Detection of multiple flaws in piezoelectric structures using XFEM and level sets

Abstract An iterative procedure to solve the inverse problem of detecting multiple voids in piezoelectric structure is proposed. In each iteration the forward problem is solved for various void configurations, and at each iteration, the mechanical and electrical responses of a piezoelectric structure is minimized at known specific points along the boundary to match the measured data. The Extended Finite Element method (XFEM) is employed for determining the responses as it allows the use of a fixed mesh for varying void geometries. The numerical method based on combination of classical shape derivative and of the level-set method for front propagation used in structural optimization is utilized to minimize the cost function. The results obtained show that this method is effectively able to determine the number of voids in a piezoelectric structure and its corresponding locations and shapes.

[1]  Zhenhan Yao,et al.  FEM analysis of electro-mechanical coupling effect of piezoelectric materials , 1997 .

[2]  Dan Givoli,et al.  XFEM‐based crack detection scheme using a genetic algorithm , 2007 .

[3]  Marc Duflot,et al.  Meshless methods: A review and computer implementation aspects , 2008, Math. Comput. Simul..

[4]  M. Kuna.  Finite element analyses of cracks in piezoelectric structures: a survey , 2006 .

[5]  Ted Belytschko,et al.  A finite element method for crack growth without remeshing , 1999 .

[6]  T. Rabczuk,et al.  Extended finite element method for dynamic fracture of piezo-electric materials , 2012 .

[7]  Timon Rabczuk,et al.  Detection of flaws in piezoelectric structures using extended FEM , 2013 .

[8]  Y. E. Pak,et al.  Linear electro-elastic fracture mechanics of piezoelectric materials , 1992 .

[9]  Meinhard Kuna,et al.  A cyclic viscoplastic and creep damage model for lead free solder alloys , 2010 .

[10]  Hehua Zhu,et al.  HIGH ROCK SLOPE STABILITY ANALYSIS USING THE ENRICHED MESHLESS SHEPARD AND LEAST SQUARES METHOD , 2011 .

[11]  I. Babuska,et al.  The partition of unity finite element method: Basic theory and applications , 1996 .

[12]  T. Belytschko,et al.  MODELING HOLES AND INCLUSIONS BY LEVEL SETS IN THE EXTENDED FINITE-ELEMENT METHOD , 2001 .

[13]  Haim Waisman,et al.  Detection and quantification of flaws in structures by the extended finite element method and genetic algorithms , 2010 .

[14]  Zhigang Suo,et al.  Fracture mechanics for piezoelectric ceramics , 1992 .

[15]  S.S. Udpa,et al.  Model-Based Inversion Technique Using Element-Free Galerkin Method and State Space Search , 2009, IEEE Transactions on Magnetics.

[16]  S. Osher,et al.  Algorithms Based on Hamilton-Jacobi Formulations , 1988 .

[17]  T. Rabczuk,et al.  A Meshfree Method based on the Local Partition of Unity for Cohesive Cracks , 2007 .

[18]  Hehua Zhu,et al.  A GENERALIZED AND EFFICIENT METHOD FOR FINITE COVER GENERATION IN THE NUMERICAL MANIFOLD METHOD , 2013 .

[19]  Arnold Neumaier,et al.  Global Optimization by Multilevel Coordinate Search , 1999, J. Glob. Optim..

[20]  Guillermo Rus,et al.  Optimal measurement setup for damage detection in piezoelectric plates , 2009 .

[21]  G. Allaire,et al.  Structural optimization using sensitivity analysis and a level-set method , 2004 .

[22]  Charles E. Augarde,et al.  A meshless sub-region radial point interpolation method for accurate calculation of crack tip fields , 2014 .

[23]  T. Belytschko,et al.  Analysis of three‐dimensional crack initiation and propagation using the extended finite element method , 2005 .

[24]  Hehua Zhu,et al.  An improved meshless Shepard and least squares method possessing the delta property and requiring no singular weight function , 2014 .

[25]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[26]  Ted Belytschko,et al.  Modelling crack growth by level sets in the extended finite element method , 2001 .

[27]  X. Zhuang,et al.  A continuous/discontinuous deformation analysis (CDDA) method based on deformable blocks for fracture modeling , 2013, Frontiers of Structural and Civil Engineering.

[28]  Meinhard Kuna,et al.  Application of the X‐FEM to the fracture of piezoelectric materials , 2009 .

[29]  N. Moës,et al.  Improved implementation and robustness study of the X‐FEM for stress analysis around cracks , 2005 .

[30]  H. Sosa.  Plane problems in piezoelectric media with defects , 1991 .

[31]  R.K.N.D. Rajapakse,et al.  Analytical solution for an arbitrarily oriented void/crack and fracture of piezoceramics , 1999 .

[32]  Barbara Kaltenbacher,et al.  PDE based determination of piezoelectric material tensors , 2006, European Journal of Applied Mathematics.

[33]  B. Kaltenbacher,et al.  FEM-Based determination of real and complex elastic, dielectric, and piezoelectric moduli in piezoceramic materials , 2008, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[34]  M. Kuna.  Fracture mechanics of piezoelectric materials – Where are we right now? , 2010 .

[35]  Michel Salaün,et al.  Study of Some Optimal XFEM Type Methods , 2007 .

[36]  Hao Tian-hu,et al.  A new electric boundary condition of electric fracture mechanics and its applications , 1994 .

[37]  Charles E. Augarde,et al.  Fracture modeling using meshless methods and level sets in 3D: Framework and modeling , 2012 .