On applicability and uniqueness of the correspondence principle to pie-shaped wedge (“wedge paradox”) with various boundary conditions

Abstract

A new paradigm for re-examination of the concept of the correspondence principle (originally due to Dundurs) in association with the much-studied issue of “wedge paradox” is presented. This study connects for the first time two parallel streams of research: (i) Carothers-Sternberg-Koiter’s wedge paradox study and (ii) Williams' eigenfunction approach. First, a three-dimensional eigenfunction expansion approach for determination of the asymptotic (singular) stress fields in the vicinity of the fronts of infinite wedges of finite thickness, subjected to various wedge-flank boundary conditions, is presented. This analysis is then exploited to establish rigorous rules or conditions, which would depend on the prescribed wedge-flank boundary conditions, the related state of deformation and the elastic property (Poisson’s ratio), for validity (or lack thereof) of the assumptions implicit in the heuristic enunciation of the correspondence principle. More important, a hitherto unavailable analysis for uniqueness (or lack thereof) of the prevalence of such a heuristically postulated correspondence is also developed. Finally, the present study offers both mathematical as well as (heretofore missing) physical explanations behind the working of the correspondence principle.