Int. 1. Engtrg Sci. Vol. 27, No. 11, PP. 1287-1298,1989 0020-7225/89 $3.00+ 0.00 Printed in Great Britain. AI1rights reserved Copyright @ 1989Pergamon Press plc zyxwvu A RIGID CURVILINEAR INCLUSION PARTIALLY BONDED IN AN ELASTIC MATRIX E. E. GDOUTOS and M. A. KATTIS School of Engineering, Democritus University of Thrace, GR-671 00 Xanthi, Greece Abatrnet-The plane elastostatic problem of a rigid curvilinear inclusion partially bonded in an elastic infinite matrix is studied. The inclusion boundary can take any shape that can be mapped on to the unit circle by a rational function while the matrix is subjected to general biaxial loads at infinity. Using the method of analytic continuation of the complex potentials for curvilinear boundaries the problem is reduced to a non-homogeneous Hilbert problem whose solution gives the stress and displacement field in the matrix in a closed form. A general method for the determination of the various unknown coefficients of the solution which can easily be computerized is developed for any type of inclusion. The solution for the elliptical inclusion is obtained as a special case of the general solution. INTRODUCTION A commonly observed failure mode of multi-phase materials is the debonding of the different phases due to manufacturing and/or loading conditions. Because of its significance this problem has attracted the interest of many investigators. In modelling this kind of failure for the case of particulate composites special interest has been paid to the problem of an inclusion partially bonded in an elastic matrix. From the theoretical point of view and within the framework of linear elasticity this problem has received considerable attention in the past. England [l] was the first who almost two decades ago studied the problem of an arc crack lying along the interface of a circular inclusion embedded in an infinite matrix of a different material. Using the complex variable approach to plane elasticity he obtained a closed-form solution for the stress and displacement field. The more general problem of any number of cracks lying along the interface of the circular inclusion was considered by Perlman and Sih [2] along the same lines. Toya [3,4] for the problem studied in [l] used the stress field in conjunction with the Griffith virtual work theory to obtain a criterion of crack extension along the interface. Furthermore, he studied the case of crack extension into the matrix based on the maximum circumferential stress theory. The stress distribution and the fracture process for the problem of a rigid circular inclusion with two symmetric interfacial cracks embedded in a matrix was analyzed by Piva and Viola [5]. The above results were extended to the case of an elliptic inclusion partially bonded to an elastic matrix. Toya [6] studied the problem of an elliptic rigid inclusion with an interfacial crack embedded in a matrix. As in [3,4] he investigated the growth of the debonding of the interface and obtained the critical values of the applied loads as a function of the geometrical configuration of the composite plate. Viola and Piva [7] analyzed the fracture process of an infinite plate with a rigid elliptic inclusion which has two symmetric interfacial cracks and is perfectly bonded to the plate. For the case of curvilinear inclusions, Sendeckyj [8] considered the situation of two symmetrical cracks lying along the inclusion boundary which otherwise is perfectly bonded to the matrix under longitudinal shear. The same author [9] gave the general form of the solution for an elastic inclusion embedded in an infinite solid and analyzed particularly the elliptic inclusion. Panasyuk zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA et al. [lo] studied the case of a rigid inclusion with cuspidal points on its boundary and perfectly bonded to a matrix. They gave the local stress distribution in the vicinity of the cuspidal points in terms of two concentration factors. For this situation, Gdoutos [ll, 121 studied the problem of fracture initiation from the cuspidal points of the inclusion and gave numerical results for the cases of a rectilinear, astroidal and hypocycloidal inclusion. In the present work, the case of a rigid curvilinear inclusion partially bonded to an infinite elastic plate is considered. The unbonded part of the inclusion boundary forms an interfacial 1287 ES 21:11-1