Gradient catastrophe and Peregrine soliton in nonlinear flexible mechanical metamaterials

We investigate the emergence of extreme wave events in mechanical metamaterials by leveraging the mathematical framework of gradient catastrophe regularization developed by A. Tovbis and M. Bertola for the focusing nonlinear Schrödinger (NLS) equation. While the formation of Peregrine solitons, using this process, in the semiclassical limit of the NLS equation is well established in optics and hydrodynamics, its relevance to architected mechanical systems has not yet been explored. This study fills that gap by demonstrating, for the first time, that the gradient catastrophe can occur in a class of architected mechanical structures known as flexible mechanical metamaterials. Specifically, we consider a chain of coupled units possessing rotational and translational degrees of freedom, a canonical example previously shown to support nonlinear excitations such as elastic vector solitons. We show both theoretically and numerically that this metamaterial can support the emergence of extreme events consistent with NLS predictions. We further assess the robustness of this phenomenon in the presence of weak damping and find that while losses reduce the amplitude and delay the onset of the extreme events, the underlying gradient catastrophe mechanism remains intact. Our results highlight a new regime of nonlinear dynamics in mechanical metamaterials, and have the potential to guide future experiments on the controlled generation of extreme events in experimentally realizable lattice systems.