Fracture & Fatigue Analyses: SGBEM-FEM or XFEM? Part 1: 2D Structures

In this paper, and its companion Part 2 [Dong and Atluri (2013b)], the Symmetric Galerkin Boundary Element Method (SGBEM), and the SGBEMFEM alternating/coupling methods, are compared with the recently popularized Extended Finite Element Method (XFEM), for analyzing fracture and fatigue crack propagation in complex structural geometries. The historical development, and the theoretical/algorithmic formulations, of each method are succinctly reviewed. The advantages and disadvantages of each method are critically discussed. A comprehensive evaluation of the performances of the SGBEM-based methods, and their comparison with XFEM, in modeling cracked solid structures undergoing fatigue crack-growth is carried out. A thorough examination of a large set of numerical examples of varying degrees of complexity shows that, the SGBEM-based methods: (a) are far more accurate than XFEM for computing stress intensity factors, and thus the fatigue-crack-growth-rates; (b) require significantly coarser and lower-quality meshes than in XFEM, and thus result in significant savings of computational costs, and more importantly in considerable savings of the human-labor-costs of generating meshes; (c) require minimal effort for modeling the non-collinear/non-planar propagation of cracks under fatigue, without using the Level Set or Fast Marching methods to track the crack surface; (d) can easily perform fracture and fatigue analysis of complex structures, such as repaired cracked structures with composite patches, and damage in heterogeneous materials. It is thus concluded that the SGBEM-based methods, and alternating methods, which were developed over the past 20-30 years by Atluri and his many collaborators, are by far the best methods for analyzing fracture and non-planar fatigue crack propagation in complex structures, and are thus valuable for inclusion in general-purpose, off-the-shelf commercial software for structural analyses. This objective is pursued by the authors.