finite elements; extended finite element method; piezoelectric materials; convergence; crack
Abstract :
[en] This paper presents an application of the extended finite element method (X-FEM) to the analysis of fracture in piezoelectric materials. These 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 X-FEM has been applied mostly to model cracks in structural materials. The present paper focuses at first on the definition of new enrichment functions suitable for cracks in piezoelectric structures. At second, generalized domain integrals are used for the determination of crack tip parameters. The approach is based on specific asymptotic crack tip Solutions, derived for piezoelectric materials. We present convergence results in the energy norm and for the stress intensity factors, in various settings. Copyright (C) 2008 John Wiley & Sons, Ltd.
Disciplines :
Mathematics Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Béchet, Eric ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Conception géométrique assistée par ordinateur
Scherzer, M.; 2Institut f¨ur Mechanik und Fluiddynamik, TU Bergakademie Freiberg, Lampadiusstraße 4, 09596 Freiberg, Germany
Kuna, M.; 2Institut f¨ur Mechanik und Fluiddynamik, TU Bergakademie Freiberg, Lampadiusstraße 4, 09596 Freiberg, Germany
Language :
English
Title :
Application of the X-FEM to the fracture of piezoelectric materials
Publication date :
2009
Journal title :
International Journal for Numerical Methods in Engineering
ISSN :
0029-5981
eISSN :
1097-0207
Publisher :
John Wiley & Sons, Inc, Chichester, United Kingdom
Moës N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering 1999; 46:131-150.
Osher S, Sethian JA. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics 1988; 79:12-49.
Bechet E, Minnebo H, Moës N, Burgardt B. Convergence and conditioning issues with x-fem in fracture mechanics. International Journal for Numerical Methods in Engineering 2005; 64:1033-1056.
Ji H, Chopp D, Dolbow JE. A hybrid extended finite element/levelset method for modeling phase transformations. International Journal for Numerical Methods in Engineering 2002; 54:1209-1233.
Song JH, Areias PMA, Belytschko T. A method for dynamic crack propagation and shear band propagation with phantom nodes. International Journal for Numerical Methods in Engineering 2006; 67:868-893.
Areias P, Song JH, Belytschko T. Analysis of fracture in thin shells by overlapping paired elements. Computer Methods in Applied Mechanics and Engineering 2006; 195:5343-5360.
Waisman H, Belytschko T. Parametric enrichment adaptivity by the extended finite element method. International Journal for Numerical Methods in Engineering 2008; 73:1671-1692.
Pak YE. Linear electro-elastic fracture mechanics of piezoelectric materials. International Journal of Fracture 1992; 54(1):79-100.
Scherzer M, Kuna M. Combined analytical and numerical solution of 2d interface corner configurations between dissimilar piezoelectric materials. International Journal of Fracture 2004; 127(1):61-99.
Zhang TY, Zhao M, Tong P. Fracture of piezoelectric ceramics. Advances in Applied Mechanics 2002; 38:147-289.
Kuna M. Finite element analyses of cracks in piezoelectric structures: a survey. Archives in Applied Mechanics 2006; 76:725-745.
Koy YL, Chiu KW, Marshall IH, Rajic N, Galea SC. Detection of disbonding in a repair patch by means of an array of lead zirconate titanate and polyvinylidene fluoride sensors and actuators. Smart Materials and Structures 2001; 10:946-962.
Suo Z, Kuo CM, Barnett DM, Willis JR. Fracture mechanics for piezoelectric ceramics. Journal of the Mechanics and Physics of Solids 1992; 40(4):739-765.
Sosa H. Plane problems in piezoelectric media with defects. International Journal of Solids and Structures 1991; 28(4):491-505.
Mußchelichwili NI. Einige Grundaufgaben zur mathematischen Elastizitaetstheorie. VEB Fachbuchverlag: Leipzig, 1971.
Savin GN. Distribution of Stresses at Holes (in Russian). Naukova Dumka: Kiew, 1968.
Landis CM. Energetically consistent boundary conditions for electromechanical fracture. International Journal of Solids and Structures 2004; 41:6291-6315.
Enderlein M, Ricoeur A, Kuna M. Finite element techniques for dynamic crack analysis in piezoelectrics. International Journal of Fracture 2005; 134:191-208.
Xu XL, Rajapakse RKND. Analytical solution for an arbitrarily oriented void/crack and fracture of piezoceramics. Acta Materialia 1999; 47(6):1735-1747.
Xu XL, Rajapakse RKND. On plane cracks in piezoelectric solids. International Journal of Solids and Structures 2001; 38:7643-7658.
Lekhnitskii SG. Theory of Elasticity of an Anisotropic Body. Mir: Moscow, 1981.
Pan E. A BEM analysis of fracture mechanics in 2d anisotropic piezoelectric solids. Engineering Analysis with Boundary Elements 1999; 23:67-76.
Babuska I, Melenk JM. The partition of unity method. International Journal for Numerical Methods in Engineering 1997; 40:727-758.
Strouboulis T, Babuska I, Copps K. The design and analysis of the generalized finite element method. Computer Methods in Applied Mechanics and Engineering 2000; 181:43-69.
Strouboulis T, Copps K, Babuska I. The generalized finite element method: an example of its implementation and illustration of its performance. International Journal for Numerical Methods in Engineering 2000; 47:1401-1417.
Belytschko T, Black T. Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering 1999; 44:601-620.
Moës N, Gravouil A, Belytschko T. Non-planar 3d crack growth by the extended finite element and level sets - part i: Mechanical model. International Journal for Numerical Methods in Engineering 2002; 53:2549-2568.
Sih GC, Liebowitz H. Fracture, an Advanced Treatise, vol. 2. Academic Press: London, U.K., 1968.
Bui HD. Mécanique de la rupture fragile. Masson: Paris, 1978.
Laborde P, Pommier J, Renard Y, Salaün M. High order extended finite element method for cracked domains. International Journal for Numerical Methods in Engineering 2005; 64:354-381.
Shih CF, Moran B, Nakamura T. Energy release rate along a three-dimensional crack front in a thermally stressed body. International Journal of Fracture 1986; 30:79-102.
Abendroth M, Groh U, Kuna U, Ricoeur A. Finite element-computation of the electromechanical J-Integral for 2-D and 3-D crack analysis. International Journal of Fracture 2002; 114:359-378.
Yau J, Wang S, Corton H. A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity. Journal of Applied Mechanics 1980; 47:335-341.
Gosz M, Moran B. An interaction energy integral method for computation of mixed-mode stress intensity factors along non-planar crack fronts in three dimensions. Engineering Fracture Mechanics 2002; 69:299-319.
Elguedj T, Gravouil A, Combescure A. Appropriate extended functions for x-fern simulation of plastic fracture mechanics. Computer Methods in Applied Mechanics and Engineering 2005; 195(7-8):501-515.
Wang X, Shen YP. Exact solution for mixed boundary value problems at anisotropic piezoelectric bimaterial interface and unification of various interface defects. International Journal of Solids and Structures 2002; 39:1591-1619.
