Programmable and robust static topological solitons in mechanical metamaterials

Solitary, persistent wave packets called solitons hold potential to transfer information and energy across a wide range of spatial and temporal scales in physical, chemical, and biological systems. Mechanical solitons characteristically emerge either as a single wave packet or uncorrelated propagating topological entities through space and/or time, but these are notoriously difficult to control. Here, we report a theoretical framework for programming static periodic topological solitons into a metamaterial, and demonstrate its implementation in real metamaterials computationally and experimentally. The solitons are excited by deformation localizations under quasi-static compression, and arise from buckling-induced kink-antikink bands that provide domain separation barriers. The soliton number and wavelength demonstrate a previously unreported size-dependence, due to intrinsic length scales. We identify that these unanticipated solitons stem from displacive phase transitions with periodic topological excitations captured by the well-known $${\varphi }^{4}$$φ4 theory. Results reveal pathways for robust regularizations of stochastic responses of metamaterials.