The Boussinesq–Mindlin problem for a non-homogeneous elastic halfspace

Abstract

Boussinesq’s problem for the indentation of an isotropic, homogeneous elastic halfspace by a rigid circular punch constitutes a seminal problem in the theory of contact mechanics as does Mindlin’s problem for the action of a concentrated force at the interior of an isotropic, homogeneous elastic halfspace. The combined action of the surface indentation in the presence of the interior loading is referred to as the Boussinesq–Mindlin problem, which has important applications in the area of geomechanics. The Boussinesq–Mindlin problem, which represents a self-stressing loading configuration, serves as a useful model for interpreting the mechanics of indentation of geologic media for purposes of estimating their bulk elasticity properties. In this paper, the analysis of the problem is extended to include an exponential variation in the linear elastic shear modulus of the halfspace region.