Global-Local model for guided wave scattering problems with application to defect characterization in built-up composite structures

Predicting scattering of elastic guided waves in multi-layered solid plates with geometrical and/or material discontinuities is of great interest to many fields, including ultrasonic-based Non-Destructive Testing (NDT) and health monitoring of critical structural components (SHM). The problem is complicated by the multimode and dispersive behaviour of the guided waves. This paper describes a unified Global-Local (GL) approach that is computationally efficient in cases that can be very complex in terms of geometry and/or material properties. One example of this is a composite built-up structure. The proposed GL procedure discretizes the “local” region with the scattering discontinuity by regular finite elements, and utilizes the efficient Semi-Analytical Finite Element solutions in the “global” region away from the scatterer. The GL formulation that is presented includes the dispersive unforced solutions for each applicable mode, the mode tracking, the scattered spectra (reflection and transmission), and the energy balance calculations. The algorithm is applied to the case of a composite skin-to-stringer assembly used in modern aircraft construction. Various representative defects in this assembly are modelled, and transmission spectra are calculated for both axial or flexural guided wave modes used in excitation. The resulting scattered spectra (which are the broadband transfer functions of the structure) can be useful to either select suitable wave mode-frequency combinations or to identify specific defects in guided-wave NDT or SHM tests of these components.