8. Bridging Scales Analysis of Wave Propagation in Heterogeneous Structures with Imperfections

The analysis of wave propagation has been extensively used as a tool for non destructive evaluation of structural components. The numerical analysis of wavefield in damaged media can be useful to investigate the problem theoretically and to support the interpretation of experimental measurements. A finite element analysis of non homogeneous media can be computationally very expensive, especially when a fine mesh is required to properly model the geometric and/or material discontinuities that are characteristic of the damaged areas. The computational cost associated with wave propagation simulations motivates the development of the simplified damage models presented in Chaps.​ 6 and 7. This chapter presents a different approach whereby the computational cost is reduced through a multi-scale analysis. A coarse mesh is employed to capture the macroscopic behavior of the structure, and a refined mesh is limited to the small region around the discontinuity. The co-existence of two scales in the model is handled through the application of proper bridging relations between the two scales, and the generation of interaction forces at the interfaces according to the Bridging Scales Method. This technique allows a coarse description of the global behavior of the structure while simultaneously obtaining local information regarding the interaction of propagating waves with a localized discontinuity in the domain. Time and frequency domain formulations of the Bridging Scales Method are illustrated through examples on simulations of 1D and 2D waveguides.