Silveira, N. P. P.; Guimarães, S.; Telles, J. C. F. A numerical Green’s function BEM formulation for crack growth simulation. (English) Zbl 1182.74236 Eng. Anal. Bound. Elem. 29, No. 11, 978-985 (2005). Summary: This paper presents a crack growth prediction analysis based on the numerical Green’s function (NGF) procedure and on the minimum strain energy density criterion for crack extension, also known as S-criterion. In the NGF procedure, the hypersingular boundary integral equation is used to numerically obtain the Green’s function which automatically includes the crack into the fundamental infinite medium. When solving a linear elastic fracture mechanisms (LEFM) problem, once the NGF is obtained, the classical boundary element method can be used to determine the external boundary unknowns and, consequently, the stress intensity factors needed to predict the direction and increment of crack growth. With the change in crack geometry, another numerical analysis is carried out without need to rebuilding the entire element discretization, since only the crack built in the NGF needs update. Numerical examples, contemplating crack extensions for two-dimensional LEFM problems, are presented to illustrate the procedure. Cited in 3 Documents MSC: 74S15 Boundary element methods applied to problems in solid mechanics 74R10 Brittle fracture 65N80 Fundamental solutions, Green’s function methods, etc. for boundary value problems involving PDEs Keywords:Green’s function; boundary element method (BEM); crack propagation; boundary integral equation method (BIE); linear elastic fracture mechanics (LEFM); S-criterion PDFBibTeX XMLCite \textit{N. P. P. Silveira} et al., Eng. Anal. Bound. Elem. 29, No. 11, 978--985 (2005; Zbl 1182.74236) Full Text: DOI References: [1] Snyder, M. D.; Cruse, T. A., Boundary integral equation analysis of cracked anisotropic plates, Int J Fract Mech, 11, 2, 315-328 (1975) [2] Telles, J. C.F.; Castor, G. S.; Guimaraes, S., A numerical green’s function approach for boundary elements applied to fracture mechanics, Int J Numer Methods Eng, 38, 3259-3274 (1995) · Zbl 0836.73079 [3] Silveira, N. P.P.; Guimaraes, S.; Telles, J. C.F., (Sladek, J.; Sladek, V., Singular integrals in boundary element methods (1998), Computational Mechanics Publication: Computational Mechanics Publication Southhampton), [chapter 11] [4] Barra, L. P.S.; Telles, J. C.F., A hyper-singular numerical green’s function generation for BEM applied to dynamic SIF problems, Eng Anal Bound Elem, 23, 77-87 (1999) · Zbl 0953.74069 [5] Castor, G. S.; Telles, J. C.F., The 3-D BEM implementation of a numerical green’s function for fracture mechanics applications, Int J Numer Meth Eng, 48, 1199-1214 (2000) · Zbl 0974.74073 [6] Sih, C. G., Mechanics of fracture initiation and propagation (1991), Kluwer Academic Publishers: Kluwer Academic Publishers Boston [7] Irwin, G. R., (Fracture. Fracture, Handbook der physik, vol. 39 (1958), Springer: Springer Berlim), 551-590 [8] Guo, H.; Aziz, N. I.; Schimidt, Linear elastic crack tip modelling by displacement discontinuity method, Eng Fract Mech, 36, 6, 943-993 (1990) [9] Prasad, N. N.V.; Aliabadi, M. H.; Rooke, D. P., Incremental crack growth in termoelastic problems, Int J Fract, 66, R45-R50 (1994) [10] Portela, A.; Aliabadi, M. H.; Rooke, D. P., Dual boundary element incremental analysis of crack propagation, Comput Struct, 46, 2, 237-247 (1993) · Zbl 0825.73888 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.