Some Numerical Studies with X-FEM for Cracked Piezoelectric Media

  • Éric Béchet
  • Meinhard Kuna
Conference paper
Part of the IUTAM Bookseries book series (IUTAMBOOK, volume 24)


Piezoelectric materials are increasingly used in actuators and sensors. New applications can be found as constituents of smart composites for adaptive electromechanical structures. Under in service loading, phenomena of crack initiation and propagation may occur due to high electromechanical field concentrations. In the past few years, the extended finite element method (X-FEM) has been gained much attention to model cracks in structural materials. This paper presents the application of X-FEM to the coupled electromechanical crack problem in two-dimensional piezoelectric structures. The convergence of solutions is investigated in the energy norm and for the stress intensity factors. Then, some studies about inaccuracies in the stresses near the crack tip are reported.


Stress Intensity Factor Piezoelectric Material Enrichment Function Isotropic Elasticity Conventional Finite Element 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Babuska I, Melenk JM (1997) The partition of unity method. Int J Numer Method Eng 40:727–758MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Béchet E, Scherzer M, Kuna M (2009) Application of the x-fem to the fracture of piezoelectric materials. Int J Numer Method Eng 77(11):1535–1565zbMATHCrossRefGoogle Scholar
  3. 3.
    Béchet E, Minnebo H, Moës N, Burgardt B (2005) Convergence and conditioning issues with x-fem in fracture mechanics. Int J Numer Method Eng 64:1033–1056zbMATHCrossRefGoogle Scholar
  4. 4.
    Chen YH, Hasebe N (2005) Current understanding on fracture behavior of ferroelectric / piezoelectric materials. J Intel Mater Syst Struct 16:673–687CrossRefGoogle Scholar
  5. 5.
    Elguedj T, Gravouil A, Combescure A (2005) Appropriate extended functions for x-fem simulation of plastic fracture mechanics. Comput Method Appl Mech Eng 195(7-8):501–515Google Scholar
  6. 6.
    Koy YL, Chiu KW, Marshall IH, Rajic N, Galea SC (2001) Detection of disbonding in a repair patch by means of an array of lead zirconate titanate and polyvinylidene fluoride sensors and actuators. Smart Mater Struct 10:946–962CrossRefGoogle Scholar
  7. 7.
    Kuna M (2006) Finite element analyses of cracks in piezoelectric structures: A survey. Arch Appl Mech 76:725–745zbMATHCrossRefGoogle Scholar
  8. 8.
    Kuna M (2010) Fracture mechanics of piezoelectric materials – Where are we right now? Eng Fract Mech 77:309–326CrossRefGoogle Scholar
  9. 9.
    Moës N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Method Eng 46:131–150zbMATHCrossRefGoogle Scholar
  10. 10.
    Osher S, Sethian JA (1988) Fronts propagating with curvature-dependent speed: Algorithms based on hamilton-jacobi formulations. J Comput Phys 79:12–49MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Scherzer M, Kuna M (2004) Combined analytical and numerical solution of 2d interface corner configurations between dissimilar piezoelectric materials. Int J Fract 127(1):61–99zbMATHCrossRefGoogle Scholar
  12. 12.
    Zhang TY, Zhao M, Tong P (2002) Fracture of piezoelectric ceramics. Adv Appl Mech 38:147–289CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of Aerospace and Mechanical EngineeringUniversité de LiégeLiégeBelgium
  2. 2.Institut für Mechanik und FluiddynamikTechnische Universität Bergakademie FreibergFreibergGermany

Personalised recommendations