Grounded reconfigurable metamaterials with customized mapping-invariant behavior.

Mechanical behavior of synthetic materials depends on their microstructure and geometric configurations. This dependency leads to unintended performance when the material remaps its microstructures for shape reconfigurations, such as diminished rigidity in unfolded aerospace morphing structures and reduced sensitivity in twisted soft sensors. Breaking this dependency through material design to improve overall performance has been a long-standing challenge. This work develops a transformation method to design a class of grounded metamaterials that decouples mechanical behavior from microstructure and shape reconfigurations. We fabricate these metamaterials and experimentally demonstrate both configuration-mapping-invariant displacement behavior and unconventional displacement control functions that have not previously been observed. We identify two physical principles that underpin the useful, but counterintuitive behavior: (i) Mapping-invariant displacement fields are the result of body torques that automatically balance non-concurrent internal forces from microstructure reconfigurations; (ii) Tailored displacement control functions are determined by Willis springs pinned to the ground. As a result, the grounded metamaterials are shown to enable the design of highly reconfigurable material systems that demonstrate tailored deformation behavior regardless of their microscopic and geometric configurations.