Bisection Method Based Technique for Analyzing Semipermeable Cracks in a Piezoelectric Material Using XFEM
摘要
This study focuses on the analysis of semipermeable cracks in piezoelectric materials using the extended finite element method (XFEM). A bisection method (BM) based iterative scheme is employed to achieve convergence of the electric displacement across the crack surfaces. This approach requires fewer iterations in comparison to the existing iterative capacitor analogy (ICA) approach, thereby reducing the overall computational cost. An interaction integral-based formulation is adopted to evaluate the electric displacement intensity factor. The accuracy and robustness of the proposed methodology are verified through benchmark problems, including center, edge, and double-edge cracks, and further validated through comparisons with both analytical and ICA-based results. Considering the computational efficiency of the BM approach, the study extends to macro-micro crack interaction analyses, considering various spatial configurations of micro-crack arrays and their influence on the crack-face electric displacement and intensity factors at the macro-crack tip. The results reveal alternating amplification and shielding effects depending on the positioning and density of micro-cracks, with horizontal arrays exhibiting stronger interactions than vertical ones. Additionally, the intensity factor results obtained using the BM approach show good agreement with those derived from the ICA method.