On enrichment strategies and methods to extract stress intensity factors using extended finite element method for bimaterials

Abstract

The eXtended Finite Element Method (X-FEM) is a versatile tool to model cracks and interfaces where sharp gradients and even discontinuity of deformation across the interface may occur. The enrichment functions are introduced to depict possible discontinuity and singularity known from analytical solutions. For bimaterials, the gradients of the displacements are discontinuous across the interface, which can be modeled by ramp functions. In this work, we check the role of the enrichment strategies with and without ramp functions for the accuracy of enriching schemes, and also compare three different methods, i.e. the Interaction Integral Method (IIM), Contour Integration Method (CIM), and Displacement Correlation Method (DCM), to extract the Stress Intensity Factors (SIFs). Both planar and non-planar examples are employed to examine the enriching strategies and the three SIF extraction methods. We find that the enriched ramp functions can improve the accuracy in terms of strain energy, but do not significantly affect the SIFs. The IIM is the best choice to extract SIFs and the DCM can provide enough accuracy with a careful choice of extraction parameters. This work can help a reader when choose the enriching strategies and the extraction methods of the SIFs for interface cracks between dissimilar materials.