Crack analysis using numerical manifold method with strain smoothing technique and corrected approximation for blending elements

Although numerical manifold element (NMM) is particularly suitable for crack analysis, the accuracy of standard NMM on traditional triangular mesh is not good enough. On the one hand, the stiffness of NMM is overly stiff, leading to inferior results, similar to the linear triangular FEM models. On the other hand, blending elements induced issues have seldom been taken into account in the framework of NMM. In this paper, these two issues are separately addressed. For the first issue, the edge-based strain smoothing technique (originated from the ES-FEM, Liu et al., 2009) is tailored for crack analysis and incorporated to improve the accuracy of NMM (abbreviated as ES-NMM). In this way, the stiffness of NMM can be much softer and much more accurate results can be obtained without increasing the DOFs. To study the second issue, different kinds of enrichment schemes are considered, such as one-layer enrichment, two-layer enrichment and corrected enrichment (enlightened by corrected XFEM, Fries, 2008). A number of numerical examples are carried out to validate the effectiveness and accuracy of the present ES-NMM. It is found that, by taking advantages of ES-FEM, corrected XFEM and NMM, the corrected ES-NMM yields the most accurate results and thus is suggested.