Multiple cracks identification for piezoelectric structures

We propose a novel iterative procedure to solve the inverse problem of detecting multiple cracks in two-dimensional piezoelectric structures under dynamic electric loads. The effect of dynamic electric loads and a time-harmonic excitation with a single frequency is investigated. The crack is detected through the solution of an inverse time-dependent problem. The 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 crack geometries. The Newmark-beta method is employed for the time integration. In each iteration the forward problem is solved for various crack geometries, and at each iteration, the mechanical and electrical response of the piezoelectric structure is minimized at known specific points along the boundary to match the measured data. The minimization of the objective 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 under the dynamic electric load is applied to two-dimensional electromechanical problems where different number of straight cracks are considered. The results show that this methodology can be effectively employed for detecting multiple cracks in piezoelectric materials.