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Advances in Materials Science and Engineering
Volume 2016, Article ID 4125307, 14 pages
Research Article

A Cell-Based Smoothed XFEM for Fracture in Piezoelectric Materials

School of Mechanical Science and Engineering, Jilin University, Changchun 130025, China

Received 29 July 2015; Revised 23 November 2015; Accepted 9 December 2015

Academic Editor: Bert Blocken

Copyright © 2016 Li Ming Zhou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents a cell-based smoothed extended finite element method (CS-XFEM) to analyze fractures in piezoelectric materials. The method, which combines the cell-based smoothed finite element method (CS-FEM) and the extended finite element method (XFEM), shows advantages of both methods. The crack tip enrichment functions are specially derived to represent the characteristics of the displacement field and electric field around the crack tip in piezoelectric materials. With the help of the smoothing technique, integrating the singular derivatives of the crack tip enrichment functions is avoided by transforming interior integration into boundary integration. This is a significant advantage over XFEM. Numerical examples are presented to highlight the accuracy of the proposed CS-XFEM with the analytical solutions and the XFEM results.