Elastic responses of bi-material media reinforced by interfacial thin films under asymmetric loading

Analysis of a Thin Membrane Coated Half-Space under Arbitrary Buried Loads

“…To impose perfect adhering assumption between the thin film and its lower half-space, and also other boundary conditions, Eqs. ( 13) and ( 14) should be developed in Hankel transformed domain concerning the same radial component of cylindrical coordinate, r. The th m -order Hankel transform of the displacement field leads to the following relations, [52]:  leads to inexplicable results whereas the procedure itself is exhausting. Here, a simple yet useful method for surface conditions is proposed by Ahmadi et al [52] in a way that by removal of thin film, its impact is remained by tending F t to zero and simultaneously tending…”

“…According to the new introduced approach, by utilizing Eqs. ( 17) and ( 18) the shear stresses transmission conditions at the same depth at which the thin film is located, here at the surface of half-space 0 z  , links to in-plane deformations thoughtfully whilst normal stresses transmit without any disturbance across thin film (for more demonstrations, please refer to [52]):…”

“…Based on Muki's potential functions, the governing equilibrium equations are rewritten in harmonic and biharmonic equations. With the aid of Fourier expansion and Hankel transform of potential functions and by approaching the thickness of the thin film to zero whereas its shear modulus goes to infinity simultaneously, in section 2, proposed interfacial conditions by Ahmadi et al [52] are employed and the problem is solved completely. The proposed equivalent surface boundary conditions can be utilized in wide range of research areas such as contact mechanics, different mixed boundary value problems and so on, both in symmetric and asymmetric cases in the context of a half-space.…”