Computational stress formulation for ultrasonic wave dispersion and attenuation in polycrystalline materials

Ultrasonic wave propagation in polycrystalline materials is governed by grain scattering, which causes frequency-dependent attenuation and dispersion that are directly linked to the underlying microstructure. Accurate numerical modeling of these phenomena is essential for nondestructive evaluation (NDE) and materials characterization, yet traditional displacement-based finite difference (FD) methods face numerical challenges at grain boundaries due to spatial derivatives of the stiffness tensor. We present a stress-based FD formulation that reformulates the elastodynamic equations in terms of stress components only, eliminating stiffness spatial derivatives and naturally enforcing traction continuity at grain boundaries. The formulation is implemented with GPU acceleration and validated against theoretical predictions based on the Von Kármán correlation function for aluminum, iron, and lithium polycrystals. The results demonstrate good agreement within the investigated frequency range for both attenuation and phase velocity dispersion, with normalized results revealing material-dependent scattering behavior. The formulation is further extended to coupled fluid-solid systems, demonstrating accurate attenuation predictions in immersion-based NDE configurations. Compared to displacement-based methods, the stress-based approach offers improved numerical stability, a 39% reduction in GPU memory usage, and a unified treatment of fluid-solid coupling through a single primary variable.