Elastic crack growth in finite elements with minimal remeshing

International Journal for Numerical Methods in EngineeringVolume 45, Issue 5 p. 601-620 Research Article Elastic crack growth in finite elements with minimal remeshing T. Belytschko, Corresponding Author T. Belytschko [email protected] Departments of Mechanical and Civil Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, U.S.A. Walter P. Murphy, Professor of Computational MechanicsDepartment of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3111, U.S.A.Search for more papers by this authorT. Black, T. Black Departments of Mechanical and Civil Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, U.S.A. Research Assistant, Theoretical and Applied MechanicsSearch for more papers by this author T. Belytschko, Corresponding Author T. Belytschko [email protected] Departments of Mechanical and Civil Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, U.S.A. Walter P. Murphy, Professor of Computational MechanicsDepartment of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3111, U.S.A.Search for more papers by this authorT. Black, T. Black Departments of Mechanical and Civil Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, U.S.A. Research Assistant, Theoretical and Applied MechanicsSearch for more papers by this author First published: 21 April 1999 https://doi.org/10.1002/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-SCitations: 3,239 AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Abstract A minimal remeshing finite element method for crack growth is presented. Discontinuous enrichment functions are added to the finite element approximation to account for the presence of the crack. This method allows the crack to be arbitrarily aligned within the mesh. For severely curved cracks, remeshing may be needed but only away from the crack tip where remeshing is much easier. Results are presented for a wide range of two-dimensional crack problems showing excellent accuracy. Copyright © 1999 John Wiley & Sons, Ltd. REFERENCES 1 Melenk JM, Babuška I. The partition of unity finite element method: basic theory and applications. Computer Methods in Applied Mechanics and Engineering 1996; 39: 289–314. 2 Durate C, Oden J. hp clouds—a meshless method to solve boundary-value problems. Technical Report, TICAM, 1995. 3 Belytschko T, Lu YY, Gu L. Element-free Galerkin methods. International Journal of Numerical Methods in Engineering 1994; 37: 229–256. 4 Fleming M, Chu YA, Moran B, Belytschko T. Enriched element-free Galerkin methods for singular fields. International Journal for Numerical Methods in Engineering 1997; 40: 1483–1504. 5 Belytschko T, Krongauz Y, Organ D, Fleming M, Krysl P. Meshless methods: an overview and recent developments. Computer Methods in Applied Mechanics and Engineering 1996; 139: 3–47. 6 Swenson D, Ingraffea A. Modeling mixed-mode dynamic crack propagation using finite elements: theory and applications. Computational Mechanics 1988; 3: 381–397. 7 Oliver J. Continuum modelling of strong discontinuities in solid mechanics using damage models. Computational Mechanics 1995; 17: 49–61. 8 Ewalds H, Wanhill R. Fracture Mechanics; Edward Arnold: New York, 1989. 9 Yau J, Wang S, Corten H. A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity. Journal of Applied Mechanics 1980; 47: 335–341. 10 Moran B, Shih C. Crack tip and associated domain integrals from momentum and energy balance. Engineering Fracture Mechanics 1987; 127. 11 Gdoutos E. Fracture Mechanics; Kluwer Academics Publishers: Boston, 1993. 12 Black T. Mesh-free applications to fracture mechanics and an analysis of the corrected derivative method. Ph.D. Thesis, Northwestern University, 1998. 13 Nuismer RJ. An energy release rate criterion for mixed mode fracture. International Journal of Fracture 1975; 11: 245–250. 14 Erdogan F, Sih G. On the crack extension in plates under plane loading and transverse shear. Journal of Basic Engineering 1963; 85: 519–527. 15 Sih GC. Strain-energy-density factor applied to mixed mode crack problems. International Journal of Fracture 1974; 10: 305–321. 16 Shih C, Asaro R. Elastic–plastic analysis of cracks on bimaterial interfaces: Part i-small scale yielding. Journal of Applied Mechanics 1988; 55: 299–316. Citing Literature Volume45, Issue520 June 1999Pages 601-620 ReferencesRelatedInformation