Detection of multiple flaws in Piezoelectric Structures using XFEM and Level sets S.S.Nanthakumar a T.Lahmer a T. Rabczuk a,b,∗ a Institute of Structural Mechanics, Bauhaus-University Weimar,Marienstr. 15, D-99423 Weimar Germany. b School of Civil, Environmental and Architectural engineering, Korea University, Seoul, Korea. Abstract An iterative procedure to solve the inverse problem of detecting multiple voids in piezoelec- tric 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 piezoelec- tric structure is minimized at known specific points along the boundary to match measured data. The extended finite element method (XFEM) is employed for determining the re- sponses 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. Key words: Inverse problem, XFEM, level set method, Piezoelectric ceramics 1 Introduction Piezoelectric materials deform when subjected to an electric field and produce an electric field when stressed. This intrinsic coupling behavior of piezoelectric ma- terials has attracted wide applications in electro-mechanical and electronic devices such as electro-mechanical actuators, sensors and transducers. In general, some ∗ Corressponding Author Email addresses: nanthakumar.srivilliputtur.subbiah@uni-weimar.de (S.S.Nanthakumar), tom.lahmer@uni-weimar.de (T.Lahmer), timon.rabczuk@uni-weimar.de (T. Rabczuk). Preprint submitted to Elsevier 31 January 2014