A coupled extended meshfree–smoothed meshfree method for crack growth simulation

Abstract A coupled extended meshfree–smoothed meshfree method (CXSMM) is presented for simulating crack growth in 2D solids. In terms of the relationship between the crack surface and the background integration cells, the analysis domain is easy to be divided into discontinuous and continuous regions, in which the meshfree Galerkin method and the smoothed meshfree method are employed to construct the discretized system equations, respectively. To precisely capture the singular stress field near the crack tip, higher order Gauss integration rules are used in the discontinuous region. At the same time, the general smoothed strain technique is utilized in the continuous region for efficient evaluation of the domain integration. In this work, the initiation and propagation of the crack are treated by the aid of the level set algorithm. The CXSMM has the advantages of both extended meshfree method and smoothed meshfree method and can accurately and efficiently model the linear elastic fracture. Several benchmark problems are used to evaluate the accuracy, efficiency and robustness of the proposed method.