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Active solids consist of elastically coupled out-of-equilibrium units performing work. They are central to autonomous processes in biological systems, e.g. locomotion, self-oscillations and morphogenesis. Moreover, their shape-preserving property and their intrinsic non-equilibrium nature make active solids a promising framework to create multifunctional metamaterials with bona fide autonomy. Yet, the feedback mechanism between elastic and active forces, and the possible emergence of collective behaviors remains poorly understood. We take advantage of centimetric models of self-propelled active units and introduce a minimal realization of an active elastic solid. Polar active agents exert forces on the nodes of a two-dimensional elastic lattice, and the resulting displacement field nonlinearly reorients the active agents. From this so-called elasto-active feedback emerges numerous new collective behaviors. In the first part, we show that for weak enough coupling, the presence of zero modes dictates the nature and the geometry of the collective behaviors. Rigid body motions in free boundary conditions thus provide a way to set a population a rigidly coupled active units into collective motion. Then, we find that for large enough coupling, a collective oscillation of the lattice nodes around their equilibrium position emerges, the so-called collective actuation. We find that only a few elastic modes are actuated and, crucially, they are not necessarily the lowest energy ones. Combining experiments with the numerical and theoretical analysis of an agents model, we unveil the bifurcation scenario and the selection mechanism by which the collective actuation takes place. We propose a hydrodynamic theory of active solids to describe their large-scale properties, and analyze some of its consequences. Playing with the vibrational properties of the lattice, we also explore the wide variety of collective actuations, and find control parameters and design strategies for the emerging dynamics. Finally, we study how the coupling with an external field polarizes active solids and affects the emergence of collective actuation. Altogether, beyond the understanding of our particular system, this manuscript is an attempt to unveil the mechanical functionality of active matter as a continuum.
PARISTECH
BY: Paul Baconnier.
collective motion, collective actuation & polarization. Mechanics of materials [physics.class-ph]. Université Paris sciences et lettres, 2023.
https://pastel.hal.science/tel-04081179