On the state of stress in an elastic body with a plane crack (cut)

Abstract

The frictional sliding contact problem between a homogeneous magneto-electro-elastic material (MEEM) and a perfectly conducting rigid circular punch subjected to magneto-electro-mechanical loads is considered in this paper. The problem is formulated under plane strain conditions and the resulting plane magneto-electro-elasticity equations are converted analytically using Fourier transform into three coupled singular integral equations in which the main unknowns are the normal contact stress, the electric displacement and the magnetic induction. The main contribution of this work is the derivation of an analytical closed-form solution for the normal contact stresses, electric displacement and magnetic induction distributions. The primary purpose of this investigation is to study the effect of the friction coefficient, the punch radius, the applied magneto-electro-mechanical loadings, the material composition on the contact surface and in-plane surface stresses, electric displacement and magnetic induction distributions for the case of a circular stamp profile.