An enriched improved complex variable element-free Galerkin method for efficient fracture analysis of orthotropic materials

Abstract

The fracture problem of orthotropic materials has been widely concerned by researchers in the fields of mechanics and engineering. The meshless method using nodes to discrete the problem domain is an effective way to analyze cracked structures. In this paper, an enriched improved complex variable moving least squares (EICVMLS) approximation, in which a group of intrinsic enrichments is introduced into the conventional ICVMLS adopting a well-defined weighted complex variable error norm, is proposed for capturing the crack-tip fields in orthotropic media accurately. Then, an enriched improved complex variable element-free Galerkin (EICVEFG) method is developed to simulate fracture behavior in orthotropic media. The visibility criterion is used to model the discontinuity behavior around cracks and the M−integral is considered to evaluate stress intensity factor (SIF). The stress field and the displacement field at the crack tip, the SIF for different crack inclinations, and different directions of orthotropy axes are investigated to verify the validity of the proposed method. In addition, the effects of linear basis functions and enriched basis functions on the results are compared in this study. The numerical results reveal that the established EICVEFG approach can achieve higher accuracy than the extended finite element method (XFEM) and traditional meshless methods such as the element-free Galerkin (EFG) method and the meshless finite volume (MFV) method. Similarly, the EICVEFG method has been proved to offer a higher convergence rate by parameter studies (including dimensionless factor dmax, integral size, and the number of integral cells in M−integral).