The Sternberg-Koiter Conclusion and Other Anomalies of the Concentrated Couple

Abstract

A notable conclusion reached by Sternberg and Koiter 30 years ago is that an elastic wedge loaded by a concentrated couple at its vertex remains a well-posed elasticity problem only as long as the wedge does not degenerate into a reentrant corner. A closely related problem is that of a concentrated couple approaching the tip of a crack. It is shown in this article that the corresponding limits in the stress fields do not exist, but that the Bueckner weight function is obtained by appropriately diminishing the magnitude of the couple. It is also shown that the elastic fields, when a concentrated couple approaches an interface between two materials, depend on the direction from which the interface is approached. Moreover, the elastic wedge embedded in another material is discussed.