Edge mode amplification in disordered elastic networks.

  title={Edge mode amplification in disordered elastic networks.},
  author={Le Yan and J. Bouchaud and M. Wyart},
  journal={Soft matter},
  volume={13 34},
Understanding how mechanical systems can be designed to efficiently transport elastic information is important in a variety of fields, including in materials science and biology. Recently, it has been discovered that certain crystalline lattices present "topologically-protected" edge modes that can amplify elastic signals. Several observations suggest that edge modes are important in disordered systems as well, an effect not well understood presently. Here we build a theory of edge modes in… Expand

Figures from this paper

Density scaling in the mechanics of a disordered mechanical meta-material
Nature provides examples of self-assemble lightweight disordered network structures with remarkable mechanical properties which are desirable for many application purposes but challenging toExpand
Principles for Optimal Cooperativity in Allosteric Materials.
It is shown, using an in silico evolution scheme and theoretical arguments, that architectures optimized to be cooperative, which efficiently propagate energy, qualitatively differ from previously investigated materials optimized to propagate strain. Expand
Architecture and Co-Evolution of Allosteric Materials
This work introduces a numerical scheme to evolve functional materials that can accomplish a specified mechanical task and finds that functioning materials evolve a less-constrained trumpet-shaped region connecting the stimulus and active sites, and that the amplitude of the elastic response varies non-monotonically along the trumpet. Expand
Localizing softness and stress along loops in 3D topological metamaterials
The design of a 3D topological metamaterial without Weyl lines and with a uniform polarization that leads to an asymmetry between the number of soft modes on opposing surfaces is reported, suggesting a strategy for preprogramming failure and softness localized along lines in 3D, while avoiding extended soft Weyl modes. Expand
Stress Response of Granular Systems
We develop a framework for stress response in two dimensional granular media, with and without friction, that respects vector force balance at the microscopic level. We introduce local gauge degreesExpand
Architecture and coevolution of allosteric materials
It is shown that functioning materials evolve a less-constrained trumpet-shaped region connecting the stimulus and active sites, and that the amplitude of the elastic response varies nonmonotonically along the trumpet. Expand
Controlling the deformation of metamaterials: Corner modes via topology
Topological metamaterials have invaded the mechanical world, demonstrating acoustic cloaking and waveguiding at finite frequencies and variable, tunable elastic response at zero frequency.Expand
Periodic topological lattice with different indentation hardness on opposite surfaces
Abstract Different surface properties are needed simultaneously in many applications, especially under an indentation load or impact load. This study proposes one class of novel periodic topologicalExpand
Allostery in Its Many Disguises: From Theory to Applications.
An overview of the progress and remaining limitations in the understanding of the mechanistic foundations of allostery gained from computational and experimental analyses of real protein systems and model systems is provided. Expand


Elastic collapse in disordered isostatic networks
Isostatic networks are minimally rigid and therefore have, generically, nonzero elastic moduli. Regular isostatic networks have finite moduli in the limit of large sizes. However, numericalExpand
Phonon gap and localization lengths in floppy materials
Gels of semi-flexible polymers, network glasses made of low valence elements, softly compressed ellipsoid particles and dense suspensions under flow are examples of floppy materials. These systemsExpand
Nonlinear conduction via solitons in a topological mechanical insulator
This work builds a topologically protected mechanism that can perform basic tasks such as transporting a mechanical state from one location to another and paves the way toward adopting the principle of topological robustness in the design of robots assembled from activated linkages as well as in the fabrication of complex molecular nanostructures. Expand
On the rigidity of amorphous solids
We poorly understand the properties of amorphous systems at small length scales, where a continuous elastic description breaks down. This is apparent when one considers their vibrational andExpand
Fractal free energy landscapes in structural glasses.
It is shown, using theory and numerical simulation, that the landscape is much rougher than is classically assumed and undergoes a 'roughness transition' to fractal basins, which brings about isostaticity and marginal stability on approaching jamming. Expand
Disordered surface vibrations in jammed sphere packings.
In bulk systems, without surfaces, it is well understood that such systems have a plateau in the density of vibrational modes extending down to a frequency scale ω*, but in the presence of a free surface this frequency is controlled by ΔZ. Expand
Effects of coordination and pressure on sound attenuation, boson peak and elasticity in amorphous solids.
An effective medium theory of elasticity is presented that unifies sound attenuation, transport and length scales entering elasticity in a single framework where disorder is not the main parameter controlling the boson peak, in agreement with observations. Expand
Phonons and elasticity in critically coordinated lattices.
This pedagogical review focuses on the properties of frames with z at or near zc, which model systems like randomly packed spheres near jamming and network glasses, and shows how modifications to the periodic kagome lattice can eliminate all but trivial translational zero modes and create topologically distinct classes. Expand
Breakdown of continuum elasticity in amorphous solids.
Numerically, the response of simple amorphous solids to a local force dipole is characterized by a lengthscale lc that diverges as unjamming is approached as lc ∼ (z - 2d)(-1/2), at odds with previous numerical claims. Expand
Effects of compression on the vibrational modes of marginally jammed solids.
The requirement of stability despite the destabilizing effect of pressure yields a lower bound on the number of extra contact per particle deltaz:deltaz> or =p1/2, which generalizes the Maxwell criterion for rigidity when pressure is present. Expand