Transition waves in multi-stable metamaterials with space-time modulated potentials

摘要

This Letter introduces a strategy for transition wave (soliton) management in multi-stable mechanical metamaterials, enabling on-demand, post-fabrication control of the associated phase transformation kinetics and distribution. Specifically, the wave dynamics are controlled by a small, kinematically prescribed spatiotemporal variation in the elastic potential, constituting a driving force. The stability of the wave profile under slow-propagation conditions and the characteristic spatial localization of the Hamiltonian energy support an analogy with a Newtonian particle traversing a viscous medium under forcing. The theoretical analysis adopts this particle perspective, describing the soliton dynamics through ordinary, rather than partial, differential equations. While myriads of definitions for the potential modulation are possible, a traveling sinusoid assists the development of analytical solutions. Following this prescription, two wave propagation regimes are revealed: in one, the soliton is carried by the modulation with a commensurate velocity; in the other, the soliton is out-paced by the modulation and, thus, travels at reduced velocity. To illustrate the utility of this method, we demonstrate both the tractor and repulsor effects in multi-stable systems away from equilibrium: as a tractor (repulsor), the potential variation attracts (repels) the transition wave front in opposition to the system's energy-minimizing tendency. This method provides greater flexibility to the transformation performance of multi-stable metamaterials and supports the adoption of such systems in applications demanding multi-functionality.