Stimuli-assisted smooth topological transition in a hydrogel-filled Maxwell lattice

Flexible mechanical structures are ubiquitous in both natural and engineered systems. Among them, Maxwell lattices that host topologically protected zero-frequency modes have attracted significant attention, as they enable robust and highly directional boundary or surface mechanical responses governed by the topological bulk-boundary correspondence. These lattices can reversibly transform between nonpolarized and topologically polarized states through uniform soft twisting. However, achieving smooth and synchronized transitions remains challenging, as it requires strict mechanical and geometrical constraints, including precise boundary control during transformation. Previous studies have shown that introducing identical bistable elements at the unit-cell level enables snapping transitions, yet smooth transitions remain elusive. To address this challenge, we investigate the conditions for realizing smooth transitions in Maxwell lattices and find that the area enclosed by constituent triangles varies systematically with twisting. Motivated by this observation, we integrate stimuli-responsive hydrogels as fillings to achieve smooth, stimuli-assisted topological transitions. The hydrogel transforms the discrete lattice into a continuum-like medium with tunable mechanical properties.