ECCOMAS 2024

An extended isogeometric boundary element formulation for three-dimensional crack growth analysis

  • Rocha, Matheus (University of São Paulo)
  • Leonel, Edson Denner (University of São Paulo)
  • Trevelyan, Jon (Durham University)

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The Isogeometric Boundary Element Method (IGABEM) is a suitable numerical approach for fracture mechanics, particularly crack growth analysis. Due to the boundary-only mesh of BEM, there is no need for domain re-meshing during crack propagation. Additionally, the direct coupling between BEM and the isogeometric approach eliminates the necessity for mesh generation, once it utilises the same CAD model basis functions for approximating mechanical fields. IGABEM has been successfully applied to elasto-statics [1] and fracture mechanics [2.3]. However, the analysis of three-dimensional crack propagation requires time-consuming post-processing to determine Stress Intensity Factors (SIFs). This study proposes the application of the eXtended Isogeometric Boundary Element Method (XIGABEM) for crack growth analysis, incorporating SIFs as unknowns for direct calculation. A numerical study on the enrichment zone length is conducted to account for its influence. Moreover, the crack growth direction follows the Schollman criterion, suitable for mixed I/II/III opening modes. Applications demonstrate robustness and accuracy of the XIGABEM in crack propagation analysis. [1] R. Simpson, S. Bordas, J. Trevelyan, T. Rabczuk, A two-dimensional isogeometric boundary element method for elastostatic analysis. Comp Meth in App Mech and Eng. Vol. 209-212, pp. 87-100,2012 [2] B.H. Nguyen, H.D. Tran, C. Anitescu, X. Zhuang, T. Rabczuk, An isogeometric symmetric Galerkin boundary element method for two-dimensional crack problems. Comp Meth in App Mech and Eng. Vol. 306, pp. 252-275,2016 [3] X. Peng, E. Atroshchenko, P. Kerfriden, S.P.A. Bordas, Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth. Comp Meth in App Mech and Eng. Vol. 316, pp. 151-185,2017