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SINGULAR ENRICHMENT FINITE ELEMENT METHOD FOR ELASTODYNAMIC CRACK PROPAGATION

TED BELYTSCHKO

Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3111, USA

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and

HAO CHEN

Livermore Software Technology Corporation, 7374 Las Positas Road, Livermore, CA 94550, USA

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https://doi.org/10.1142/S0219876204000095Cited by:43 (Source: Crossref)

Abstract

An enrichment technique for accurately modeling two dimensional crack propagation within the framework of the finite element method is presented. The technique uses an enriched basis that spans the asymptotic dynamic crack-tip solution. The enrichment functions and their spatial derivatives are able to exactly reproduce the asymptotic displacement field and strain field for a moving crack. The stress intensity factors for Mode I and Mode II are taken as additional degrees of freedom. An explicit time integration scheme is used to solve the resulting discrete equations. Numerical simulations of linear elastodynamic problems are reported to demonstrate the accuracy and potential of the technique.

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References

Z. P. Bazant, Journal of Applied Mechanics 18(1), 1 (1975). Web of Science, Google Scholar
S. N. Alturi and T. Nishioka, International Journal of Fracture 27, 245 (1985), DOI: 10.1007/BF00017971. Web of Science, Google Scholar
S. N. Atluri, A. S. Kobayashi and M. Nakagaki, International Journal of Fracture 11(2), 257 (1975), DOI: 10.1007/BF00038893. Web of Science, Google Scholar
T. Belytschko and M. Tabbara, International Journal for Numerical Methods in Engineering 39, 923 (1996). Web of Science, Google Scholar
T. Belytschko and T. Black, International Journal for Numerical Methods in Engineering 45(5), 601 (1999). Web of Science, Google Scholar
T. Belytschkoet al., International Journal for Numerical Methods in Engineering 50(4), 993 (2001). Web of Science, Google Scholar
S. E. Benzley, International Journal for Numerical Methods in Engineering 8, 537 (1974), DOI: 10.1002/nme.1620080310. Web of Science, Google Scholar
Blacker, T. (1993). Enhanced stress projections for error estimation and a singular floating node element for static and dynamic fracture. PhD Thesis . Google Scholar
L. B. Freund and R. J. Clifton, Journal of Elasticity 4(4), 293 (1974). Web of Science, Google Scholar
L. B. Freund , Dynamic Fracture Mechanics ( Cambridge University Press , Cambridge , 1990 ) . Google Scholar
Gerlach, C. (1999). Computational methods for the dynamic response of cracked specimens. PhD Thesis . Google Scholar
M. F. Kanninen and C. H. Popelar , Advanced Fracture Mechanics ( Oxford University Press , New York , 1985 ) . Google Scholar
K. Kishimoto, S. Aoki and M. Sakata, Engineering Fracture Mechanics 13, 501 (1980), DOI: 10.1016/0013-7944(80)90081-8. Web of Science, Google Scholar
A. S. Kobayashi, A. F. Emery and S. Mall, Experimental Mechanics 16, 321 (1976), DOI: 10.1007/BF02330248. Web of Science, Google Scholar
Y. J. Lee and L. B. Freund, Journal of Applied Mechanics 57, 104 (1990). Web of Science, Google Scholar
J. M. Melenk and I. Babuska, Computer Methods in Applied Mechanics and Engineering 139, 289 (1996), DOI: 10.1016/S0045-7825(96)01087-0. Web of Science, Google Scholar
N. Moës, J. Dolbow and T. Belytschko, International Journal for Numerical Methods in Engineering 46(1), 133 (1999). Web of Science, Google Scholar
L. Nash Gifford and P. D. Hilton, Engineering Fracture Mechanics 10, 485 (1978), DOI: 10.1016/0013-7944(78)90059-0. Web of Science, Google Scholar
D. V. Swenson and A. R. Ingraffea, Computational Mechanics 3, 381 (1988), DOI: 10.1007/BF00301139. Google Scholar