Analytical and numerical modeling of non-collinear wave mixing due to material and interface nonlinearity

Previous research established a nonlinear stiffness model for imperfect interfaces and analyzed non-collinear wave mixing at such interfaces for two incident shear waves. This study extends those results to encompass five possible non-collinear wave mixing modalities involving longitudinal and shear vertical waves, considering both material and interfacial nonlinearities. By simultaneously applying the conditions for both bulk resonance and interface phase-matching, the two required incident wave angles are determined, allowing the mixing efficiency to be directly characterized by the frequency ratio. The analytical predictions for both types of nonlinearities are numerically validated using COMSOL finite element simulations. Quantitative comparisons across different wave mixing scenarios reveal the relative contributions of material and interface nonlinearity. These findings offer valuable insights and guidelines for designing and interpreting future experimental studies involving non-collinear ultrasonic wave mixing.