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Article
Peer Reviewed

Multi-stable acoustic metamaterials with re-configurable mass distribution

Frazier, Michael J

UC San Diego Previously Published Works (2022)

This article proposes a design strategy for acoustic metamaterial lattices which leverages the characteristic multi-stability and kinematic amplification of the internal architecture to realize a re-configurable effective mass distribution, enabling a corresponding frequency band structure of extreme tunability. The approach builds metamaterial lattices from bi-stable elastic elements featuring the typical two-bar inertial amplification mechanism, whose deformation axis is uniquely misaligned with that of its elastic support such that the realized amplification is configuration-specific. Conveniently, a change in the configuration does not simultaneously alter the element dimensions and, therefore, the size/shape of the finite metamaterial structure remains constant. Moreover, as the multi-stability and kinematic amplification are each based on geometry, scaling the resulting metamaterial structure is expected to be straightforward. The dynamic performance of 1D/2D metamaterial architectures exhibiting the proposed design strategy is analytically determined via Bloch wave analysis and supported by numerical demonstration of the corresponding finite structures.

Cover page: Multi-stable acoustic metamaterials with re-configurable mass distribution

Creative Commons 'BY' version 4.0 license

Article
Peer Reviewed

Phase transitions in hierarchical, multi-stable metamaterials

UC San Diego Previously Published Works (2023)

Article
Peer Reviewed

Acoustic metamaterials with independently tunable mass, damping, and stiffness

UC San Diego Previously Published Works (2022)

Over the past decades, metamaterials—whose engineered internal architecture grants unusual or extraordinary macroscopic response—have garnered increasing attention from researchers as the desire to shape material behavior beyond natural limitations (e.g., chemistry) arises within several areas of materials science and engineering. The bulk of reported acoustic metamaterial architectures are passive such that their properties and functions are fixed at fabrication. Nevertheless, a tuning capacity is desirable to expand the range of response, in general, and to allow for adaptation in the face of changing service requirements. Despite the diversity of proposed tuning strategies, most target the stiffness parameter alone, leaving the inertial and dissipative properties unaffected. In this presentation, we present a novel implementation of (geometric) bi-stability and kinematic amplification to independently tune the value and distribution of the effective mass, stiffness, and viscous damping within acoustic metamaterials, which impacts the dynamic response. Through analytical and numerical investigations of a 1D system, we show that the corresponding frequency band structure depends on the specific configurations of bi-stable elements within the unit cell. As the number of bi-stable elements per unit cell increases, so to do the number of unique dynamic responses to which to tailor the system. The proposed strategy significantly expands the property set available for tuning acoustic metamaterial performance post-fabrication.

Cover page: Acoustic metamaterials with independently tunable mass, damping, and stiffness

Article
Peer Reviewed

Transition waves in multi-stable metamaterials with space-time modulated potentials

UC San Diego Previously Published Works (2020)

This Letter introduces a strategy for transition wave (soliton) management in multi-stable mechanical metamaterials, enabling on-demand, post-fabrication control of the associated phase transformation kinetics and distribution. Specifically, the wave dynamics are controlled by a small, kinematically prescribed spatiotemporal variation in the elastic potential, constituting a driving force. The stability of the wave profile under slow-propagation conditions and the characteristic spatial localization of the Hamiltonian energy support an analogy with a Newtonian particle traversing a viscous medium under forcing. The theoretical analysis adopts this particle perspective, describing the soliton dynamics through ordinary, rather than partial, differential equations. While myriads of definitions for the potential modulation are possible, a traveling sinusoid assists the development of analytical solutions. Following this prescription, two wave propagation regimes are revealed: in one, the soliton is carried by the modulation with a commensurate velocity; in the other, the soliton is out-paced by the modulation and, thus, travels at reduced velocity. To illustrate the utility of this method, we demonstrate both the tractor and repulsor effects in multi-stable systems away from equilibrium: as a tractor (repulsor), the potential variation attracts (repels) the transition wave front in opposition to the system's energy-minimizing tendency. This method provides greater flexibility to the transformation performance of multi-stable metamaterials and supports the adoption of such systems in applications demanding multi-functionality.

Cover page: Transition waves in multi-stable metamaterials with space-time modulated potentials

Article
Peer Reviewed

Phase patterning in multi-stable metamaterials: Transition wave stabilization and mode conversion

UC San Diego Previously Published Works (2023)

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.

Cover page: Phase patterning in multi-stable metamaterials: Transition wave stabilization and mode conversion

Article
Peer Reviewed

Architected material with independently tunable mass, damping, and stiffness via multi-stability and kinematic amplification

UC San Diego Previously Published Works (2023)

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.

Cover page: Architected material with independently tunable mass, damping, and stiffness via multi-stability and kinematic amplification

Thesis
Peer Reviewed

Phase transition and domain wall control in multistable metamaterials

Ramakrishnan, Vinod
Advisor(s): Frazier, Michael J

UC San Diego Electronic Theses and Dissertations (2023)

Ferroics and metal alloys are naturally occurring materials, whose constituent unit cells can co-exist in multiple stable configurations. These different configurations organize into regions (domains) separated by boundaries (domain walls). The stable configurations (phases) are associated with a unique set of properties (e.g., dipole orientation, stiffness), rendering the mesoscale phase distributions a crucial factor in determining macroscale material behavior; hence, the desire to control the distribution. Inspired by non-linear physics and potential applications of these natural materials, this dissertation explores similar physics in materials of an engineered microstructure (metamaterials) featuring purely geometric phases, and develops strategies to control domain walls. The domain management strategies enable control of the phase distribution and thereby the macroscale properties, allowing for a highly tunable post-fabrication performance.

In my primary investigation, I leverage both geometric multistability and kinematic amplification in the metamaterial architecture to enable the effective mass, damping and stiffness to be tuned independently post-fabrication to control wave dispersion. In my second project, I introduce an alternate, less invasive strategy utilizing strain engineering to precisely control the phase distribution. In my third project, I propose a general theory to predict the position and velocity of mobile domain walls (i.e., transition waves) when subjected to a small spatio-temporal modulation. The modulations provide a mechanism to counter domain wall motion spurred by inherent energy minimizing affects (e.g., biased potential, domain wall curvature) which can be leveraged for stabilizing and arbitrarily shaping domain contours. Finally, inspired by the pattern forming dynamics of certain biological and chemical systems, I mimic the effects of the underlying driving and dissipative mechanisms within the context of a customizable mechanical system: an elastic metamaterial incorporating active elements (i.e., electric motors) facilitating non-reciprocal interactions. This construction encodes certain periodic phase distributions to be triggered as an inherent response of the metamaterial to perturbation, which may find utility in morphable surfaces.

In providing several strategies to realize and control the phase distributions within multistable metamaterials, this dissertation promotes their adoption for applications in energy harvesting, mechanical memory devices and deployable structures.

Cover page: Phase transition and domain wall control in multistable metamaterials

Article
Peer Reviewed

Atomimetic Mechanical Structures with Nonlinear Topological Domain Evolution Kinetics

UC San Diego Previously Published Works (2017)

A mechanical metamaterial, a simple, periodic mechanical structure, is reported, which reproduces the nonlinear dynamic behavior of materials undergoing phase transitions and domain switching at the structural level. Tunable multistability is exploited to produce switching and transition phenomena whose kinetics are governed by the same Allen-Cahn law commonly used to describe material-level, structural-transition processes. The reported purely elastic mechanical system displays several key features commonly found in atomic- or mesoscale physics of solids. The rotating-mass network shows qualitatively analogous features as, e.g., ferroic ceramics or phase-transforming solids, and the discrete governing equation is shown to approach the phase field equation commonly used to simulate the above processes. This offers untapped opportunities for reproducing material-level, dissipative and diffusive kinetic phenomena at the structural level, which, in turn, invites experimental realization and paves the road for new active, intelligent, or phase-transforming mechanical metamaterials bringing small-scale processes to the macroscopically observable scale.

Cover page: Atomimetic Mechanical Structures with Nonlinear Topological Domain Evolution Kinetics

Article
Peer Reviewed

Metamaterial design strategy for mechanical energy absorption under general loading

UC San Diego Previously Published Works (2022)

Article
Peer Reviewed

Non-Reciprocal Supratransmission in Mechanical Lattices with Non-Local Feedback Control Interactions

UC San Diego Previously Published Works (2021)

We numerically investigate the supratransmission phenomenon in an active nonlinear system modeled by the 1D/2D discrete sine-Gordon equation with non-local feedback. While, at a given frequency, the typical passive system exhibits a single amplitude threshold marking the onset of the phenomenon, we show that the inclusion of non-local feedback manifests additional thresholds that depend upon the specific boundary from which supratransmission is stimulated, realizing asymmetric (i.e., non-reciprocal) dynamics. The results illustrate a new means of controlling nonlinear wave propagation and energy transport for, e.g., signal amplification and mechanical logic.

Cover page: Non-Reciprocal Supratransmission in Mechanical Lattices with Non-Local Feedback Control Interactions