Wave propagation in highly anisotropic polycrystals: a numerical perspective from an unstructured-mesh-based high-order finite element method

Ultrasonic non-destructive testing provides an important means to characterize grain size and orientation distribution of polycrystalline materials. Analytical and numerical modeling of ultrasound propagation offer an insight into how ultrasound interacts with polycrystalline materials. However, in highly anisotropic polycrystals, there is still no mature and accurate analytical formulation to describe the strong wave scattering, while the numerical modeling often relies on extremely dense structured meshes to conform to the grain boundary. This study proposes to use a high-order unstructured mesh with added internal nodes to obtain diagonal mass matrices, in order to accurately model wave propagation in strongly anisotropic polycrystals with complex grain boundary. Firstly, polycrystalline geometry was constructed with the Voronoi-based tessellation. Then an explicit dynamics solution was to simulate ultrasonic propagation with the improved element and several typical structured and unstructured elements. The influence of mesh type on calculation accuracy and convergence rate shows that the improved high-order mass-lumped elements, by retaining the true geometry of grain boundaries with unstructured meshes, significantly enhance both computational efficiency and accuracy. Lastly, the simulated results of ultrasonic attenuation and phase velocity in polycrystals show good agreement with both modified analytical models and results obtained with structured meshes. This confirms the effectiveness of the proposed high-order mass-lumped unstructured meshes for accurately simulating wave propagation in polycrystals for the characterization of grain features.