Mathematical modeling of structural and near-surface non-homogeneities in thermoelastic thin films

We propose a model that is aimed to study the stress–strain state of nanoelements including size effects of surface stresses, effective elastic moduli and strength within the one-continuum approach. The size effects are caused by the non-homogeneity of the density. Non-homogeneity in the density distribution originates from taking into account the structure of the material and geometric irregularity of the real solid surface. Thermoelastic solid is considered as an open thermodynamic system. It is assumed that the material structure and real solid surface suddenly originate at the initial time while the phenomenological coefficients in the state equation for stress tensor depend on density. The obtained key system of equations is used to study the equilibrium state of thin film as a layer with the thickness comparable with characteristic sizes of near-surface and structural non-homogeneity regions. The multiscale type of size effects is indicated and the limits of applicability of the linear approximation are discussed.