Interacting cracks and inclusions in a solid by multipole expansion method

An accurate series solution is obtained of the elastic problem for a solid containing penny-shaped cracks and spheroidal inclusions or cavities. The method of solution is based on the general solution procedure developed by Kushch [(1996) Elastic equilibrium of a solid containing a finite number of aligned inclusions. International Journal of Solids and Structures 33, 1175-1189] and consists in representation of the displacement vector by a series of the vectorial partial solutions of Lame's equation, written in a spheroidal basis. By using the addition theorems for these partial solutions the primary boundary-value problem is reduced to an infinite set of linear algebraic equations. An asymptotic analysis of the problem is performed and the series expansion of the opening-mode stress intensity factor is obtained. Numerical analysis of model problems is performed and some results demonstrating the effect on the stress intensity factor of the pair interactions in crack-crack, crack-cavity and crack-inclusion geometries are presented. (C) 1998 Elsevier Science Ltd.