The contact problem for FGPM coatings considering the surface effect

Ma, Zhan-Zhou; Liu, Tie-Jun

doi:10.2140/jomms.2025.20.553

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The contact problem for FGPM coatings considering the surface effect

Zhan-Zhou Ma and Tie-Jun Liu

Vol. 20 (2025), No. 5, 553–585

DOI: 10.2140/jomms.2025.20.553

Abstract

We investigate the contact problem of a functionally graded piezoelectric material (FGPM) under a cylindrical indenter by considering the surface effect. The electromechanical properties of the FGPM coating vary as an exponential function along the thickness direction. The Fourier integral transform method is employed to obtain the fundamental solution of the two-dimensional contact problem of FGPM considering the surface effect. Numerical results are obtained to analyze the effects of the material gradient and surface effect on the distributions of normal contact stress, in-plane stress, and in-plane electric displacement. The results show that surface effect play a crucial role in the contact problem of the FGPM. The contact behavior of the FGPM at micro/nano-scales can be improved by adjusting the gradient index.

Keywords

surface effect, functionally graded piezoelectric material (FGPM), contact mechanics, Fourier integral transform

Mathematical Subject Classification

Primary: 74F99

Milestones

Received: 24 April 2025

Revised: 29 September 2025

Accepted: 9 November 2025

Published: 29 November 2025

Authors

Zhan-Zhou Ma
Department of Mechanics Inner Mongolia University of Technology Hohhot, 010051 China

Tie-Jun Liu
Department of Mechanics Inner Mongolia University of Technology Hohhot, 010051 China

Vol. 20, No. 5, 2025