The periodic contact problem for spherical indenters and viscoelastic half-space*

The interaction of a periodic system of rigid spherical indenters with a viscoelastic half-space is considered. The linear viscoelastic models (the standard viscoelastic solid model and the Maxwell model) are used to describe the mechanical behavior of the half-space. The case of a constant load applied to each indenter is investigated. Using the localization method and the solution of the corresponding elastic problem, the analytical expressions for the contact pressure under a single indenter, the radius of a single contact spot, and for the additional displacement function are derived. The influence of the contact density and the viscoelastic half-space mechanical properties on the variation of the contact characteristics in time is analyzed.

Automated summary

This study investigates the interaction between a periodic system of rigid spherical indenters and a viscoelastic half-space using linear viscoelastic models. The case of constant load applied to each indenter is explored. Analytical expressions for contact pressure, radius of contact spot, and additional displacement function are derived using the localization method and the solution of the corresponding elastic problem. The influence of contact density and viscoelastic mechanical properties of the half-space on the variation of contact characteristics in time is analyzed.