Flexible mechanical metamaterials: solitary waves and phase transitions

Abstract

Over the last two decades, metamaterials — materials whose properties are defined by their structure rather than their composition — have been a magnet for scientists, generating significant interest in the research community. In this dissertation, I explore the nonlinear mechanics of flexible mechanical metamaterials (flexMMs) focusing on: (i) the propagation of solitary waves, and (ii) structural phase transitions. I first investigate the nonlinear dynamic behavior of flexMMs based on the rotating squares mechanism. I experimentally and numerically demonstrate that this system supports the propagation of elastic vector solitons and construct a theoretical framework to capture them. Next, I investigate the formation of multiple phases in the rotating squares systems and the evolution of domain walls between these phases. I derive an analytical solution that captures the profiles and locations of such domain walls and exploits it to guide the design of flexMMs with new functionalities. Finally, I explore topological phase transitions in micrometer-scale cellular flexMMs. I present a two-tiered strategy based on swelling that is able to fast, reversibly, and robustly change the fundamental topology of cellular lattices, e.g., connectivity and number of the nodes. I then harness these topological changes to design active surfaces with tunable properties and functionalities.