Explicit homogenized equations of the piezoelectricity theory in a two-dimensional domain with a very rough interface of comb-type

Abstract

The main purpose of this paper is to derive explicit homogenized equations of the linear piezoelectricity in two-dimensional domains separated by a very rough interface of comb-type. In order to do that, first, the basic equations of the theory of piezoelectricity are written down in matrix form. Then, following the techniques presented recently by these authors, the explicit homogenized equation in matrix form and the associate continuity condition, for generally anisotropic piezoelectric materials, are derived. They are then written down in component form for a special case when the solid$ are made of tetragonal crystals of class 42m. Since the obtained equations are totally explicit, they are significant in use.