Yao Du

Tuning Nonlinear Waves in Nonreciprocal Active Filaments

The instabilities of slender structures power biological locomotion across scales, and offer a compelling method to actuate soft robots. Nonreciprocal elastic solids have been found to amplify flexural waves in one direction only, but design principles to tune and stabilize these waves are missing. Here we develop a geometrically exact theory of nonreciprocal filaments and provide simulations that capture their post-instability nonlinear dynamics. We find that nonreciprocity, when coupled to inertia or pre-stress, amplifies and advects curvature variations. The resulting one-way patterns of shape morphing can then be selected via dissipative interactions with the environment. Our work offers a continuum-based strategy for how internal stresses can drive active unidirectional waves without need for additional degrees of freedom.

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Nonreciprocal Buckling Makes Active Filaments Polyfunctional

Active filaments are a workhorse for propulsion and actuation across biology, soft robotics, and mechanical metamaterials. However, artificial active rods suffer from limited robustness and adaptivity because they rely on external control, or are tethered to a substrate. Here, we bypass these constraints by demonstrating that nonreciprocal interactions lead to large-scale unidirectional dynamics in free-standing slender structures. By coupling the bending modes of a buckled beam antisymmetrically, we transform the multistable dynamics of elastic snap-through into persistent cycles of shape change. In contrast to the critical point underpinning beam buckling, this transition to self-snapping is mediated by a critical exceptional point, at which bending modes simultaneously become unstable and degenerate. Upon environmental perturbation, our active filaments exploit self-snapping for a range of functionality including crawling, digging, and walking. Our work advances critical exceptional physics as a guiding principle for programming instabilities into functional active materials.

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