Unraveling SH Wave Harmonic Scattering in Layered Nonlinear Localized Damages

This study investigates higher harmonic generation in ultrasonic waves caused by localized early-stage damages, like dislocations, micro-cracks, etc. While existing research focused on uniformly distributed damage, this paper systematically explores harmonic scattering of SH waves from multiple local damages, modeled as a nonlinear material with linear regions. Finite element case studies, including monochromatic wave interaction, one-way two-wave mixing, and two-way two-wave mixing, reveal how damage size and arrangement affect harmonic responses. Odd harmonics are absent in back and forward scattered SH waves, while even harmonics and static terms are observed. Sum and difference frequency combinations, as well as odd and even harmonics due to wave mixing, are also demonstrated. Multiple local damages act as a metamaterial, influencing backscattered harmonic amplitudes during wave propagation. Notably, harmonically backscattered waves differ between a single local damage and two local nonlinear damages with the same total width, separated by a linear region. Harmonic energy trapping results in intriguing effects, offering insights for designing laboratory experiments and nonlinear metamaterials to control nonlinear ultrasonic waves.