Numerical study on the phononic band-structure of soft granular crystals

The discrete element method has been widely adopted to study the phononic dispersion relation of granular crystals, but its intrinsic limitations in the conventional particle contact model are often overlooked. In this study, we numerically investigate both the quasi-static nonlinear behavior and the phononic dispersion relation of a pattern-transformable 2-D soft granular crystal using discrete element method (DEM) and finite element method (FEM). Regarding the quasi-static analysis at low strain levels, the DEM simulation results show good qualitative and quantitative agreement with the corresponding FEM results. However, our study reveals that the dispersion relations obtained by the stiffness matrix method coupled with DEM are substantially different from the corresponding FEM results. We find that independent rotational stiffness in the DEM contact models has little effect on the quasi-static motion and some lowest eigenmodes of dispersion relations, but it plays a pivotal role in the overall dispersion relation of granular crystals. Thus, we demonstrate that special care should be taken when DEM is adopted for calculating the phononic dispersion relation of soft granular crystals.