Multi-step Pathways of a Spherical Shell Structure with a Hierarchical Architecture

Structures with a hierarchical architecture are crucial to create functionality in nature, where reconfiguration necessitates a clear sequence of actions, with deformations between hierarchical levels that are typically non-commutative. The shape shifting functionality of such a system is thus realized by a multi-step pathway, carefully navigating its energy landscape. In artificial systems, analogue multi-step pathways have been explored using hierarchical metamaterials, harnessing beam-buckling and hard contact. Here we focus on hierarchical spherical shell structures, inspired by Pop It Ball and Buckliball, and characterize their sequence of reconfiguration under predefined volume control. The dominance of some buckling modes over others is embedded in the hierarchy of the architecture, which is reflected as a nonreciprocal transition among steps or the exclusion of some steps in the pathway. By tuning geometrical parameters, we can control the occurrence of buckling modes and influence the self-folding behavior of such meta-shells, and tailor their overall nonlinear pressure-volume response.