Green's function: a numerical generation for fracture mechanics problems via boundary elements J.C.F. Telles * , S. Guimar~ aes COPPE/UFRJ, Progama de Engenharia Civil, Caixa Postal 68506, CEP 21945-970, Rio de Janeiro, Brazil Received 30 March 1999 Abstract The paper discusses the application of the hyper-singular boundary integral equation to obtain Green's function solution to general geometry fracture mechanics problems, such as curved multifracture crack simulation, static and harmonic (extended to transient dynamic through inverse numerical transforms), in 2D and 3D. The numerical Green's function (NGF) can be implemented into a boundary element computer program, as the fundamental solution, to produce an accurate and ecient boundary element procedure. The complete formulation is presented in a uni®ed manner, generalizing previous problem oriented procedures proposed by the au- thors. The results to some typical linear fracture mechanics problems are presented. Ó 2000 Elsevier Science S.A. All rights reserved. Keywords: Green's function; Hyper-singular formulation; Fracture mechanics 1. Introduction Since Irwin postulated that crack behaviour is determined only by the value of the stress intensity factor (SIF or K) which depends on the stress ®eld accuracy in the vicinity of the crack tip, the appropriate numerical modelling of linear elastic fracture mechanics problems became a challenge for engineers. The numerical modelling diculties reside, generically, in the accurate determination of the stress ®eld (in®nite at tip) near the crack tip, and, speci®cally to BEM, in the degeneration of the integral equation when crack surfaces coincide. A good re®nement of the mesh associated to the usage of special tip elements are usually enough to overcome the ®rst diculty while the degeneration in BEM is usually avoided by: · modelling the crack as a narrow elliptic cavity; · considering symmetry, whenever possible; · applying the sub-region technique [1]; · employing the mixed or dual formulation [2±4]; · using the associated Green's function [5]. The last three procedures above are the most important and widely used techniques in BEM to solve LEFM problems. To illustrate the dierences in these approaches one could say that the integral equations necessary to solve crack problems by the subregion technique, Fig. 1, are (superscript * represents fun- damental solution, e.g., Kelvin): www.elsevier.com/locate/cma Comput. Methods Appl. Mech. Engrg. 188 (2000) 847±858 * Corresponding author. E-mail address: telles@coc.ufrj.br (J.C.F. Telles). 0045-7825/00/$ - see front matter Ó 2000 Elsevier Science S.A. All rights reserved. PII: S 0 0 4 5 - 7 8 2 5 ( 9 9 ) 0 0 3 6 6 - 7