Response of a thin coating of a porous elastic material whose generalised Young’s modulus depends on the density

Abstract

Mechanics of a thin elastic coating is analysed using nonlinear constitutive relations based on the concept of a density-dependent Young’s modulus. In contrast to previous considerations on the subject, the proposed framework does not assume weak nonlinearity. Two-term asymptotic expansions are derived for four setups of boundary conditions along the upper face of the coating; in doing so, the lower face is supposed to be clamped. Explicit approximate formulae obtained in the paper have the potential to be implemented in diverse industrial applications related to thin porous coatings.