The Interface Anticrack and Green’s Functions for Interacting Anticracks and Cracks/Anticracks

Abstract

Solution is obtained for an anticrack-a bonded rigid lamella inclusion-at the interface between two isotropic elastic solids. The problem is formulated in terms of distributed line-loads at the anticrack which constitute the Green’s functions and the system of the governing coupled integral equations is solved analytically in closed form for the cases of uniform biaxial tension and of anticracks loaded by concentrated forces or moment. Solutions are also obtained by the interaction of an interface anticrack with a first-order singularity (concentrated force and dislocation) and second-order singularity (doublet of forces) at the interface. In the latter case the limit as the second-order singularity approaches the tip of the anticrack does not exist, but neither can a finite limit be obtained by reseating as in the homogeneous material. The solution of the interface anticrack exhibits the oscillatory singularities that appear at interface cracks which indicates that the overlapping of the displacement on the crack faces is not’the reason for this anomalous behavior. Moreover, it should be pointed out that the material condition that the stress does not exhibit oscillatory behavior is not the same as for interface cracks: for anticracks it is κ1 (1−β) = κ2 (1 + β) while for cracks it is β = 0.