An extended consecutive-interpolation quadrilateral element (XCQ4) applied to linear elastic fracture mechanics

A novel extended 4-node quadrilateral finite element (XCQ4) based on a consecutive-interpolation procedure (CIP) with continuous nodal stress for accurately modeling singular stress fields near crack tips of two-dimensional (2D) cracks in solids is presented. In contrast to the traditional approaches, the approximation functions constructed based on the CIP involve both nodal values and averaged nodal gradients as interpolation conditions. Our objective is to exhibit a pioneering extension of the recently developed CQ4 element enhanced by enrichment to precisely model 2D elastic crack problems, taking advantages of the strengths and making use all the desirable features of both techniques, the CIP and the local enriched partition of unity method. The stress intensity factors (SIFs) are estimated using the interaction integral. The accuracy and performance of the proposed XCQ4 and its numerical properties are illustrated by numerical examples, considering both single and mixed-mode problems with complicated configurations. Compared with reference solutions available in the literature and the conventional XQ4 results, it is found that the accuracy of the XCQ4 is high. Studies on the convergence rate of the SIFs in relative errors also reveal a better performance of the XCQ4 over the classical XQ4. The fracture parameters are found to be stable for different areas of integration paths around the crack tip. Further applications of the developed XCQ4 to other complex problems are potential.