Open Access

ARTICLE

Fracture & Fatigue Analyses: SGBEM-FEM or XFEM? Part 2: 3D Solids

Leiting Dong^1,2, Satya N. Atluri^1,3

1 Center for Aerospace Research & Education, University of California, Irvine
2 Department of Engineering Mechanics, Hohai University
3 Distinguished Adjunct-Professor of Multi-Disciplinary Engineering and Computer Science, King Abdulaziz University, Saudi Arabia

Computer Modeling in Engineering & Sciences 2013, 90(5), 379-413. https://doi.org/10.3970/cmes.2013.090.379

Abstract

The SGBEM-FEM alternating method is compared with the recently popularized XFEM, for analyzing mixed-mode fracture and fatigue growth of 3D nonplanar cracks in complex solid and structural geometries. A large set of 3D examples with different degrees of complexity is analyzed by the SGBEM-FEM alternating method, and the numerical results are compared with those obtained by XFEM available in the open literature. It is clearly shown that: (a) SGBEM-FEM alternating method gives extremely high accuracy for the stress intensity factors; but the XFEM gives rather poor computational results, even for the most simple 3D cracks; (b) while SGBEM-FEM alternating method requires very coarse meshes, which are independent of each other, for both the uncracked solid as well as the non-planar crack-surface, XFEM requires, on the other hand, an extremely fine mesh for 3D solids, which can sometimes be un-usable on a normal PC; (c) the SGBEM-FEM alternating method requires very minimal computational as well as human-labor costs for modeling the non-planar fatigue growth of 3D cracks; on the other hand, fatigue analysis by XFEM requires intensive computational as well as human-labor costs even for the most simple problems; (d) because of the very poor accuracy for the stress intensity factors as computed by XFEM, the number fatigue cycles for crack-growth and failure as predicted by XFEM are meaningless for the most part, even for the most simple 3D problems computed even with extremely fine meshes; (e) with very low computational as well as human-labor costs, the SGBEM-FEM alternating method can very accurately model complex 3D cracked-solids easily, even for those cases which are too complex to be solved by XFEM . It is thus concluded that the SGBEM-FEM alternating method, among the many alternating methods developed in the past 20-30 years by Atluri and his many collaborators, are far more efficient, far more accurate, and far more reliable than XFEM for analyzing fracture and 3D non-planar fatigue crack propagation in complex structures. The implementation of the SGBEM-related method as presented in this study, as well as those presented in its companion Part 1 [Dong and Atluri (2013b)], in general-purpose off-the-shelf commercial software, is greatly valuable and is thus being pursued by the authors.

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