Evolution of Wave Propagation in Two-Dimensional Hexagonal Packed Granules with Defects

A two-dimensional hexagonal packed granules wave propagation model with defects is established by using the discrete element method (DEM) and studied under the impact load. The effect of defects on wave propagation is analyzed by changing the materials and the number of the defect layers in the granular system. The results show that the defect granules can affect the propagation path and velocity of the wave, and the influence of different defect types on wave propagation is different. The waveform near the symmetry axis of the non-defective granular system is approximately circular, while the waveform near the symmetry axis of the defective granular system changes due to the different elastic modulus of the defect region. Due to the difference between the defect region and the normal region, when the wave passes through the defect region, the velocity vector of granules at the junction of the two regions converges or moves away from the symmetry axis, so that the system accumulates more energy locally. The type of defect will also have different influences on this phenomenon. In conclusion, this study systematically analyzes the wave propagation characteristics of two-dimensional hexagonal packed granules with defects, which provides an important reference for practical engineering applications. The research findings can be applied to the design and optimization of impact protection devices, while also laying the groundwork for future research exploring other types of defects or higher-dimensional systems.