Interaction of a horizontal finite crack with a center of dilatation in elastic half-planes

This paper summarizes the recent results obtained by Chau and Wong [1] on the interaction of a two-dimensional crack parallel to the free surface of a half-plane subject to the action of an internal center of dilatation. The method of solution follows the principle of superposition. The problem is first decomposed into two auxiliary problems: (I) a half-plane containing a center of dilatation; and (II) a finite crack in half-plane subjected to traction that cancel those induced by the Auxiliary Problem I. The final solution is obtained as the summation of those of the two Auxiliary Problems. Numerical results suggest that as long as the crack is not too close to the free surface of the half-plane, the present solution is accurate enough for practical applications. If the overburden stress due to gravity and the friction on crack surface are neglected, both mode I and II stress intensity factors are induced at the crack tips.