Small-scale indentation of an elastic coated half-space: Influence of Poisson’s ratios on the substrate effect

Frictionless indentation of an elastic layer attached to an elastic half-space is considered in the small-scale contact range. Based on the first-order asymptotic solution, a simple analytical approximation is suggested for the indentation scaling factor that takes into account the elastic layer’s finite thickness as well as the effect of the elastic substrate. The influence of both Poisson’s ratios on the substrate effect is studied in detail, and the error of the 1/10 rule of Buckle is estimated for a relatively large range of the elastic moduli mismatch.