A numerical study of singular stress field of 3D cracks
Finite Elements in Analysis and Design
Computer Aided Geometric Design
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Polygonal elements are very attractive in many aspects, e.g., (a) they provide greater flexibility in mesh generation; (b) they have less sensitivity to lock under volume-preserving deformation states; (c) they are suitable for material design and modeling of polycrystalline materials (Sukumar and Tabarraei (2004) [21]). In the present paper, the numerical manifold method (NMM), combined with Wachspress-type honeycomb elements, is applied to solve 2-D elastostatic crack problems. Due to the use of two cover systems, that is, the mathematical cover system and the physical cover system, the NMM can naturally manifest displacement discontinuity across the crack surface; in addition, by the proper choice of cover functions, the NMM can accurately represent the gradient singularity around the crack tip. Through the domain form of the interaction integral, stress intensity factors are extracted for several typical examples and the results show that the NMM on honeycomb elements bears high accuracy and efficiency for crack problems.