Effects of an axisymmetric rigid punch on a nonhomogeneous transversely isotropic half-space

TLDR: In this article, the authors studied the elastic behavior of a nonhomogeneous transversely isotropic half-space under the action of a smooth rigid axisymmetric indentor.

Abstract: Elastic behaviour of a nonhomogeneous transversely isotropic half-space is studied under the action of a smooth rigid axisymmetric indentor. Hankel transforms of different orders have been used. It is observed that in contrast to a homogeneous medium, the pressure distribution in the contact region in a nonhomogeneous medium is not directly available, rather it is obtainable from the solution of a Fredholm integral equation. The integral equation is solved for a flat-ended punch and paraboloidal indentations for various values of the nonhomogeneity parameter, and the effects of nonhomogeneity in elastic behaviour on stresses have been shown graphically. The results of the associated homogeneous case are readily available from the results of the present study.