Asymptotic analysis of a multimaterial with a thin piezoelectric interphase

We study the electromechanical behavior of a multimaterial constituted by a linear piezoelectric transversely isotropic plate-like body with high rigidity embedded between two generic three-dimensional piezoelectric bodies by means of the asymptotic expansion method. After defining a small real dimensionless parameter ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon $$\end{document}, which will tend to zero, we characterize the limit model and the associated limit problem. We give also a mathematical justification of the model by means of a functional convergence argument. Moreover, we identify the non classical electromechanical transmission conditions between the two three-dimensional bodies.