Smooth Indentation of Finite Strip Reinforced by Rigid Inclusion

Abstract

Symmetric frictionless indentation of a reinforced, two‐dimensional, finite rectangular elastic strip by a flat or rounded stamp is studied. The reinforcement consists of a rigid one‐dimensional inclusion parallel to the indented side of the strip. Boundary conditions are chosen in such a way that the strip models an indented, reinforced beam with built‐in edges. In this analysis the Fourier transformation method is used, modified to include field discontinuities due to the presence of the inclusion. The unknown quantities are represented as sums of singular parts with known singularities and of regular parts expanded into Fourier series. The effect of the reinforcement on the displacements, on the stress intensity factors, and on the distribution of the contact stress, and of stress discontinuities across the inclusion is investigated. The results indicate, among other things, that the reinforcement has a “shielding” effect on the region below it: the normal stresses in the direction perpendicular to the inclusion are negligible in this region, which displaces almost like a rigid solid.