In-Plane Indentation and Separation of a Flat, or Rounded Rigid Stamp from an Elastic, Finite Layer

Abstract

This paper describes symmetric, frictionless indentation of a two-dimensional, rectangular, elastic solid, with two parallel edges constrained against displacements, by a flat, rigid, or rounded stamp pressed against one of the remaining edges. Comparison with the classical problem of indentation of the elastic half-plane by a flat rigid stamp reveals new interesting features of the present analysis: 1) For each relative stamp length a critical aspect ratio of the indented rectangle exists such that for a narrower rectangle the separation of the midsection of the stamp occurs. 2) The stress intensity factors at the ends of the stamp are found to depend strongly on the relative depth of the “beam”; they also depend, but to a lesser degree, on the relative length of the stamp. 3) Unlike in the classical problem here the penetration of the stamp is uniquely determined. Numerical results are provided. The numerical results obtained for the case of the rounded stamp are compared with the results available from earlier studies.