13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- 6. Conclusions Transient dynamic crack problems in piezoelectric thin structures are considered. Two methods are presented to deal with the nearly singular problems in the Laplace domain fundamental solutions. The first method for quadratic element is semi-analytical and the second method for straight line element is analytical. Static stress intensity factor of a piezoelectric plate is obtained for different structural dimensions. The results have been compared with FEM results and the agreement verifies the accuracy of the present methods. Then cracks in thin structures are considered, normalized intensity factors of both static and dynamic cases are obtained. The results indicate that the two methods function well when the ratio of the film thickness to the crack length is as small as 10-6 which is sufficient for modeling many thin piezoelectric films and coatings. Acknowledgements This work is supported by the Natural Science Foundation of China under Grant No. 11002006 and the German Research Foundation (DFG) under the project number ZH 15/6-1 and ZH 15/6-3, which are gratefully acknowledged. References [1] F. García-Sánchez, C.H. Zhang, A. Sáez, 2-D transient dynamic analysis of cracked piezoelectric solids by a time-domain BEM. Comput. Methods Appl. Mech. Engrg., 197 (2008) 3108–3121. [2] Y.J. Liu, H. Fan, Analysis of thin piezoelectric solids by the boundary element method. Comput. Methods Appl. Mech. Engrg., 191 (2002) 2297–2315. [3] C.Y. Wang, C.H. Zhang, 3-D and 2-D dynamic Green’s functions and time-domain BIEs for piezoelectric solid. Engineering Analysis with Boundary Elements, 29 (2005) 454–465. [4] J.F. Luo, Y.J. Liu, E.J. Berger, Analysis of two-dimensional thin structures (from micro- to nano-scales) using the boundary element method. Computational Mechanics, 22 (1998) 404–412. [5] Z.J. Cao, Z.B. Kuang, A finite element modeling for directly determining intensity factors of piezoelectric materials with cracks. Int J Fract, 149 (2008) 67–85.
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