Soft actuators typically require time-varying or spatially modulated control to be operationally effective. The scope of the present paper is to show, theoretically and experimentally, that a natural way to overcome this limitation is to exploit mechanical instabilities. We report experiments on active filaments of polyelectrolyte (PE) gels subject to a steady and uniform electric field. A large enough intensity of the field initiates the motion of the active filaments, leading to periodic oscillations. We develop a mathematical model based on morphoelasticity theory for PE gel filaments beating in a viscous fluid, and carry out the stability analysis of the governing equations to show the emergence of flutter and divergence instabilities for suitable values of the system’s parameters. We confirm the results of the stability analysis with numerical simulations for the nonlinear equations of motion to show that such instabilities may lead to periodic self-sustained oscillations, in agreement with experiments. The key mechanism that underlies such behaviour is the capability of the filament to undergo active shape changes depending on its local orientation relative to the external electric field, in striking similarity with gravitropism, the mechanism that drives shape changes in plants via differential growth induced by gravity. Interestingly, the resulting oscillations are nonreciprocal in nature, and hence able to generate thrust and directed flow at low Reynolds number. The exploitation of mechanical instabilities in soft actuators represents a new avenue for the advancement in engineering design in fields such as micro-robotics and micro-fluidics.

软致动器通常需要时变或空间调制控制才能有效运行。本文的范围是从理论上和实验上表明，克服这种限制的自然方法是利用机械不稳定性。我们报告了受稳定均匀电场影响的聚电解质 (PE) 凝胶活性细丝的实验。足够大的场强会启动有源灯丝的运动，从而导致周期性振荡。我们开发了一种基于形态弹性理论的 PE 凝胶丝在粘性流体中跳动的数学模型，并对控制方程进行了稳定性分析，以显示系统参数的合适值出现颤动和发散不稳定性。我们通过非线性运动方程的数值模拟证实了稳定性分析的结果，表明这种不稳定性可能导致周期性自持振荡，这与实验一致。这种行为背后的关键机制是细丝根据其相对于外部电场的局部方向进行主动形状变化的能力，与向地性惊人相似，通过重力诱导的差异生长驱动植物形状变化的机制. 有趣的是，由此产生的振荡本质上是不可逆的，因此能够在低雷诺数下产生推力和定向流。