Circular surface loading on a layered multiferroic half space

By introducing the cylindrical system of vector functions and the corresponding propagating matrix, we present a semi-analytical solution for a layered multiferroic half space under a uniform vertical circular load on its surface. A two-layered system made of BaTiO₃ and CoFe ₂O₄ is analyzed by the proposed method. The coupling feature among the elastic, electric, and magnetic fields and the interplay between the adjacent layers are investigated. In particular, we find that the interfacial elastic, electric, and magnetic fields are very sensitive to the thickness of the surface layer. Consequently, a critical thickness is found for each field quantity when it reaches its extreme value for varying thickness of the surface layer. This striking feature could be very useful as a theoretical reference for the optimal design of surface coatings.