Goal
The observed properties of materials — optical, acoustic, mechanical, etc. — are the cumulative result of many small-scale processes and interactions occurring within the material microstructure. With the advent of additive manufacturing technology, the microstructure may be designed, fabricated, and implemented at larger scales to elicit unique, even counterintuitive performance from the emerging architected material. From a combined theoretical, numerical, and experimental approach, the goal of the Frazier Research Group is to understand the link between the microstructural design and the macroscale dynamic performance in order to realize architected materials that exhibit novel behavior and open new technological frontiers.
Current Research
Transition Wave Management
Phase transformations are a hallmark of materials whose microstructure possesses more than one stable equilibrium configuration (i.e., phase, state) as distinguished by a set of order parameters. In lowering the free energy of a sample, regions of homogeneous configuration (i.e., domains) emerge, separated by an interface (i.e., domain wall) that interpolates the adjoining phases and, in propagating, constitutes a transition wave. The physical properties can vary drastically between domains of different phase and even within the domain walls, a condition that, with the aid of transition wave management, is exploited for a variety of applications.
Intriguingly, transformation phenomena are not limited to natural materials systems and to the molecular scale; rather, phase-transforming mechanical metamaterials comprising arrays of coupled, multi-stable structural elements have been shown to not only mimic material-level processes at the structural level, but also serve as versatile platforms within which to engineer novel transformation behavior. However, despite the greater accessibility afforded by the metamaterial platform compared to its molecular-scale counterpart, for metamaterials, methods of transition wave management are still underdeveloped. Moreover, most metamaterial designs are uniform, one-dimensional geometries from within which transition waves transform the whole system from one uniform phase to another; thus, effectively relinquishing opportunities engendered by phase patterning. Consequently, the transformation potential of current phase-transforming metamaterials is yet to be fully realized.
We break with these paradigms in order to devise and characterize new methods of domain wall management that may, ultimately, enable more complex responses for applications (e.g., morphable surfaces for optical devices, improvised waveguides). Specifically, we investigate the phase-transforming characteristics of two-dimensional, heterogeneous (e.g., hierarchical) systems, and systems with strain- and time-dependent material properties.
Non-destructive Mechanical Energy Absorption
Energy-absorbing materials are ubiquitous in nature and engineering applications demanding, e.g., shock/impact mitigation and stress redistribution/relief. A quasistatic loading-unloading cycle generates a characteristic hysteresis in the load-displacement diagram which, by the enclosed area, quantifies the absorbed energy. While conventional energy-absorbing materials (e.g., polymers, gels, and foams) have their advantages, the material-specific composition/microstucture and absorption mechanism manifest inherent limitations as well. Among several desirable characteristics, the ideal energy-absorbing material is low-density, and delivers predictable and repeatable performance under general loading.
Over the past decade, researchers have developed mechanical metamaterials, which leverage an engineered, highly-tunable microstructure geometry in order to realize an unconventional performance. In the context of energy absorption, cellular metamaterials inherit the low density quality of foams, while enhancing predictabililty and re-usability with ordered microstructures that remain elastic during the loading-unloading process. Although, currently, the energy-absorption capacity is not comparable to conventional materials, cellular metamaterials may serve a complementary or even principal role in absorption applications. However, most of the cellular metamaterials exhibit a significant energy absorption capacity for loads directed along only a single axis. Moreover, despite the complex loading of real-world environments, current designs accommodate either tension, compression, or shear, and thus possess a specialized, rather than general absorption capability. The constraints on the loading direction and mode follows from the utilization of translation-based snapping elements in the metamaterial architecture. A desirable cellular metamaterial will exhibit a universal mechanical energy absorption capability, i.e., effective absorption from loading (i) along any axis and (ii) of any modality.
We propose an alternative strategy based on snap-through transitions in the rotational degrees of freedom to create cellular metamaterials capable of energy absorption from mechanical loading along any axis and in any modality. In addition, the adoption of rotation-based snapping elements expands the metamaterial design space from strictly periodic to quasi-periodic, polycrystalline, and amorphous arrangements.
Previous Research
Non-linear Supratransmission
Phononic materials emerge from the periodic arrangement of small-scale building blocks which, through management of scattering and resonance phenomena, act to control the propagation of mechanical waves. This ability is demonstrated by the appearance of band gaps in the frequency spectrum, i.e., frequency ranges where the material microstructure scatters and/or absorbs the wave energy, prohibiting its penetration into the material in all or specific directions. This response adheres to a linear theory of wave propagation, and thus, pertains to waves of sufficiently small amplitude. Large amplitudes activate non-linear mechanisms within the phononic material, leading to the self-modulation of the wave field. Thus, the dynamic response of a phononic material may be amplitude dependent. In particular, the non-linear response may be significantly different from that predicted by a linear analysis.
Non-linear supratransmission is the sudden transparency exhibited by non-linear media subject to persistent boundary excitation at a frequency within the linear band gap. Below a critical amplitude, the energy injected into the system by the excitation spatially attenuates away from the boundary (acquiring an evanescent profile) due to internal wave reflections and is, ultimately, removed from the system by the same excitation. Above this amplitude threshold, the evanescent wave profile predicted by a linear analysis is unstable, resulting in the generation of mobile non-linear wave modes (e.g., breathers, solitons, etc.) capable of transporting energy into the system, i.e., spontaneous transmission within the band gap.
Typically, the amplutide threshold for supratransmission is sinlge valued and independent of which of two boundaries perpendicular an axis is selected for excitation (i.e., reciprocal). However, we leverage phononic material architectures characterized by multi-stability and active feedback to realize two thresholds and non-reciprocal behavior.
Dissipation in Phononic Materials
Phononic materials are a type of architected material that leverages its internal structure toward the control of elastic waves. The generation of band gaps, i.e., specific frequency ranges over which wave propagation is prohibited, is the typical response with consequences for, e.g., wave filtering and guiding applications. More exotic results include, e.g., negative or amplified (effective) material properties for sub-wavelength imaging, and the realization of dynamic states that are the classical analogues of certain topologically protected electronic states described by quantum mechanics. Apparently, phononic materials possess a broad and growing range of response supporting novel applications. The observed dynamics are, ultimately, the cumulative result of scattering and resonance phenomena induced by and occurring at the level of the cleverly designed internal structure.
Complementing numerical and experimental studies, theoretical work helps to identify the key geometric/material parameters and clarify their relationship to the observed response, which fosters the understanding necessary to engineer phononic materials for applications. However, in the early theoretical and numerical studies, dissipative effects — inherent to all physical systems — were only rarely accounted for, representing a disregard for fundamental physics. Of the theoretical investigations of the role dissipation in phononic material dynamics, as if driven by an external agent, most assumed waves of prescribed frequency that dissipation compels to propagate with spatially decreasing amplitude. Our prior research expanded the literature with an alternative perspective: dissipation induces decay in both space and time. This perspective reveals the intrinsic (rather than the extrinsic) dynamic response of dissipative phononic materials, including the manifestation of a wave-dependent damping ratio.
In the phononic material field, research into the role of dissipation in observed dynamics continues, perhaps, most notably, in the direction of metadamping, the amplified dissipation observed in resonant phononic materials compared to their statically equivalent scattering counterparts, which is a concept that emerged from our research.
