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A variational boundary integral method for the analysis of 3-D cracks of arbitrary geometry modelled as continuous distributions of dislocation loops

Xu, G. and Ortiz, M. (1993) A variational boundary integral method for the analysis of 3-D cracks of arbitrary geometry modelled as continuous distributions of dislocation loops. International Journal for Numerical Methods in Engineering, 36 (21). pp. 3675-3701. ISSN 0029-5981. https://resolver.caltech.edu/CaltechAUTHORS:20171213-160315284

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Abstract

A finite element methodology for analysing propagating cracks of arbitrary three-dimensional geometry is developed. By representing the opening displacements of the crack as a distribution of dislocation loops and minimizing the corresponding potential energy of the solid, the kernels of the governing integral equations have mild singularities of the type 1/R. A simple quadrature scheme then suffices to compute all the element arrays accurately. Because of the variational basis of the method, the resulting system of equations is symmetric. By employing six-noded triangular elements and displacing midside nodes to quarter-point positions, the opening profile near the front is endowed with the correct asymptotic behaviour. This enables the direct computation of stress intensity factors from the opening displacements. The special but important cases of periodic and semi-infinite cracks are addressed in some detail. Finally, the geometry of propagating cracks is updated incrementally by recourse to a pseudodynamic crack-tip equation of motion. The crack is continuously remeshed to accommodate the ensuing changes in geometry. The performance of the method is assessed by means of selected numerical examples.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://dx.doi.org/10.1002/nme.1620362107DOIArticle
http://onlinelibrary.wiley.com/doi/10.1002/nme.1620362107/abstractPublisherArticle
Additional Information:© 1993 John Wiley & Sons. Received 13 October 1992. Revised 28 December 1992. The support of the U.S. Office of Naval Research through grant N00014-90-J-1758 is gratefully acknowledged.
Group:GALCIT
Funders:
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-90-J-1758
Issue or Number:21
Record Number:CaltechAUTHORS:20171213-160315284
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20171213-160315284
Official Citation:Xu, G. and Ortiz, M. (1993), A variational boundary integral method for the analysis of 3-D cracks of arbitrary geometry modelled as continuous distributions of dislocation loops. Int. J. Numer. Meth. Engng., 36: 3675–3701. doi:10.1002/nme.1620362107
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83902
Collection:CaltechAUTHORS
Deposited By: Lydia Suarez
Deposited On:14 Dec 2017 22:11
Last Modified:03 Oct 2019 19:12

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