Stability loss of a thin subsurface layer as a result of stresses caused by the distributed electric charge

Abstract

A new variant of the analysis of the mechanical behaviour of an elastic layer with uniformly distributed electric charges is proposed. With a special term in the equation, written on the basis of the first beginnings of thermodynamics, it is proposed to take into account the work done when the layer is deformed by electric charges. A new element in the theory is the use of a special tensor (orthoprojector) in recording the work done by electric charges. The article derives the defining equations from the laws of thermodynamics. It is shown that the Cauchy stress tensor is the sum of two terms. The first term determines the stresses arising from the interaction of the charges.

The application of the theory to the modelling of processes during ion plasma treatment of polymeric materials is considered. The purpose of the considered example is the analysis of the hypothesis that the phenomenon of the appearance of the wavy relief of the appeared carbonised layer on the surface of the polymer material can be connected with the stresses arising due to the fact that the charges try to deform the material at the repulsion. A methodology for estimating the stresses arising from the described process is proposed. A calculation is carried out which shows that the hypothesis passes numerical verification. A comparative analysis of the relief characteristics obtained by calculation according to the proposed model and the relief obtained by atomic force microscopy (AFM) of plasma-treated polyurethanes is carried out.