Uncovering pattern-transformable soft granular crystals induced by microscopic instability

Upon compression, some soft granular crystals undergo pattern transformation. Recent studies have unveiled that the underlying mechanism of this transformation is closely tied to microscopic instability, resulting in symmetry breaking. This intriguing phenomenon gives rise to unconventional mechanical properties in the granular crystals, paving the way for potential metamaterial application. However, no consistent approach has been reported for studying other unexplored transformable granular crystals. In this study, we propose a systematic approach to identify a new set of pattern-transformable diatomic granular crystals having tunable phononic band-gaps. Utilizing diatomic compact packing as a foundation, we first present a catalog of viable particle arrangements, considering the instability arising from kinematic constraints between articles. Subsequently, simple mass-spring models are constructed based on the contact network of the aforementioned particle arrangements. To identify pattern-transformable granular crystals, these mass-spring models are employed for both instability analyses within the linear perturbation framework and quasi-static analyses involving infinitely-periodic configurations. The conclusive pattern transformation in these chosen granular crystals is ultimately validated through detailed finite element models employing continuum elements. Furthermore, the impact of their pattern transformation under compression is highlighted by observing the evolution in their phononic band structure.