Abstract
In this paper, the elastic solution to the problem of an isotropic bi-material full-space reinforced by a perfectly bonded thin film across the media interface and subjected to arbitrary asymmetric interfacial loading is addressed. To not include any simplifications, the thin film is first considered as a layer having a finite thickness, and with the aid of Fourier expansion of Muki’s potential functions in Hankel transformed space, the formulation of the problem is obtained for a tri-material full-space. Then, knowing that the flexural stiffness of the thin film is negligible, its thickness and shear modulus are assumed to tend to zero and infinity, respectively, such that its in-plane rigidity remains constant. Utilizing this approach, in addition to the obtained closed-form solution to the considered problem, a set of equivalent interfacial boundary conditions in the transformed domain are introduced for the first time. These equivalent interfacial boundary conditions can be used for simplifying more general problems, such as elastic media reinforced by multi-layered thin films under arbitrary loading. Some limiting cases including axisymmetric loading, inextensible thin film, coated half-space, and unreinforced bi-material are used for verification purposes. In order to show the robustness of the proposed method, some numerical examples are studied. The approximate results of the current approach are in good agreement with the exact solution to the tri-material model. The proposed method significantly facilitates the numerical calculations, for instance, the required run-time decreases by two orders of magnitude in comparison to that of the exact tri-material solution.
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