotropic body in curvilinear coordinates”, Int. Appl. Mech., 39, no. 2, pp. 14–54, 2003.

M.O. Shulga and V.L. Karlash, Resonant electromechanical oscillations of piezoelectric plates. Kyiv: Nauk. dumka, 2008, 270 p.

V.S. Kirilyuk and O.I. Levchuk, “Stress State of an Orthotropic Piezoelectric Body with a Triaxial Ellipsoidal Inclusion Subject to Tension Crack”, Int. Appl. Mech., 55, no. 3, pp. 305–310, 2019.

V.S. Kirilyuk and O.I. Levchuk, “Stress State of an Orthotropic Piezoelectric Material with an Elliptic Crack”, Int. Appl. Mech., 53, no. 3, pp. 305–312, 2017.

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”, International Journal of Solids and Structures, vol. 94–95, pp. 50–59, 2016.

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, pp. 493–509, 1994.

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, pp. 1256–1269, 2006.