X. Markenscoff et al., THE INTERFACE ANTICRACK AND GREENS-FUNCTIONS FOR INTERACTING ANTICRACKS AND CRACKS ANTICRACKS, Journal of applied mechanics, 61(4), 1994, pp. 797-802
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 coupl
ed integral equations is solved analytically in closed form for the ca
ses of uniform biaxial tension and of anticracks loaded by concentrate
d forces or moment. Solutions are also obtained by the interaction of
an interface anticrack with a first-order singularity (concentrated fo
rce and dislocation) and second-order singularity (doublet of forces)
at the interface. In the latter case the limit as the second-order sin
gularity approaches the tip of the anticrack does not exist, but neith
er can a finite limit be obtained by rescaling as in the homogeneous m
aterial. The solution of the interface anticrack exhibits the oscillat
ory singularities that appear at interface cracks which indicates that
the overlapping fo the displacement on the crack faces is not the rea
son for this anomalous behavior. Moreover, it should be pointed out th
at the material condition that the stress does not exhibit oscillatory
behavior is not the same as for interface cracks: for anticracks it i
s kappa(1) (1 - beta) = kappa(2) (1 + beta) while for cracks it is bet
a = 0.