Effective Elastic Moduli of Thin Films with Rough Surfaces: A Modeling Approach

The governing system of equations for the model of a locally inhomogeneous elastic body is based on constitutive equations generalized to account for local inhomogeneity of the binding energy and includes an equation for the mass density in the form of an inhomogeneous Helmholtz equation. This paper shows that, by selecting appropriate mass sources (the inhomogeneous term in the mass density equation), it is possible to obtain a mass density distribution in the near-surface region that reflects the characteristics of the Abbott–Firestone curve, which is widely used in engineering practice to describe surface roughness. Using a flat surface as an example, the influence of the model parameters on the core, peak, and valley zones of the material ratio curve is investigated. When modeling the influence of the surface roughness parameters of a real body on the effective elastic moduli of thin films, it is assumed that the local Young’s modulus and Poisson’s ratio are functions of the mass density. The solution to the problem for a stretched layer is expressed in quadratures, and its analysis is performed using numerical methods. In particular, it is shown that the characteristic length scales of the size effects of the effective elastic moduli depend on the structural heterogeneity of the material and on the sizes of the core, peak, and valley zones of the roughness profile.