Analysis of indentation of a 3m trigonal piezoelectric half-plane under a smooth insulating punch

• Published in: Acta mechanica 2022-12, Vol.233 (12), p.5137-5161
• Main Authors: Kharrazi, Hossein, Khojasteh, Ali, Rahimian, Mohammad, Pak, Ronald Y. S.
• Format: Article
• Language: English
• Subjects: Anisotropy; Asymmetry; Boundary value problems; Classical and Continuum Physics; Control; Dynamical Systems; Electric contacts; Engineering; Engineering Fluid Dynamics; Engineering Thermodynamics; Fourier transforms; Heat and Mass Transfer; Indentation; Indenters; Integral equations; Lithium niobates; Original Paper; Piezoelectricity; Singular integral equations; Solid Mechanics; Theoretical and Applied Mechanics; Vibration; Zinc oxide
• ISSN: 0001-5970; 1619-6937
• DOI: 10.1007/s00707-022-03369-2

This paper analytically investigates the indentation problem of a 3m trigonal piezoelectric half-plane under a frictionless insulating punch for the first time. To this end, the general solutions of the governing equations are determined for an x -cut 3m piezoelectric half-plane using Fourier transform. The mixed value boundary problem of contact is reduced to a new Cauchy-type singular integral equation by a mathematical approach, and the integral equation is solved numerically for the trigonal material. It is also shown that the obtained integral equation can be degenerated to an equation with closed-form solution for 6mm piezoelectric material as a limiting case. To analyze the contact behavior of a 3m piezoelectric material and comparing its response to a 6mm material, two practical piezoelectric materials belonging to 3m and 6mm crystal classes including lithium niobate and zinc oxide were considered. The mechanical and electric responses contour lines were depicted under flat, wedge and cylindrical indenters for the selected materials. The comparison of numerical results revealed that the stress and electric displacement responses of 3m piezoelectric material are asymmetric with respect to the 3-fold axis due to the anisotropy of trigonal material. This asymmetric contact behavior is more pronounced in electric responses than mechanical ones. In addition, the distribution and variation of the considered materials responses were investigated to determine the locations prone to both mechanical and electric failures.