1 ICF100241OR A COMPLEX VARIABLE FORMULATION FOR THE INTERACTIONS BETWEEN RIGID INCLUSIONS AND CRACKS K.T. Chau1 and Y.B. Wang2 1Department of Civil and Structural Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China 2Department of Mechanics, Lanzhou University, Lanzhou, China ABSTRACT This paper summarizes the recent formulation by Wang and Chau [1] on a new boundary element method (BEM) in terms of complex variables for plane elastic bodies containing cracks, holes and rigid inclusions subjected to mixed displacement/ traction boundary conditions. A complex boundary function H(t), which is a linear combination of the boundary traction and boundary displacement density, is introduced. The present Boundary Integral Formulation can be related directly to Muskhelishvili’s formalism. Singular interpolation functions of order 1/ 2 - r (where r is the distance measured from the crack tip) are introduced such that singular integrand involved at the element level can be integrated analytically. The interaction between a rigid circular inclusion and a crack is investigated in details. Our results for the stress intensity factor are comparable with those given by Erdogan and Gupta [2] and Gharpuray et al. [3] for a crack emanating from a stiff inclusion, and with those by Erdogan et al. [4] for a crack in the neighborhood of a stiff inclusion. KEYWORDS Crack, Circular inclusions, Boundary element method, Complex variable INTRODUCTION In recent years, boundary element method (BEM) has widely been applied in solving linear elastic problems and fracture mechanics problems, and has been developed into a powerful numerical technique. In the traditional approach, boundary integral equations are derived by from the Somigliana’s identity (e.g. Rizzo [5]; Cruse [6]; Lachat and Watson [7]; Brebbia [8]). The application of BEM has been focused mainly on traction boundary value problems (BVPs), and there is relatively few BEM studies on solving mixed BVPs,
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