Numerous soft materials jam into an amorphous solid at high packing fraction. This non-equilibrium phase transition is best understood in the context of a model system in which particles repel elastically when they overlap. Recently, however, it was shown that introducing any finite amount of attraction between particles changes the universality class of the transition. The properties of this new ``sticky jamming'' class remain almost entirely unexplored. We use molecular dynamics simulations and scaling analysis to determine the shear modulus, bulk modulus, and coordination of marginal solids close to the sticky jamming point. In each case, the behavior of the system departs sharply and qualitatively from the purely repulsive case.
The theory of mechanical response and stress transmission in disordered, jammed solids poses several open questions of how non-periodic networks -- apparently indistinguishable from a snapshot of a fluid -- sustain shear. We present a stress-only theory of emergent elasticity for a non-thermal amorphous assembly of grains in a jammed solid, where each grain is subjected to mechanical constraints of force and torque balance. These grain-level constraints lead to the Gauss's law of an emergent $U(1)$ tensor electromagnetism, which then accounts for the mechanical response of such solids. This fo…
The shear response of soft solids can be modeled with linear elasticity, provided the forcing is slow and weak. Both of these approximations must break down when the material loses rigidity, such as in foams and emulsions at their (un)jamming point -- suggesting that the window of linear elastic response near jamming is exceedingly narrow. Yet precisely when and how this breakdown occurs remains unclear. To answer these questions, we perform computer simulations of stress relaxation and shear startup experiments in athermal soft sphere packings, the canonical model for jamming. By systematical…
We demonstrate that the elasticity of jammed solids is nonlocal. By forcing frictionless soft sphere packings at varying wavelength, we directly access their transverse and longitudinal compliances without resorting to curve fitting. The observed wavelength dependence of the compliances is incompatible with classical (local) elasticity, and hence quantifies the amplitude of nonlocal effects. Three distinct length scales, two of which diverge, control the amplitude of both nonlocal effects and fluctuations about the mean response. Our results identify new, more accurate constitutive relations f…
We use Photon Correlation Imaging, a recently introduced space-resolved dynamic light scattering method, to investigate the spatial correlation of the dynamics of a variety of jammed and glassy soft materials. Strikingly, we find that in deeply jammed soft materials spatial correlations of the dynamics are quite generally ultra-long ranged, extending up to the system size, orders of magnitude larger than any relevant structural length scale, such as the particle size, or the mesh size for colloidal gel systems. This has to be contrasted with the case of molecular, colloidal and granular ``supe…
The role of fixed degrees of freedom in soft/granular matter systems has broad applicability and theoretical interest. Here we address questions of the geometrical role that a scaffolding of fixed particles plays in tuning the threshold volume fraction and force network in the vicinity of jamming. Our 2d simulated system consists of soft particles and fixed "pins", both of which harmonically repel overlaps. On one hand, we find that many of the critical scalings associated with jamming in the absence of pins continue to hold in the presence of even dense pin latices. On the other hand, the pre…
Penrose tilings form lattices, exhibiting 5-fold symmetry and isotropic elasticity, with inhomogeneous coordination much like that of the force networks in jammed systems. Under periodic boundary conditions, their average coordination is exactly four. We study the elastic and vibrational properties of rational approximants to these lattices as a function of unit-cell size $N_S$ and find that they have of order $\sqrt{N_S}$ zero modes and states of self stress and yet all their elastic moduli vanish. In their generic form obtained by randomizing site positions, their elastic and vibrational pro…
We present a statistical mechanical description of randomly packed spherical particles, where the average coordination number is treated as a macroscopic thermodynamic variable. The overall packing entropy is shown to have two contributions: geometric, reflecting statistical weights of individual configurations, and topological, which corresponds to the number of topologically distinct states. Both of them are computed in the thermodynamic limit for isostatic packings in 2D and 3D, and the result is further expanded to the case of "floppy" particle clusters. The theory is directly applicable t…
We explore the rheology predicted by a recently proposed constitutive model for jammed suspensions of soft elastic particles derived from particle-level dynamics [Cuny et al., Phys. Rev. Lett. 127, 218003 (2021)]. Our model predicts that the orientation of the anisotropy of the microstructure, governed by an interplay between advection and contact elasticity, plays a key role at yielding and in flow. It generates normal stress differences contributing significantly to the yield criterion and Trouton ratio. It gives rise to non-trivial transients such as stress overshoots in step increases of s…
By calculating the linear response of packings of soft frictionless discs to quasistatic external perturbations, we investigate the critical scaling behavior of their elastic properties and non-affine deformations as a function of the distance to jamming. Averaged over an ensemble of similar packings, these systems are well described by elasticity, while in single packings we determine a diverging length scale $\ell^*$ up to which the response of the system is dominated by the local packing disorder. This length scale, which we observe directly, diverges as $1/Δz$, where $Δz$ is the difference…
The mechanical response of naturally abundant amorphous solids such as gels, jammed grains, and biological tissues are not described by the conventional paradigm of broken symmetry that defines crystalline elasticity. In contrast, the response of such athermal solids are governed by local conditions of mechanical equilibrium, i.e., force and torque balance of its constituents. Here we show that these constraints have the mathematical structure of a generalized electromagnetism, where the electrostatic limit successfully captures the anisotropic elasticity of amorphous solids. The emergence of …
It is well known that jammed soft materials will flow if sheared above their yield stress - think mayonnaise spread on bread - but a complete microscopic description of this seemingly sim- ple process has yet to emerge. What remains elusive is a microscopic framework that explains the macroscopic flow, derived from a 3-D spatially resolved analysis of the dynamics of the droplets or particles that compose the soft material. By combining confocal-rheology experiments on compressed emulsions and numerical simulations, we unravel that the primary microscopic mechanisms for flow are strongly influ…
We present a driven diffusive model which we call the Bus Route Model. The model is defined on a one-dimensional lattice, with each lattice site having two binary variables, one of which is conserved (``buses'') and one of which is non-conserved (``passengers''). The buses are driven in a preferred direction and are slowed down by the presence of passengers who arrive with rate lambda. We study the model by simulation, heuristic argument and a mean-field theory. All these approaches provide strong evidence of a transition between an inhomogeneous ``jammed'' phase (where the buses bunch togethe…
Granular jamming has been identified as a fundamental mechanism for the operation of robotic grippers. In this work, we show, that soft particles like expanded polystyrene beads lead to significantly larger gripping forces in comparison to rigid particles. In contradiction to naive expectation, the combination of jamming and elasticity gives rise to very different properties of the jammed phase, compared to hard-particle systems. This may be of interest also beyond the application in robotic grippers.
We propose here that certain observational features of granular matter in the infrared limit, exhibiting the phenomenon of {\it jamming}, arise from an underlying effective general relativistic description. The proposal stems from the assumption (which we justify on physical grounds) that grains in granular matter move freely in an {\it effective} curved Riemannian space. The termination of their trajectories at the onset of jamming is obtained from the focussing of a converging congruence of geodesics in such a space, as a solution of the Raychaudhuri equation for such congruences. This may h…
