Fracture of piezoelectric materials with the X-FEM
DOI:
https://doi.org/10.13052/REMN.17.637-649Keywords:
piezoelectric materials, crack, finite elements, X-FEMAbstract
We present an application of X-FEM to the fracture analysis of piezoelectric materials. These materials are increasingly used in actuators and sensors. 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 applied mostly to model cracks in structural materials. The present paper focuses on the definition of new enrichment functions suitable for cracks in piezolectric structures. The approach is based on specific asymptotic crack tip solutions, derived for piezoelectric materials.
Downloads
References
B´echet E., Minnebo H., Mo¨es N., Burgardt B., “ Convergence and conditioning issues
with X-FEM in fracture mechanics”, International Journal for Numerical Methods
in Engineering, vol. 64, p. 1033-1056, 2005.
B´echet E., Scherzer M., Kuna M., “ Application of the X-FEM to the fracture of piezoelectric
materials”, Submitted to International Journal for Numerical Methods in
Engineering, 2008.
Belytschko T., Black T., “ Elastic crack growth in finite elements with minimal
remeshing”, International Journal for Numerical Methods in Engineering, vol. 44,
p. 601-620, 1999.
Elguedj T., Gravouil A., Combescure A., “ Appropriate extended functions for XFEM
simulation of plastic fracture mechanics”, Computer Methods in Applied
Mechanics and Engineering, vol. 195, n°7-8, p. 501-515, 2005.
Mo¨es N., Dolbow J., Belytschko T., “ A finite element method for crack growth
without remeshing”, International Journal for Numerical Methods in Engineering,
vol. 46, p. 131-150, 1999.
Mußchelichwili N., Einige Grundaufgaben zur mathematischen Elastizitaetstheorie,
VEB Fachbuchverlag (Leipzig), 1971.
Osher S., Sethian J., “ Fronts propagating with curvature-dependent speed: algorithms
based on Hamilton-Jacobi formulations”, Journal of Computational
Physics, vol. 79, p. 12-49, 1988.
Scherzer M., Kuna M., “ Combined analytical and numerical solution of 2D interface
corner configurations between dissimilar piezoelectric materials”, International
Journal of Fracture, vol. 127, n°1, p. 61-99, 2004.
Sih G., Liebowitz H., Fracture,an advanced treatise, vol. 2, Academic Press, London,
UK, 1968.
Sosa H., “ Plane problems in piezoelectric media with defects”, International Journal
of Solids and Structures, vol. 28, n°4, p. 491-505, 1991.
Suo Z., Kuo C., Barnett D.,Willis J., “ Fracture mechanics for piezoelectric ceramics”,
Journal of the Mechanics and Physics of Solids, vol. 40, n°4, p. 739-765, 1992.