Keele Research Repository

The 3D problem in linear elasticity for a layer lying on a half-space is subject to a two-parametric asymptotic treatment using the small parameters corresponding to the relative thickness of the layer and stiffness of the foundation. General scaling for the displacements and stresses is inspired by the analysis of the exact solution of the toy plane strain problem for a vertical sinusoidal load. The direct asymptotic procedure widely used in mechanics of thin structures is adapted for the layer. It is demonstrated that the Kirchhoff theory for thin plates is only applicable for sufficiently high contrast of the coating and half-space stiffnesses. In the scenario, in which the Kirchhoff theory fails, alternative approximate formulations are introduced, reducing the original problem for a coated solid to problems for a homogeneous half-space with Neumann, mixed or effective boundary conditions along its surface.