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

• An algorithm to detect multiple flaw location in a piezoelectric specimen is proposed.
• XFEM is used to solve the direct problem, so remeshing in each iteration is avoided.
• The shape derivative and level sets are used to minimize the objective function.
• An adjoint problem is solved in each iteration to determine the shape derivative.

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.