Magnetoelectroelastic response of functionally graded multiferroic coatings under moving Hertzian contact

Abstract

A multilayer approach is developed to solve the moving Hertzian contact problem involving a circular punch and a functionally graded multiferroic coating. The mathematical model constructed consists of arbitrary numbers of multiferroic layers and elastic interlayers, and a half-plane substrate. The formulation is based on wave equations of plane elastodynamics and Maxwell’s equations. The problem is reduced to a singular integral equation by applying Galilean and Fourier transformations. The integral equation is solved numerically through an expansion-collocation technique. A convergence analysis is performed to determine the number of homogeneous multiferroic layers required to simulate the behavior of functionally graded coatings. Presented parametric analyses illustrate the influences of coating type, punch speed, kinetic friction coefficient, and coating thickness upon contact stresses, electric displacement, magnetic induction, and the required contact force. Magnetoelectricity of the system is shown to be significantly coupled with mechanical parameters such as the kinetic friction coefficient and coating thickness.