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Interaction of a parabolic notch with a generalized singularity

Ma, Lifeng; Hills, David A.


Sir Joseph Pope Fellowship

David A. Hills


In this paper, the interaction of a parabolic notch with a generalized singularity is studied and its analytical solution is derived. The generalized singularity may represent a concentrated force or an edge dislocation. As an example, the parabolic notch interacting with a dislocation is studied in details, and the driving force on the dislocation due to the notch configuration is obtained in terms of the vector J-integral. It is found that a dislocation-free zone may exist beneath the notch root surface. The solutions developed in this study give, on the one hand, basic information about the state of stress induced in the notch neighborhood, and, on the other hand, can be used as building blocks to model damage at the notch root under complex load conditions.


Ma, L., & Hills, D. A. (2022). Interaction of a parabolic notch with a generalized singularity. International Journal of Engineering Science, 176, Article 103685.

Journal Article Type Article
Acceptance Date Apr 9, 2022
Online Publication Date Apr 14, 2022
Publication Date Jun 1, 2022
Deposit Date Jul 29, 2022
Journal International Journal of Engineering Science
Print ISSN 0020-7225
Publisher Elsevier BV
Peer Reviewed Peer Reviewed
Volume 176
Article Number 103685
Keywords General Engineering; Mechanics of Materials; General Materials Science; Mechanical Engineering
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