Michael J. Frazier

ABSTRACT Spatio‐temporal patterns emerging from an initial quiescent, uniform state is a phenomenon observed in many dynamical systems sustained far from thermodynamic equilibrium, the practical application of which has only recently begun to be explored. As the underlying dynamics are typically complex, pattern formation is often theoretically analyzed and understood via phenomenological models, which effectively represent the causal mechanisms, but obscure the link between the small‐scale interactions/processes and the observed macroscopic behavior. Moreover, efforts to prescribe the patterning response are often undercut by the difficulty in exercising precise control over the small‐scale constituents and their interactions. This article demonstrates an artificial system (i.e., a robotic mechanical metamaterial) as an accessible and versatile platform within which to explore and prescribe the patterning response of non‐equilibrium systems. Specifically, in varying a feedback parameter within the prescribed reaction kinetics, the robotic mechanical metamaterial alternately develops spatial and temporal oscillations in the displacement field following a perturbation of the initial quiescent, uniform state. The platform is amenable to a first‐principles analytical description so that corresponding theoretical results possess qualitative and quantitative significance, and maintain connection to the specific system parameters.

In this article, we consider the dynamics of transition waves in phase-transforming metamaterials with hierarchical architecture, i.e., 1D/2D periodic systems comprising a network of intersecting chains of elastically-coupled bi-stable elements. To this end, we develop continuum models of discrete 1D systems that, nevertheless, also elucidate the transition wave dynamics in 2D environments, which have received little attention in the literature. We find the potential driving and the wavelength relative to the hierarchical dimensions to play important roles in determining the wave mobility. The unique construction provokes some interesting results, including the growth of non-circular domains and the stabilization of domains of arbitrarily prescribed morphology; the latter representing an avenue toward reconfigurable performance via domain patterning. Altogether, in a break from the paradigm of homogeneity, the results not only elucidate the influence of hierarchy on the dynamics of phase-transforming metamaterials, but also its potential utility.

This Letter proposes a design strategy leveraging tunable structural defects in multi-stable mechanical metamaterials for manipulating the propagation of the supported transition waves toward the endowment of a multi-phase patterning capability. The defect reversibly adjusts the on-site potential in order to affect the motion of the transition waves which traverse it, either prohibiting wave transmission (i.e., stabilization) or permitting transmission of specific modes, possibly converting one mode into another. Thus, the defect is able to control the occurrence and distribution of the structural phases and realize the desired phase patterns. Although the metamaterial model for our analytical and numerical study is a one-dimensional (1D) architecture comprising tri-stable elements, the proposed method is shown to apply to 2D architectures and is amenable to elements possessing more than three stable states, demonstrating greater flexibility in metamaterial design than current approaches. The proposed method expands the configuration space of phase-transforming metamaterials, which contributes to efforts aimed at re-programmable mechanical/dynamic performance.

In this Letter, we consider the dynamics of a multi-stable metamaterial with an elastic substrate to realize a mechanical system within which the position of a transition wavefront can be precisely controlled and remotely determined. This ability is enabled, in part, by a (strain-)tunable potential energy landscape that conveys the wavefront from one stabilizing defect site to another. In separating two acoustically distinct domains, the wavefront reflects small-amplitude waves of appropriate frequency back toward the source whereupon the time interval between excitation and echo reveals the position of the front. In a numerical study, we exploit these mechanisms for mechanical multi-level memory, which may find applications, e.g., in soft robots as a flexible alternative to current rigid memory technologies. More generally, we anticipate that the concepts presented here toward a command of the transition wave position will enhance the development and applicability of multi-stable metamaterials.

We report on a class of architected material lattices that exploit multi-stability and kinematic amplification to independently adjust the local effective mass, damping, and stiffness properties, thereby realizing congruent alterations to the acoustic dispersion response post-fabrication. The fundamental structural tuning element permits a broad range in the effective property space; moreover, its particular design carries the benefit of tuning without altering the original size/shape of the emerging structure. The relation between the tuning element geometry and the achieved variability in effective properties is explored. Bloch's theorem facilitates the dynamic analysis of representative one- and two-dimensional (1D/2D) systems, revealing, e.g., bandgap formation, migration, and closure and positive/negative metadamping in accordance with the tuning element configuration. To demonstrate a utility, we improvise a waveguide by appropriately patterning the tuning element configuration within a 2D system. We believe that the proposed strategy offers a new way to expand the range of performance and functionality of architected materials for elastodynamics.