On the phenomenon of shear wave velocity faster than that of compression wave induced by particle shape

This study provides a series of ellipsoidal aggregates in which the shear wave travels faster than the compressional one as the shape becomes more oblate. The propagation of elastic wave is simulated by the discrete element method, and the velocity is calculated by the time-of-flight method. An increase in the aspect ratio α leads to a significant reduction in the velocities of both compression (P) and shear (S) waves. As $\alpha <6$, the compression wave velocity is bigger than the shear wave velocity. However, when $\alpha >6$, the shear wave velocity becomes the faster one. According to the anisotropy coefficients of different ellipsoidal assemblies, the phenomenon of a faster shear wave is explained, and the equivalent propagation direction is also calculated. It is not that the shape induces a larger shear modulus, but rather that the variation in shape causes elastic waves to preferentially propagate along specific contact points, where the contact normals are similarly oriented. This normal vector is referred to as the equivalent propagation direction. As $\alpha$ increases, the equivalent propagation direction of the shear wave becomes more aligned with the vertical (height) direction of the sample, whereas the direction of the compression wave changes less significantly and tends to stabilize. A closer direction implies a shorter propagation path and a faster velocity. This study demonstrates a distinctive acoustic property induced by shape, which provides references for probing the interior structure of granular material by elastic waves. It also gives an idea to construct material in which wave can propagate along the designated path.