Model of Active Solids: Rigid Body Motion and Shape-Changing Mechanisms (2024)

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Model of Active Solids: Rigid Body Motion and Shape-Changing Mechanisms

Claudio Hernández-López, Paul Baconnier, Corentin Coulais, Olivier Dauchot, and Gustavo Düring
Phys. Rev. Lett. 132, 238303 – Published 7 June 2024
Model of Active Solids: Rigid Body Motion and Shape-Changing Mechanisms (1) See Focus story: Theory Predicts Collective States of Mobile Particles
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Abstract

Active solids such as cell collectives, colloidal clusters, and active metamaterials exhibit diverse collective phenomena, ranging from rigid body motion to shape-changing mechanisms. The nonlinear dynamics of such active materials remains, however, poorly understood when they host zero-energy deformation modes and when noise is present. Here, we show that stress propagation in a model of active solids induces the spontaneous actuation of multiple soft floppy modes, even without exciting vibrational modes. By introducing an adiabatic approximation, we map the dynamics onto an effective Landau free energy, predicting mode selection and the onset of collective dynamics. These results open new ways to study and design living and robotic materials with multiple modes of locomotion and shape change.

  • Model of Active Solids: Rigid Body Motion and Shape-Changing Mechanisms (2)
  • Model of Active Solids: Rigid Body Motion and Shape-Changing Mechanisms (3)
  • Model of Active Solids: Rigid Body Motion and Shape-Changing Mechanisms (4)
  • Received 21 October 2023
  • Revised 26 January 2024
  • Accepted 3 April 2024

DOI:https://doi.org/10.1103/PhysRevLett.132.238303

© 2024 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas

Collective behavior

  1. Physical Systems

Auxetic materialsCollective dynamics

Condensed Matter, Materials & Applied Physics

Model of Active Solids: Rigid Body Motion and Shape-Changing Mechanisms (5) Focus

Model of Active Solids: Rigid Body Motion and Shape-Changing Mechanisms (6)

Theory Predicts Collective States of Mobile Particles

Published 7 June 2024

Collections of interacting self-propelled objects held rigidly together show patterns of organized behavior that can be predicted.

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Authors & Affiliations

Claudio Hernández-López1,4,*, Paul Baconnier2, Corentin Coulais3, Olivier Dauchot2, and Gustavo Düring4,†

  • 1Laboratoire de Physique de l’École Normale Supérieure, UMR CNRS 8023, Université PSL, Sorbonne Université, 75005 Paris, France
  • 2Gulliver UMR CNRS 7083, ESPCI Paris, Université PSL, Paris, France
  • 3Institute of Physics, Universiteit van Amsterdam, 1098 XH Amsterdam, The Netherlands
  • 4Instituto de Física, Pontificia Universidad Católica de Chile, 8331150 Santiago, Chile
  • *claudio.hernandez.lopez@bio.ens.psl.eu
  • gduring@uc.cl

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Vol. 132, Iss. 23 — 7 June 2024

Model of Active Solids: Rigid Body Motion and Shape-Changing Mechanisms (7)
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  • Model of Active Solids: Rigid Body Motion and Shape-Changing Mechanisms (11)

    Figure 1

    Active rigid body motion and active mechanisms. (a)Enlargement of the experimental active elastic lattice introduced in [22], with self-propelling units—hexbugs—trapped in 3D-printed annuli, connected by springs in a triangular lattice. (b)Experimental rotational dynamics observed under central pinning. Scale bar, 10cm. (c),(d) Experimental translational and rotational dynamics observed for a free structure. Scale bar, 20cm. (e)Alternating translational and rotation dynamics obtained numerically for the same free structure. (f)A rotational-auxetic regime observed numerically for a nonpinned auxetic square system (see the text, Fig.3, and Movie S1 [30]). Trajectories are color coded from blue to red by increasing time.

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    Figure 2

    Second-order transitions to solid body motion and mechanisms for one-mode systems. Simulations consider πr=0.001 unless specified. (a)Periodic boundary condition (translation-only) network. (b)–(d)consider a 100×100 translating system. (b)Global polarization magnitude P time series; πθ=0.4. (c)Phase diagram μP vs πθ as a function of noise. (S) for simulations, (T) for theoretical predictions. (d)Landau free energy as a function of μx and μy; left: πθ=0.1; right: πθ=0.6. (e)A two-layer hexagonal ring with the definition of the rotational angle ϕ. (f)–(h)consider a nine-layer hexagonal ring system. (f)Angular velocity ϕ˙ time series; πθ=0.4. (g)Phase diagram μϕ vs πθ (left) and μϕ vs πr, when πθ=0 (right). (h)Landau free energy as a function of μϕ; blue: πθ=0.25; orange: πθ=0.6. (i)A one-layer auxetic system with the definition of the auxetic angle γ. (j)–(l)consider an eight-layer auxetic system. (j)Auxetic angular velocity γ˙ time series; πθ=0.4. (k)Phase diagram μγ vs πθ (left) and μγ vs πr, when πθ=0 (right). (l)Landau free energy as a function of μγ. Blue: πθ=0.25; orange: πθ=0.6.

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    Figure 3

    Two-mode system phenomenology: switching between modes of actuation. (a)Time series of the magnitude of the global polarization P (blue) and of the angular velocity ϕ˙ (red) for a two-ring nonpinned triangular lattice; left to right: πθ=0.10, 0.35; πr=0.1. (b)Phase diagram μP and μϕ vs πθ of a 30-ring nonpinned triangular lattice. (c)Landau free energy for a nonpinned two-ring triangular lattice as a function of μϕ and μx; from left to right: πθ=0.10, 0.35. (d)–(f)consider an eight-layer rotational-auxetic network. (d)Time series of the auxetic angular velocity γ˙ (blue) and rotational angular velocity ϕ˙ (red); from top to bottom: πθ=0.001, 0.006, 0.014. (e)Phase diagram γ˙ (top) and ϕ˙ (bottom) vs πθ. The theoretical values are the time average of each solution obtained from following the free energy minima as γ varies. Inset: enlargement of the ϕ˙0 region. (f)Landau free energy as it varies with γ (γ=0.2+nπ/2, with n=0, 1, 2, 3); πθ=0.001, and the evolution time step Δt=0.01.

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Model of Active Solids: Rigid Body Motion and Shape-Changing Mechanisms (2024)

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