Computational Mechanics

, Volume 64, Issue 5, pp 1303–1319 | Cite as

The extended finite element method with novel crack-tip enrichment functions for dynamic fracture analysis of interfacial cracks in piezoelectric–piezomagnetic bi-layered structures

  • Z. Yan
  • W. J. FengEmail author
  • Ch. ZhangEmail author
  • J. X. Liu
Original Paper


This paper investigates the dynamic fracture problems of interfacial cracks in piezoelectric–piezomagnetic (PE–PM) bi-layered composite structures under in-plane coupled electro-magneto-mechanical impact loadings by means of the extended finite element method (X-FEM). Considering the magnetoelectrically impermeable crack-face conditions and multi-filed coupled properties in the PE–PM composites, novel and more suitable crack-tip enrichment functions for interfacial cracks in PE–PM bi-layered composite structures are newly derived and implemented in the X-FEM, where the Newmark method is applied and proved to be effective. As the fracture parameter, the J-integral is evaluated using the domain-form of the path-independent contour integral. For dynamic analysis of interfacial cracks in infinite PE–PM bi-layered composite structures, absorbing layers based on the Sarma absorbing boundary conditions are adopted and applied to avoid the unphysical wave reflections at the artificially introduced boundaries in the X-FEM meshes. In the numerical examples, the validity of the proposed scheme is verified by comparing the numerical solutions provided by the X-FEM with either analytical results obtained by solving the corresponding singular integral equations or possible stationary values obtained by introducing the corresponding absorbing layers. Finally, by the numerical examples, the effects of the applied dynamic loadings, time variable and structural geometries on the dynamic J-integral are analyzed and discussed in detail. Some important conclusions are drawn, which should be helpful for the design and applications of the PE–PM layered composite structures.


Extended finite element method Piezoelectric–piezomagnetic layered structures Interfacial crack Dynamic fracture J-integral 



This work was supported by the National Natural Science Foundation of China (Grant Nos. 11072160, 11572358 and 11272222), the General Research Fund of Hong Kong (HKU 17223916) and the German Research Foundation (DFG, Project No. ZH 15/14-1). Zhen Yan is also grateful to the financial support by the China Scholarship Council (CSC) for the Joint PhD Scholarship at the Chair of Structural Mechanics, University of Siegen, Germany.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Engineering MechanicsShijiazhuang Tiedao UniversityShijiazhuangPeople’s Republic of China
  2. 2.Department of Civil EngineeringUniversity of SiegenSiegenGermany

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