New crack front enrichment for XFEM modeling

The extended finite element method (XFEM) using a new crack front enrichment is proposed for the crack modeling in this study. The discontinuity of displacement in the element including the crack tip or front is modeled by combining the Heaviside function with a step function. The proposed enrichment scheme avoids the calculation of the geometrical characteristic lengths in the element containing the crack tip or front when using the Ramp function, and the step function only depending on the level set function is defined to activate the discontinuity. Thus, both two dimensional (2D) and three dimensional (3D) cracks can be modeled more effectively by the new crack front enrichment. The Conjunction Gradient Method (CGM) that can reduce the burden of storage and manipulation is utilized to solve the global linear algebraic system of 3D XFEM. In addition, two kinds of 3D variable-node elements are used to connect the coarse and fine elements to save the number of nodes and elements. The Westergaard's crack problem is analyzed to test the convergence rate of the proposed method, and it is found that the new crack front enrichment can match the theoretical convergence rate of the finite element method (FEM) in the presence of a dominant V r -singularity. The proposed method is applied to determine the stress intensity factors (SIFs) of straight, inclined, edge and curved cracks. Comparing with the reference solutions demonstrates that the proposed crack front enrichment exhibits significant advantages for the 3D crack modeling.