Dominique Chapelle and Klaus-Jürgen Bathe

Singular elastic stress fields are generally developed at sharp re-entrant corners and at the end of bonded interfaces between dissimilar elastic materials. This behaviour can present difficulties in both analytical and numerical solution of such problems. For example, excessive mesh refinement might be needed in a finite element solution.

Williams (1952) pioneered a method for determining the strength of the dominant singularity by expressing the local field as an asymptotic expansion. The same method has since been used for a variety of situations leading to singular points, including bonded dissimilar wedges and frictionless or frictional contact between bodies with sharp corners.