Theory of sliding contact for multiferroic materials indented by a rigid punch

The present article develops a general theory for the sliding contact of multiferroic materials under a rigid punch. Coulomb friction law is modeled inside the contact region. Based on the appropriate fundamental solutions for each case of eigenvalue distributions, Cauchy type singular integral equations of the second kind are obtained, which are solved exactly by using the excellent properties of Jacobi Polynomials. Closed-form expressions of physical quantities on the surface in terms of elementary functions are given for a punch with a flat or a parabolic profile. Formulae to determine the unknown contact length are given. Numerical analyses are detailed to show the effects of the friction coefficient on various surface stresses, electric displacement and magnetic induction. The mechanism of the surface damage for multiferroic materials is revealed. The role that the electric field and magnetic field play in decoupled case is discussed. The present investigation could provide a scientific basis for the theoretical and experimental test of contact behaviors of multiferroic materials.