Fig. 1: Design concept of reprogrammable mechanical metamaterials with functional group transformation and ring reconfiguration.

a Comparison between mechanical metamaterials composed of homogeneous elements and heterogeneous elements: mutually non-transformable behavior is observed within single-element (either red-colored complete–elastic C or blue-colored rigid–elastic R) periodic homogeneous metamaterials. Conversely, the C or R functional group composed of one C and one R elements can mutually transform. Deformation occurs exclusively along the normal direction of the colored solid element sidelines. Design and construction of triangular and quadrilateral ring metamaterial employ alternating heterogeneous C and R elements. Symbols Ω and Γ, respectively, represent the angular relationship between adjacent elements within ring metamaterials. Ring metamaterials (C ring and R ring) composed of corresponding functional groups can interconvert. Periodic homogeneous metamaterials composed of C or R-ring metamaterials can also interconvert, thereby establishing interchangeability of stress–strain relationships between C and R metamaterials. b The schematic of multimode deformation of designed mechanical metamaterials with an example of the quadrilateral ring (light cyan area). Contraction and expansion deformations are shown in dark green and dark yellow blocks, respectively. The rotational, uniaxial (zero Poisson’s ratio), auxetic (negative Poisson’s ratio) contraction, and expansion shown in the same row have the same force action mode but opposite direction (black arrows). c The schematic of quadrilateral ring reconfiguration (example: R-ring metamaterial with Ω = 0°, 60°, 90°, 120°, and 180°) and the continuously reprogrammable mechanical responses for C and R metamaterials by ring reconfigurations (light green area). The light blue and red shadings represent the reprogrammable spaces for R and C metamaterials, respectively.