Homoclinic Kinks in Multi-Stable Metamaterials

Mechanical metamaterials comprising coupled, multi-stable elements support the propagation of transition waves (i.e., topological solitons) that, upon passing, transform the local structural geometry from one stable configuration to another. Thus far, investigations have focused on systems that permit only one energetic path from a meta-stable configuration to a ground configuration. In this presentation, we introduce a new class of phase-transforming metamaterial uniquely characterized by multiple energetic paths between the same two configurations, yielding correspondingly unconventional results unreported in the current literature. The collision between a kink and antikink following distinct energetic paths between the same two configurations may form a new, joint structure (a homoclinic kink) characterized by a unique topological charge. The topological charge cannot be eliminated without overcoming a finite but tunable energy barrier, may be stationary or mobile, representing an alternative means of energy storage/release and mechanical memory. Furthermore, by modifying the system to support three stable states, we demonstrate, for the first time in the metamaterial setting, non-reciprocity of transition waves, which has consequences for proposed communications applications based upon the transition.