An extended isogeometric boundary element formulation for three-dimensional linear elastic fracture mechanics

Rocha, Matheus; Trevelyan, Jon; Leonel, Edson Denner

Abstract

This paper presents a novel extended isogeometric boundary element formulation (XIGABEM) for three-dimensional linear elastic fracture mechanics. The formulation utilises the Dual BEM to accommodate coincident geometries for opposing crack surfaces, and inherits the well-known advantages of the NURBS basis as other isogeometric implementations. The originality herein involves the extension of the above-mentioned scheme to 3D using enrichment functions derived from asymptotic solutions for near-field crack tip displacements, in which Williams’ expansions are used on the crack surfaces and on the boundaries crossed by the crack front. Besides, Heaviside functions enrich external boundaries and allow the displacement discontinuity modelling. As with most enriched formulations, additional degrees of freedom are introduced; novel strategies are presented for the generation of auxiliary equations to recover a square system. Another key element of the proposed scheme is that the stress intensity factors are recovered directly from the solution vector and no post processing is required. Four applications demonstrate the formulation robustness, with results of models having comparatively few degrees of freedom comparing well against classical and other published results.

Citation

Rocha, M., Trevelyan, J., & Leonel, E. D. (2024). An extended isogeometric boundary element formulation for three-dimensional linear elastic fracture mechanics. Computer Methods in Applied Mechanics and Engineering, 423, Article 116872. https://doi.org/10.1016/j.cma.2024.116872

• Journal Article Type: Article
• Acceptance Date: Feb 20, 2024
• Online Publication Date: Feb 26, 2024
• Publication Date: Apr 1, 2024
• Deposit Date: Feb 21, 2024
• Publicly Available Date: Feb 26, 2024
• Journal: Computer Methods in Applied Mechanics and Engineering
• Print ISSN: 0045-7825
• Electronic ISSN: 1879-2138
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 423
• Article Number: 116872
• DOI: https://doi.org/10.1016/j.cma.2024.116872
• Public URL: https://durham-repository.worktribe.com/output/2271742