Extended spectral element formulation for modeling the propagation of nonlinear ultrasonic waves produced by multiple cracks in solid media

This study presents a novel time-domain extended spectral element method (TD-XSEM) that can efficiently and accurately simulate interactions between ultrasonic waves and multiple randomly distributed and oriented cracks in solid materials. Compared to the conventional TD-SEM, which excels at large-scale structures but struggles with small discontinuities and contact issues, our TD-XSEM integrates linear finite elements to model these challenges effectively. Moreover, it preserves the efficiency of spectral elements in intact regions. Our unique frictional contact formulation employs the Heaviside function in discontinuous elements with enriched corner nodes. Rigorous validation against interactions of longitudinal waves with randomly distributed and oriented cracks shows superior convergence and accuracy of TD-XSEM. The proposed approach is further applied to capture second harmonic Lamb wave propagation and mixing bulk wave phenomena, demonstrating its feasibility and robustness in modeling complex interactions between ultrasonic waves and multiple random cracks. Implemented in C, TD-XSEM offers unprecedented accuracy and geometric flexibility in analyzing contact acoustic nonlinearity owing to multiple frictional cracks, contributing to the field of non-destructive testing. This study establishes a new framework for efficient and accurate wave-crack interaction simulations in complex solid structures.