Constructing potentials to evaluate magneto-electro-elastic materials in contact with periodically rough surface

The purpose of the present work is to construct potentials to evaluate magneto-electro-elastic materials in contact with periodically rigid surface. General solutions for magneto-electro-elastic governing equations are presented for fives cases of the eigenvalue distributions including distinctive roots case and repeated roots case. Then, harmonic functions for these fives cases are constructed, which produce uniform compression of magnitude p in the z-direction at infinity. For the stated periodic contact problem of magneto-electro-elastic materials, the stresses, electric displacements and magnetic inductions are finally expressed through the form of infinite series. It is found that the largest surface contact stress always occurs at the center of the contact region. A stress concentrator factor is introduced. Parametric studies on the numerical tests reveal that both the electrical displacement and the magnetic induction obtain their maximum magnitude at the central line of the contact area, which may imply that the electric field and the magnetic field have almost the same role in magneto-electro-elastic materials.