On the mechanism of pattern transformations in soft granular crystals

Tunable nonlinear characteristics of granular crystals can be potentially useful to a wide range of applications. Several diatomic two-dimensional granular crystals are reported showing compression-driven pattern transformations, but their underlying mechanisms are not explained. In this study, we investigate the veiled underlying mechanisms of compression-driven pattern transformations in 2-D soft granular crystals. In order to adopt a linear perturbation approach, we employ a simplified mass–spring model derived from the granular contact network and perform a series of numerical analyses including quasi-static analysis and microscopic/macroscopic instability analyses. The results show that the pattern transformation of the considered granular crystals are closely relating to instability. Furthermore, the effects of Young’s modulus and radius on the pattern transformations are studied by using the mass–spring model. We confirm the significance of instabilities in pattern transformations and the effectiveness of the simple mass–spring model by performing the corresponding finite element analyses where granular particles are modeled by continuum elements. In motions of continuum solids, instability is well known to serve as a symmetry-breaking mechanism. This study demonstrates that instability also plays a critical role to break the symmetry of deformed patterns in granular crystals.