A macro-element strategy based upon spectral finite elements and mortar elements for transient wave propagation modeling. Application to ultrasonic testing of laminate composite materials

Proposing efficient numerical modeling tools for high-frequency wave propagation in realistic configurations, such as the one appearing in ultrasonic testing experiments, is a major challenge, especially in the perspective of inversion loops or parametric studies. We propose a numerical methodology addressing this challenge and based upon the combination of the spectral finite element method and the mortar element method. From a prior decomposition of the scene of interest into macro-elements, we show how one can improve the performances of the standard finite element procedures in terms of memory footprint and computational load. Additionally, using this decomposition, we are able to efficiently reconstruct important modeling features on-the-fly, such as orientations of anisotropic materials or splitting directions of perfectly matched layers formulations, altogether in a robust and efficient manner. We believe that this strategy is particularly suitable for parametric studies and sensitivity analysis. We illustrate our strategy by simulating the propagation of an ultrasonic wave into an immersed and curved anisotropic laminate 3D specimen flawed with an internal circular delamination of varying size, thus showing the efficiency and the robustness of our approach.