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 present a systematic approach to identify a new set of pattern-transformable diatomic granular crystals induced by microscopic instability. After identifying the kinematic constraints for diatomic soft granular crystals, we have generated a list of feasible particle arrangements for instability-induced pattern transformation under compression. Instead of computationally intensive finite element models (FEMs) with continuum elements, we adopt a simplified mass-spring model derived from granular contact networks to efficiently evaluate these feasible particle arrangements for pattern transformation. Our numerical analysis encompasses quasi-static analysis and microscopic/macroscopic instability analyses within the framework of linear perturbation. Subsequently, the pattern transformation of the identified particle arrangements is confirmed through quasi-static analyses employing detailed finite element (FE) simulations with continuum elements. Additional numerical simulations with continuum elements reveal that the pattern transformations of particle arrangements are significantly influenced by the initial void volume and some transformed granular crystals may exhibit strong low-frequency directional phononic band-gaps, which were not observed in the initial granular crystals.