A further investigation of Green's functions for a piezoelectric material with a cavity or a crack Pin Lu a, *, M.J. Tan b , K.M. Liew b a Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China b School of Mechanical and Production Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 639798, Singapore Received 1 July 1998; in revised form 9 April 1999 Abstract In this paper, the Green's functions of an in®nite two-dimensional piezoelectric material containing an elliptical cavity are re-investigated by introducing exact electric boundary conditions on the hole boundary, and the corresponding modi®ed solutions are obtained. By setting E 0 , the dielectric constant in the cavity, to be zero, the modi®ed Green's functions are returned to the conventional ones (Lu and Williams, 1998). Furthermore, the hoop stresses along the hole boundary under the action of a set of generalized concentrated forces are obtained. When the hole is reduced to a slit crack, the expressions of generalized stress intensity factors are also provided. # 1999 Elsevier Science Ltd. All rights reserved. Keywords: Piezoelectric material; Green's function; Inclusion; Stroh formalism 1. Introduction The problems of Green's functions for two or three-dimensional piezoelectric materials have been studied by many researchers (e.g. Dunn, 1994a; Norris, 1994; Khutoryansky and Sosa, 1995; Lu and Williams, 1998). The electroelastic Green's functions play an important role in the analysis of piezoelectric inclusion and inhomogeneity problems, defect and crack problems, as well as stress and electric concentration problems. Especially, the Green's functions can be used as fundamental solutions of well used boundary element method for solving piezoelectric problems with ®nite boundary sizes and subjected to general mechanical±electric loading (Lu and Mahrenholtz, 1994; Lee and Jiang, 1994; International Journal of Solids and Structures 37 (2000) 1065±1078 0020-7683/00/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S0020-7683(99)00117-1 www.elsevier.com/locate/ijsolstr * Corresponding author. E-mail address: mpelup@nus.edu.sg (P. Lu)