Development of governing partial differential equations of reinforcing thin films

Abstract

In this paper, a novel interface model for elastic isotropic thin films perfectly bonded to the surrounding elastic media is introduced. Considering an average stress and displacement through the thin film thickness, the shear stress discontinuity across the interface is expressed in terms of spatial and time derivatives of displacement components. The derived interfacial equations are presented in a general form. As such, they are applicable to asymmetric elastodynamic problems of anisotropic solids with thin film interfaces. Employing the introduced interface model and Hankel transform technique, static Green's functions of an elastic isotropic half-space reinforced by a buried thin film are obtained. Results of some special cases, including axisymmetric loading, inextensible membrane, unreinforced half-space, and surface-coated half-space, are also presented. The robustness and effectiveness of the proposed interface model are shown by two solved numerical examples, and some elastic responses are plotted to show the impact of thin film stiffness. According to the numerical results, modeling elastic thin films as inextensible membranes can significantly alter the elastic responses.