Nonlinear scattering and mode conversion of Lamb waves at breathing cracks: An efficient numerical approach

This article presents an efficient numerical approach to the investigation of nonlinear scattering and mode conversion phenomena of Lamb waves as they interact with breathing cracks. A Local Interaction Simulation Approach (LISA) is adopted, which possesses the versatility to capture arbitrary damage profiles. The stick-slip contact dynamics is implemented in the LISA model via the penalty method, which captures the nonlinear interactions between Lamb waves and breathing cracks. The LISA framework achieves remarkable computational efficiency with its parallel implementation using Compute Unified Device Architecture (CUDA) executed on powerful GPUs. A small-size LISA model with absorbing boundaries is tailored for the purpose of extracting the Lamb wave scattering and mode conversion features. Due to the explicit parallel CUDA implementation and the small-size model setup, the computation is highly efficient. Numerical case studies on nonlinear scattering of Lamb waves from breathing cracks are given. Distinctive higher harmonic generation and selective mode conversion phenomena are presented using the complex-valued Wave Damage Interaction Coefficients (WDICs) containing both amplitude and phase information of the scattered wave field. The effect of oblique incident angle on nonlinear scattering phenomenon is investigated. The rough crack surface feature with initial openings and closures is also considered to better approximate fatigue cracks in practical engineering scenarios. In addition, the wave amplitude effect on the nonlinear scattering and mode conversion is studied. This research may provide guidelines for the effective design of sensor arrays utilizing nonlinear Lamb waves for fatigue crack detection.