Small-scale indentation of a hemispherical inhomogeneity in an elastic half-space

The axisymmetric problem of small-scale frictionless indentation of an elastic hemispherical inhomogeneity embedded at the free surface of a semi-infinite elastic matrix is considered. It is assumed that the radius of contact area is relatively small compared with the radius of the inhomogeneity. The first-order asymptotic model for the incremental indentation stiffness is presented in terms of the coefficient of local compliance, which is evaluated based on the analytical solution for the surface Green's function. The influence of both Poisson's ratios on the corresponding indentation scaling factor, which reflects the effect of localized inhomogeneity, is studied in detail.