Surface effect on a nano-elliptical hole or nano-crack in magnetoelectroelastic materials under antiplane shear

Based on the Gurtin-Murdoch surface/interface model, an antiplane shear problem of a magnetically and electrically impermeable nano-elliptical hole in magnetoelectroelastic (MEE) materials with surface effect is presented subjected to far-field anti-plane mechanical and in-plane electrical and magnetic loadings. By using the complex function method and conformal mapping technique, exact closed-form solutions of the stress, electric displacement and magnetic induction intensity factors near the crack tip are obtained when the nano-elliptical hole is reduced to a nano-crack. Numerical examples are provided to show the effects of size of nano-crack on the field intensity factors near the crack tip induced by mechanical, electrical and magnetic loadings for the piezoelectric (PE), piezomagnetic (PM) and MEE materials with surface effect. The interaction between the stress field, electric field and magnetic field around the nano-hole is analyzed. The results show that the obtained solution is close to the classical elasticity solution with increasing size of the nano-crack.