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Mathematical Problems in Engineering
Volume 2015, Article ID 371083, 10 pages
Research Article

Cell-Based Smoothed Finite Element Method-Virtual Crack Closure Technique for a Piezoelectric Material of Crack

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

Received 17 December 2014; Revised 5 February 2015; Accepted 5 February 2015

Academic Editor: Timon Rabczuk

Copyright © 2015 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.


In order to improve the accuracy and efficiency of solving fracture parameters of piezoelectric materials, a piezoelectric element, tailored for the virtual crack closure technique (VCCT), was used to study piezoelectric materials containing a crack. Recently, the cell-based smoothed finite element method (CSFEM) and VCCT have been used to simulate the fracture mechanics of piezoelectric materials. A center cracked piezoelectric materials with different material properties, crack length, mesh, and smoothing subcells at various strain energy release rates are discussed and compared with finite element method-virtual crack closure technique (FEM-VCCT). Numerical examples show that CSFEM-VCCT gives an improved simulation compared to FEM-VCCT, which generally simulates materials as too stiff with lower accuracy and efficiency. Due to its simplicity, the VCCT piezoelectric element demonstrated in this study could be a potential tool for engineers to practice piezoelectric fracture analysis. CSFEM-VCCT is an efficient numerical method for fracture analysis of piezoelectric materials.