XFEM with partial Heaviside function enrichment for fracture analysis

Abstract

In this work, an extended finite element method with partial Heaviside function enrichment (XFEM-P) in the crack tip element is proposed for fracture analysis for the first time. In this method, the crack tip element is divided into cracked and uncracked domains naturally by the crack geometry. In the cracked domain, Heaviside function enrichment is employed to simulate the crack discontinuity across the crack surface. In the uncracked domain, the displacement from standard finite element method is employed. Ramp function is used to ensure the displacement continuity in the method. Through this way, the crack tip can be arbitrarily located inside the crack tip element, which is a great advantage over traditional counterpart, i.e., XFEM with only Heaviside function enrichment (XFEM-H). Thus the mesh work for the XFEM-P is much easier than that of the XFEM-H, resulting in great conveniences for crack propagation. The new method is applied to several examples. From the computed results, it is observed that the XFEM-P offers more accurate results than the XFEM-H in terms of strain energy and SIFs. The XFEM-P performs better than XFEM-H in numerical properties such as convergence rate and condition number.