Modeling the effect of surface roughness on mechanical fields in an elastic solid bounded by nominally flat surfaces

In this work, the basic relationships of the local gradient approach in thermomechanics are used to build a model that accounts for the roughness of an actual body surface. This is demonstrated using examples of an elastic body with nominally flat boundaries in a stationary case. We simulate the roughness of real surface by a non-uniform mass density in the near-surface region. Within the framework of the model, the mass density satisfies the inhomogeneous modified Helmholtz equation. The inhomogeneous term in this equation (mass sources) is selected in a form that allows taking the regularities of the bearing area curve (Abbott-Firestone curve) into account. The parameters of mass sources make it possible to vary the sizes of regions of near-surface heterogeneity, as well as the dimensions of peak and valley zones. The latter is illustrated by an example of the elastic half-space. The inhomogeneity of the mass density is the cause of the non-zero stresses in a free solid. We study stresses in a thin film. Applying the maximum normal stress criterion we investigate the stretched film strength and size effect on strength for different surface roughness profiles. A significant dependence of the strength value on the ratio of the characteristic sizes of the peak and valley zones is found.