Spongelike Rigid Structures in Frictional Granular Packings

Soft matter physics of the ground beneath our feet

The soft part of the Earth's surface - the ground beneath our feet - constitutes the basis for life and natural resources, yet a general physical understanding of the ground is still lacking. In this critical time of climate change, cross-pollination of scientific approaches is urgently needed to better understand the behavior of our planet's surface. The major topics in current research in this area cross different disciplines, spanning geosciences, and various aspects of engineering, material sciences, physics, chemistry, and biology. Among these, soft matter physics has emerged as a fundamental nexus connecting and underpinning many research questions. This perspective article is a multi-voice effort to bring together different views and approaches, questions and insights, from researchers that work in this emerging area, the soft matter physics of the ground beneath our feet. In particular, we identify four major challenges concerned with the dynamics in and of the ground: (I) modeling from the grain scale, (II) near-criticality, (III) bridging scales, and (IV) life. For each challenge, we present a selection of topics by individual authors, providing specific context, recent advances, and open questions. Through this, we seek to provide an overview of the opportunities for the broad Soft Matter community to contribute to the fundamental understanding of the physics of the ground, strive towards a common language, and encourage new collaborations across the broad spectrum of scientists interested in the matter of the Earth's surface.

Properties of packings and dispersions of superellipse sector particles

Superellipse sector particles (SeSPs) are segments of superelliptical curves that form a tunable set of hard-particle shapes for granular and colloidal systems. SeSPs allow for continuous parametrization of corner sharpness, aspect ratio, and particle curvature; rods, circles, rectangles, and staples are examples of shapes SeSPs can model. We compare three computational processes: pair-wise Monte Carlo simulations that explore particle-particle geometric constraints, Monte Carlo simulations that reveal how these geometric constraints play out over dispersions of many particles, and Molecular Dynamics simulations that form random loose and close packings. We investigate the dependence of critical random loose and close packing fractions on particle parameters, finding that both values increase with opening aperture and decrease with increasing corner sharpness. The identified packing fractions are compared with the mean-field prediction of the random contact model; we find deviations from the model's prediction due to correlations between particle orientations. The complex interaction of spatial proximity and orientational alignment is also explored with a generalized spatioorientational distribution area (SODA) plot, which shows how higher density packings are achieved through particles assuming a small number of preferred configurations that depend sensitively on particle shape and system preparation.

Discontinuous rigidity transition associated with shear jamming in granular simulations

We investigate the rigidity transition associated with shear jamming in frictionless, as well as frictional, disk packings in the quasi-static regime and at low shear rates. For frictionless disks, the transition under quasi-static shear is discontinuous, with an instantaneous emergence of a system spanning rigid clusters at the jamming transition. For frictional systems, the transition appears continuous for finite shear rates, but becomes sharper for lower shear rates. In the quasi-static limit, it is discontinuous as in the frictionless case. Thus, our results show that the rigidity transition associated with shear jamming is discontinuous, as demonstrated in the past for isotropic jamming of frictionless particles, and therefore a unifying feature of the jamming transition in general.

Heterogeneous Dynamics of Sheared Particle-Laden Fluid Interfaces with Janus Particle Doping

The formation of particle clusters can substantially modify the dynamics and mechanical properties of suspensions in both two and three dimensions. While it has been well established that large network-spanning clusters increase the rigidity of particle systems, it is still unclear how the presence of localized nonpercolating clusters affects the dynamics and mechanical properties of particle suspensions. Here, we introduce self-assembled localized particle clusters at a fluid-fluid interface by mixing a fraction of Janus particles in a monolayer of homogeneous colloids. Each Janus particle binds to a few nearby homogeneous colloids, resulting in numerous small clusters uniformly distributed across the interface. Using a custom magnetic rod interfacial stress rheometer, we apply linear oscillatory shear to the particle-laden fluid interface. By analyzing the local affine deformation of particles from optical microscopy, we show that particles in localized clusters experience substantially lower shear-induced stretching than their neighbors outside clusters. We hypothesize that such heterogeneous dynamics induced by particle clusters increase the effective surface coverage of particles, which in turn enhances the shear moduli of the interface, as confirmed by direct interfacial rheological measurements. Our study illustrates the microscopic dynamics of small clusters in a shear flow and reveals their profound effects on the macroscopic rheology of particle-laden fluid interfaces. Our findings open an avenue for designing interfacial materials with improved mechanical properties via the control of formation of localized particle clusters.

Theory of rigidity and numerical analysis of density of states of two-dimensional amorphous solids with dispersed frictional grains in the linear response regime

Using the Jacobian matrix, we obtain a theoretical expression of rigidity and the density of states of two-dimensional amorphous solids consisting of frictional grains in the linear response to an infinitesimal strain, in which we ignore the dynamical friction caused by the slip processes of contact points. The theoretical rigidity agrees with that obtained by molecular dynamics simulations. We confirm that the rigidity is smoothly connected to the value in the frictionless limit. We find that there are two modes in the density of states for sufficiently small k_{T}/k_{N}, which is the ratio of the tangential to normal stiffness. Rotational modes exist at low frequencies or small eigenvalues, whereas translational modes exist at high frequencies or large eigenvalues. The location of the rotational band shifts to the high-frequency region with an increase in k_{T}/k_{N} and becomes indistinguishable from the translational band for large k_{T}/k_{N}.

Controlling rheology via boundary conditions in dense granular flows

Boundary shape, particularly roughness, strongly controls the amount of wall slip in dense granular flows. In this paper, we aim to quantify and understand which aspects of a dense granular flow are controlled by the boundary conditions, and to incorporate these observations into a cooperative nonlocal model characterizing slow granular flows. To examine the influence of boundary properties, we perform experiments on a quasi-2D annular shear cell with a rotating inner wall and a fixed outer wall; the latter is selected among 6 walls with various roughnesses, local concavity, and compliance. We find that we can successfully capture the full flow profile using a single set of empirically determined model parameters, with only the wall slip velocity set by direct observation. Through the use of photoelastic particles, we observe how the internal stresses fluctuate more for rougher boundaries, corresponding to a lower wall slip, and connect this observation to the propagation of nonlocal effects originating from the wall. Our measurements indicate a universal relationship between dimensionless fluidity and velocity.

Eigenvalue analysis of stress-strain curve of two-dimensional amorphous solids of dispersed frictional grains with finite shear strain

The stress-strain curve of two-dimensional frictional dispersed grains interacting with a harmonic potential without considering the dynamical slip under a finite strain is determined by using eigenvalue analysis of the Hessian matrix. After the configuration of grains is obtained, the stress-strain curve based on the eigenvalue analysis is in almost perfect agreement with that obtained by the simulation, even if there are plastic deformations caused by stress avalanches. Unlike the naive expectation, the eigenvalues in our model do not indicate any precursors to the stress-drop events.

Stretchy and disordered: Toward understanding fracture in soft network materials via mesoscopic computer simulations

Soft network materials exist in numerous forms ranging from polymer networks, such as elastomers, to fiber networks, such as collagen. In addition, in colloidal gels, an underlying network structure can be identified, and several metamaterials and textiles can be considered network materials as well. Many of these materials share a highly disordered microstructure and can undergo large deformations before damage becomes visible at the macroscopic level. Despite their widespread presence, we still lack a clear picture of how the network structure controls the fracture processes of these soft materials. In this Perspective, we will focus on progress and open questions concerning fracture at the mesoscopic scale, in which the network architecture is clearly resolved, but neither the material-specific atomistic features nor the macroscopic sample geometries are considered. We will describe concepts regarding the network elastic response that have been established in recent years and turn out to be pre-requisites to understand the fracture response. We will mostly consider simulation studies, where the influence of specific network features on the material mechanics can be cleanly assessed. Rather than focusing on specific systems, we will discuss future challenges that should be addressed to gain new fundamental insights that would be relevant across several examples of soft network materials.

The effect of grain shape and material on the nonlocal rheology of dense granular flows

Nonlocal rheologies allow for the modeling of granular flows from the creeping to intermediate flow regimes, using a small number of parameters. In this paper, we report on experiments testing how particle properties affect the model parameters used in the Kamrin & Koval cooperative nonlocal model, using particles of three different shapes (circles, ellipses, and pentagons) and three different materials, including one which allows for the measurement of stresses via photoelasticity. Our experiments are performed on a quasi-2D annular shear cell with a rotating inner wall and a fixed outer wall. Each type of particle is found to exhibit flows which are well-fit by nonlocal rheology, with each particle having a distinct triad of the local, nonlocal, and frictional parameters. While the local parameter b is always approximately unity, the nonlocal parameter A depends sensitively on both the particle shape and material. The critical stress ratio μ_s, above which Coulomb failure occurs, varies for particles with the same material but different shape, indicating that geometric friction can dominate over material friction.

The effect of boundary roughness on dense granular flows

In the field of granular rheology, an important open question is to understand the influence of boundary conditions on granular flows. We perform experiments in a quasi-2D annular shear cell subject to 6 different boundaries with controlled roughness/compliance. We characterize the granular slip at the boundaries to investigate which aspects of a dense granular flow can be controlled by the choice of boundary condition. Photoelastic techniques are implemented to measure the stress fields P(r) and τ(r) throughout the material. A full inverse-analysis of the fringes within each disk provides the vector force at each contact. This allows us to measure the continuum stress field by coarse-graining internal forces. We have observed that boundary roughness and compliance strongly controls the flow profile v(r) and shear rate profile γ˙(r). We also observed that boundary roughness and compliance play a significant role in the pressure profile P(r) and shear stress profile τ(r).