Exploring static responses, mode transitions, and feasible tunability of Kagome-based flexible mechanical metamaterials

Abstract

We consider the static responses of the uniaxially compressed flexible mechanical metamaterials, which integrate soft hinges and rigid bodies, constructed from the Kagome lattice. First, we experimentally find that the static responses of the regular-Kagome-based structure significantly differ from those of the twisted-Kagome-based structure with a very small twisting angle. Following this, we establish a theoretical model, which is combined with the deflated continuation algorithm for bifurcation analysis, to delve into the static responses and potential bifurcation behavior of these structures. We then experimentally and numerically investigate the mode transitions between various stable modes, and systematically study the role of the twisting angle in the occurrence of bifurcations. Our findings indicate that mode transitions can be feasibly realized according to the calculated bifurcation diagrams. They also provide direct evidence of an interesting physical mechanism that the transition between different stable deformation states can occur through multiple pathways, possibly passing through unstable deformation states. Moreover, by introducing the twisting angle or stiff defects, the response of the structure can be modulated, thereby enhancing the programmability and tunability of Kagome-based flexible mechanical metamaterials. Our research also reveals that novel phenomena such as meta-beam buckling and multi-phase dominated deformations can be triggered within these flexible structures, which offers valuable insights for future metamaterial designs and applications.