Atomimetic Mechanical Structures with Nonlinear Topological Domain Evolution Kinetics

Abstract

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.

Exploiting Microstructural Instabilities in Solids and Structures: From Metamaterials to Structural Transitions

“…Under the action of gravitational forces, tilting of the whole system mimics the application of an electric field in that it favors one of the two stable equilibria. This setup was shown to follow the same governing equations discussed earlier, and it reproduced typical behavior found in materials during domain switching as well as during second-order phase transformations [287].…”

“…3.2), whereas most applications require miniaturization Fig. 22 Periodic array of bistable rotational elements (polarization angle u) coupled to nearest neighbors by elastic bands [287]. The combination of an excentrically attached linear spring and the action of gravity results in a tunable bistable potential w which can be biased as in domain switching (by tilting the whole setup by an angle a) and which can also mimic a second-order phase transition (by adjusting the position f x of the spring anchor points, switching between a bistable potential and a single-well potential).…”

An assessment of numerical techniques to find energy‐minimizing microstructures associated with nonconvex potentials

“…Microstructural patterns are ubiquitous across materials systems: from the laminate patterns accompanying deformation twinning and martensitic phase transformations to networks of dislocation walls in metal plasticity, to cellular arrangements from phase separation, and instability‐induced pattern formation in periodic metamaterials . The origin of those spatially complex patterns is well understood and has been traced back to nonconvex energetic potentials that result in fine‐scale microstructures as energy minimizers .…”

Programmable and robust static topological solitons in mechanical metamaterials

“…The striking size-dependent property of kink-antikink pairs, denoted by a ceiling function in our metamaterial systems, applies across multistable systems including molecular transport in restricted spaces 43 , atomic-scale frictions 16 , and domain switching 44 . This holds potential to be leveraged for a range of new metamaterials with programmable localized deformations for fields such as smart molecular robotics.…”