A Green’s Function Formulation of Anticracks and Their Interaction With Load-Induced Singularities

Abstract

This paper provides a Green’s function formulation of anticracks (rigid lamellar inclusions of negligible thickness that are bonded to the surrounding elastic material). Apart from systematizing several previously known solutions, the article gives the pertinent fields for concentrated forces, dislocations, and a concentrated couple applied on the line of the anticrack. There is a reason for working out these results: In contrast to concentrated forces, a concentrated couple approaching the tip of an anticrack makes the elastic fields explode. Finite limits can be achieved, however, by appropriately diminishing the magnitude of the couple, which then leads to fields that are intimately connected with the weight functions for the anticrack. An edge dislocation going to the tip of an anticrack puts a net force on the lamellar inclusion, which is shown to be related to a previously known feature of dislocations near a bimaterial interface.