Fatigue growth modelling of three-dimensional cracks with the Extended Isogeometric Boundary Element Method

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

Abstract

This paper proposes the fatigue crack growth modelling of three-dimensional geometries with the eXtended Isogeometric Boundary Element Method (XIGABEM). The formulation combines the advantages of the dual Boundary Element Method (BEM), the isogeometric approach, and an enrichment strategy for surfaces containing the crack front. The dual BEM approach relies on a boundary-only mesh, eliminating a re-meshing task for internal cracks. The isogeometric approach applies NURBS basis functions to describe both geometry and mechanical fields, allowing accurate representation of curved shapes and improving convergence over classical polynomial functions. The enrichment strategy stems from the Williams expansion of displacements at the crack front, with parameters directly interpolating Stress Intensity Factors (SIFs), removing costly post-processing tasks. The hoop stress criterion and Schollmann criterion are used as crack growth criteria and are combined with a novel least squares strategy to define the updated crack front. Since this study addresses multi-patch discretisation of crack surfaces, additional strategies ensure continuity between patches as required by the enrichment field. Three numerical applications demonstrate the ability of the formulation to model fatigue in curved 3D geometries under various loading conditions, allowing a novel comparison between crack growth criteria.

Citation

Rocha, M., Trevelyan, J., & Leonel, E. D. (2025). Fatigue growth modelling of three-dimensional cracks with the Extended Isogeometric Boundary Element Method. Engineering Analysis with Boundary Elements, 177, Article 106263. https://doi.org/10.1016/j.enganabound.2025.106263

• Journal Article Type: Article
• Acceptance Date: Apr 5, 2025
• Online Publication Date: May 5, 2025
• Publication Date: 2025-08
• Deposit Date: Apr 14, 2025
• Publicly Available Date: May 12, 2025
• Journal: Engineering Analysis with Boundary Elements
• Print ISSN: 0955-7997
• Electronic ISSN: 1873-197X
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 177
• Article Number: 106263
• DOI: https://doi.org/10.1016/j.enganabound.2025.106263
• Public URL: https://durham-repository.worktribe.com/output/3790471