Session G29: Emergent Mechanics of Active, Robotic, and Living Materials I

Transmisison hysteresis and edge modes in bounded space-time composites

The vibrational frequency response of bounded composites, e.g., metamaterials and sonic crystals, is often understood thanks to band diagrams established in the absence of boundaries. Introducing a pump wave that modulates in time the properties of the composite challenges the correspondence between the vibrations picture and the waves picture. The talk revisits this correspondence in the context of the nonreciprocal acoustics of space-time composites. Specifically, we establish in the weak coupling regime how the hybridization of total bandgaps into pairs of one-way bandgaps triggers nonreciprocal hysteresis transmission loops in the space-frequency domain and alters, qualitatively and quantitatively, the vibrational frequency response in the presence of reflecting boundaries. The theoretical analysis is assessed numerically and exploited to shed new light on previously obtained experimental data. Last, extrapolating our study to the strong coupling regime, transmission hysteresis is shown to explain the emergence of topological vibrational modes with one-way edge-bulk and bulk-edge transitions.   

Motion via Bistability in Viscous Fluids

We study the behavior of bistable beams in viscous media and their application to aquatic locomotion. Specifically, we exploit asymmetric actuation of bistable beams, which leads to a nonreciprocal deformation path. As an example, we use double pinned axially compressed bistable beams. We actuate the beam asymmetrically by imposing an angular position on one of the beam extremities.

Using a combination of numerical simulations and experiments, we find that when the beam is surrounded by a viscous fluid, the position of the stable states is not impacted. However, a higher moment is needed to deform the beam compared to air. Importantly, the beam motion non-reciprocity results in thrust in the axial direction, and, therefore, propulsion. The thrust increases with increasing beam compression.   

Non-reciprocal solitons in robotic materials

The recent development of robotic materials, which are assemblies of building blocks integrating sensors and actuators, enables the implementation of non-conservative interactions within mechanical systems. This opens the way to the emergence of unique large scale mechanical properties.

Here, we use this new platform to generate soliton waves that indefinitely propagate in only one direction.

We show that these waves emerge from a smart balance between mechanical non-linearities and linear non-reciprocal interactions, namely, which preferably transmit motion in one direction. Using experiments, theoretical models and simulations, we rationalize the conditions of existence of these solitons and demonstrate that they exist even in the presence of friction. These results establish new ways to reliably transport mechanical energy.   

Topological locomotion

We investigate how the propagation of the topological domain walls through a metamaterial based on the squares rotating mechanism can be harnessed to generate locomotion. First, we add internal elastic constraints to transform the system into a bi-stable system, with the two energy minima being the two symmetry-related rotated phases. Such metamaterial supports topological solitons that take the deformed metamaterial from one static equilibrium position to another one. Remarkably, our results indicate that by combining the propagation of such finite-width topological solitons with angle-dependent friction (that can be easily realized by putting the system on wheels) we can realize a crawler.
  

Topology by activity in non-Hermitian mechanical metamaterials

A simple view of an active solid is a network of masses interacting via non-conservative bonds. We examine 2D topological lattices equipped with non-reciprocal active bonds that inherit two key properties from their passive counterparts: their interactions conserve linear momentum and depend only on the relative positions of the masses. We characterize the flow of Berry curvature and exceptional points in the resulting non-Hermitian band structure as activity is tuned from the passive limit to the brink of instability. Along this flow, we find a discrete onset of topologically charged bands whose activity threshold can be controlled via zero-mode deformations of the underlying lattice. Simulations and analytical calculations reveal the emergence of persistent edge modes influenced by the interplay of a topologically protected penetration depth and an effective quality factor derived from non-Hermitian gain and loss. Our work sheds light on non-Hermitian band theory and the design of active metamaterials that conserve linear momentum.   

The topology of nonlinear mechanical systems

Following the pioneering work of Kane and Lubensky (and others), commendable advancements have been made in the field of topological mechanics. The majority of the work, however, concerns the topology of linear zero modes primarily engaging the framework of linear response theory (often drawing parallels to electronic responses in topological insulators). We, in the present work, attempt an extension to accommodate nonlinear effects that are more natural to occur in realistic mechanical systems and feature topologically protected zero modes. Invoking the tools of differential geometry, we present an exact theory to demonstrate this topology. Our theory (inspired by topological quantum field thoery), remarkably, predicts the existence of a Z-type topological invariant which arises only from the nonlinearities and does not demand any symmetry imposition (unlike the linear zero modes). We further include example systems to illustrate the physics.   

Mechanical metamaterial inspired by biological tissues

We introduce an amorphous mechanical metamaterial inspired by how cells pack in biological tissues. The spatial heterogeneity in the local stiffness of these materials has been recently shown to impact the mechanics of confluent biological tissues and cancer tumors (Li et al Phys. Rev. Lett. 123, 058101 (2019)). Here we use this bio-inspired model as a design template and show that this heterogeneity can give rise to amorphous cellular solids with large, tunable phononic bandgaps. Unlike in phononic crystals, the band gaps here are directionally isotropic due to their complete lack of positional order. The size of the bandgap can be tuned by a combination of local stiffness heterogeneity and the local elasticity modulus. Finally, we also investigated the possibility of introducing a topological nature in the mechanical response using a hexagonal lattice version of the same model. By tuning the local elasticity moduli, we demonstrate the emergence of a pseudo-spin state and as well chiral mechanical response. This constitutes a mechanical analogue of the quantum spin Hall effect.   

Modeling tunable acoustic transport in driven graphene nanoresonator arrays

Arrays of graphene nanoelectromechanical resonators show promise as a platform for precise, programmable manipulation of acoustic waves at the nanoscale. Besides harboring technologically relevant resonant frequencies and high quality factor, graphene resonators display a remarkable tunability of the local membrane tension through electrostatic back-gating or laser heating, which can be used to modulate vibrational properties. Motivated by experiments, we present a theoretical and computational study of the acoustic properties of coupled graphene resonators with dynamical spatiotemporal modulation of the tension. Starting from the theory of thin elastic plates, we develop a reduced description of the collective modes arising from the coupling of the fundamental modes on individual resonators and evaluate the effects of externally driven changes in tension on wave propagation. We will also describe early efforts at calibrating and testing the model against experimental measurements of coupled resonator acoustic modes. Our results pave the way towards designing driven graphene nanoelectromechanical resonator arrays with a manifestly out-of-equilibrium acoustic response.   

Transitions from conservative to non-conservative regimes in optical binding of colloidal matter.

We study light generated inter-particle interactions known as optical binding. These forces are mediated by the particle light scattering making it uniquely responsive to simple changes in the parameter space. For instance, we find that many colloidal particles placed in a weakly focused laser beam can self-assemble into higher-order and multi-leveled structures which can be tuned with simple alterations. We share experimental results which conclude a dramatic change in assembly patterns by changing particle index of refraction; namely, a switch between a conservative pair-wise regime to highly non-conservative many-body regime.   

What kinds of forces does optical binding produce?

Optical binding is an attractive tool for controlling colloidal forces because it offers a highly tunable method of producing inter-particle forces without chemical modifications. Previous studies of optically bound particles have tended to focus on small numbers of particles in relatively static configurations. By contrast, our experimental studies of many wavelength sized particles exhibit novel dynamics which are indicative of driven, non-conservative forces. I will discuss how these forces arise, and how they might be controlled to study colloidal dynamics in novel regimes.   

The odd flows of a colloidal chiral fluid

We report the assembly of a chiral fluid composed of millions of spinning colloidal magnets. By activating the fluid at the single unit level, we observe macroscopic flows with no counterpart in conventional fluids. Odd viscous stresses drive the propagation of unidirectional free-surface waves damped by odd (or Hall) viscosity. Further, the competition between odd stress and cohesive forces results in intermittent bulk flows, blurring the distinction between solid and liquid.