Detection of flaws in piezoelectric structures using extended FEM

An iterative method to treat the inverse problem of detecting cracks and voids in two-dimensional piezoelectric structures is proposed. The method involves solving the forward problem for various flaw configurations, and at each iteration, the response of piezoelectric material is minimized at known specific points along the boundary to match measured data. Extended finite element method (XFEM) is employed for solving the forward problem as it allows the use of a single regular mesh for a large number of iterations with different flaw geometries. The minimization of cost function is performed by multilevel coordinate search (MCS) method. The algorithm is an intermediate between purely heuristic methods and methods that allow an assessment of the quality of the minimum obtained and is in spirit similar to the direct method for global optimization. In this paper, the XFEM-MCS methodology is applied to two-dimensional electromechanical problems where flaws considered are straight cracks and elliptical voids. The results show that this methodology can be effectively employed for damage detection in piezoelectric materials.