Linear and Nonlinear Dynamics of Materials
Waves play a significant role in many areas of physics, biology, and engineering, functioning as a means of, e.g., sensing, signaling, and energy transfer. In the context of acoustics, the peculiarities of the host medium, including nonlinear and dispersive effects, influence the manner in which waves propagate. Architected materials, their performance stemming from an engineered microstructure, may be tailored for various applications in sensing, cloaking, signaling, etc. In the linear (small-amplitude, dispersive) regime, the Frazier Research Group studies, e.g., substrate curvature and time-varying constituent properties as new avenues for broadening architected material response and applicability. In addition, inspired by the success in optics, our group advances beyond the conventional plane wave (phonon) analysis to explore the unique physics of nonlinear modes (breathers, solitons). Potential applications include improved signal transmission in dissipative media and wave steering for biomedical imaging and structural health monitoring.
Figure 1: (a) Linear dispersion diagram of a bistale lattice material. (b) FFT of a point deep within the lattice as a function the excitation amplitude at one end. Below the nonlinear supratransmission threshold, except for harmonics of the excitation within the pass band, wave energy is confined to the excited end; above the threshold, energy is transmitted within the band gap. (c) Transmitted wave energy. (d) Snapshots of displacement profile along the lattice corresponding to the same excitation frequency and duration. With increasing excitation amplitude, the series shows the evolution of lattice behavior from linear spatial decay to nonlinear supratransmission.
Multistable Materials and Structures
Multistability — the quality of possessing more than one equilibrium phase (i.e., microstructure configuration) — is an apparent feature of a variety of systems, e.g., DNA molecular arrays, polycrystalline metals, and buckled plates/columns to name but a few. Remarkably, applying the appropriate stimulus provokes a phase transformation whereby one microstructure configuration evolves into another. Nevertheless, within a multistable system, several degenerate phases may exist simultaneously, although separated into homogeneous domains to minimize the corresponding interface energy. With each phase potentially distinct in its physical characteristics, multistable systems represent a unique opportunity for enhanced functionality and adaptive performance. E unum, pluribus; out of the one, many. In the context of architected materials, multistability is a relatively new feature with accompanying research in its early stages. One of the major research interests in the Frazier Research Group is the spatio-temporal control of phase expression in architected materials in order to adapt the material behavior to suit a variety of conditions. Another of our thrusts lies in bringing small-scale physics (e.g., phase transitions and spinodal decomposition) to architected materials whose tuning parameters are more accessible. Mechanical data storage, tunable dynamics, and solid-solid phase-change materials are potential applications.
Figure 2: (a) Diffusive phase separation is a materials process enabled by a multiwelled energy landscape. (b) Below the Curie temperature, ferroelectrics exhibit a spontaneous polarization due to broken crystal symmetry which displaces the central ion outside the midplane, creating a dipole. (c) In the continuum limit, the underlying kinetics of structural transformations are observed in a discrete mechanical system of coupled bistable cylinders.
Multiphysics and Materials
The central motivation for architected materials is the ability to shape macroscale performance through clever design of small-scale features (i.e., the microstructure). The approach, generally unencumbered by the restrictions of conventional materials, grants access to properties, potentially, beyond those found in nature. Yet, despite this freedom, microstructure design typically involves a single domain of physics and development efforts are generally confined to a few isolated fields (e.g., mechanics, acoustics, and optics). One goal of the Frazier Research Group is to elicit new architected material behavior from the additional complexity of multiphysics in microstructure design. A second objective of our group, given the importance of materials across a variety of disciplines, is to demonstrate architected material solutions to problems outside the traditional fields. The additional theoretical and computational effort required in multiphysics analysis of architected materials is offset by the potential for enhanced performance and broader application.