Start-up shear of spherocylinder packings: Effect of friction.

We study the response to shear deformations of packings of long spherocylindrical particles that interact via frictional forces with friction coefficient µ. The packings are produced and deformed with the help of molecular dynamics simulations combined with minimization techniques performed on a GPU. We calculate the linear shear modulus g_{∞}, which is orders of magnitude larger than the modulus g_{0} in the corresponding frictionless system. The motion of the particles responsible for these large frictional forces is governed by and increases with the length ℓ of the spherocylinders. One consequence of this motion is that the shear modulus g_{∞} approaches a finite value in the limit ℓ→∞, even though the density of the packings vanishes, ρ∝ℓ^{-2}. By way of contrast, the frictionless modulus decreases to zero, g_{0}∼ℓ^{-2}, in accordance with the behavior of density. Increasing the strain beyond a value γ_{c}∼µ, the packing strain weakens from the large frictional to the smaller frictionless modulus when contacts saturate at the Coulomb inequality and start to slide. In this regime, sliding friction contributes a "yield stress" σ_{y}=g_{∞}γ_{c} and the stress behaves as σ=σ_{y}+g_{0}γ. The interplay between static and sliding friction gives rise to hysteresis in oscillatory shear simulations.

Packings of frictionless spherocylinders.

We present simulation results on the properties of packings of frictionless spherocylindrical particles. Starting from a random distribution of particles in space, a packing is produced by minimizing the potential energy of interparticle contacts until a force-equilibrated state is reached. For different particle aspect ratios α=10⋯40, we calculate contacts z, pressure as well as bulk and shear modulus. Most important is the fraction f_{0}(α) of spherocylinders with contacts at both ends, as it governs the jamming threshold z_{c}(α)=8+2f_{0}(α). These results highlight the important role of the axial "sliding" degree of freedom of a spherocylinder, which is a zero-energy mode but only if no end contacts are present.

Unsteady flow, clusters, and bands in a model shear-thickening fluid.

We analyze the flow curves of a two-dimensional assembly of granular particles which are interacting via frictional contact forces. For packing fractions slightly below jamming, the fluid undergoes a large scale instability, implying a range of stress and strain rates where no stationary flow can exist. Whereas small systems were shown previously to exhibit hysteretic jumps between the low and high stress branches, large systems exhibit continuous shear thickening arising from averaging unsteady, spatially heterogeneous flows. The observed large scale patterns as well as their dynamics are found to depend on strain rate: At the lower end of the unstable region, force chains merge to form giant bands that span the system in the compressional direction and propagate in the dilational direction. At the upper end, we observe large scale clusters which extend along the dilational direction and propagate along the compressional direction. Both patterns, bands and clusters, come in with infinite correlation length similar to the sudden onset of system-spanning plugs in impact experiments.

Rheology in dense assemblies of spherocylinders: Frictional vs. frictionless.

Using molecular dynamics simulations, we study the steady shear flow of dense assemblies of anisotropic spherocylindrical particles of varying aspect ratios. Comparing frictionless and frictional particles we discuss the specific role of frictional inter-particle forces for the rheological properties of the system. In the frictional system we evidence a shear-thickening regime, similar to that for spherical particles. Furthermore, friction suppresses the alignment of the spherocylinders along the flow direction. Finally, the jamming density in frictional systems is rather insensitive to variations in aspect ratio, quite contrary to what is known from frictionless systems.

Linear rheology of reversibly cross-linked biopolymer networks.

We suggest a simple model for reversible cross-links, binding, and unbinding to/from a network of semiflexible polymers. The resulting frequency dependent response of the network to an applied shear is calculated via Brownian dynamics simulations. It is shown to be rather complex with the time scale of the linkers competing with the excitations of the network. If the lifetime of the linkers is the longest time scale, as is indeed the case in most biological networks, then a distinct low frequency peak of the loss modulus develops. The storage modulus shows a corresponding decay from its plateau value, which for irreversible cross-linkers extends all the way to the static limit. This additional relaxation mechanism can be controlled by the relative weight of reversible and irreversible linkers.

Rheology of Membrane-Attached Minimal Actin Cortices.

The actin cortex is a thin cross-linked network attached to the plasma membrane, which is responsible for the cell's shape during migration, division, and growth. In a reductionist approach, we created a minimal actin cortex (MAC) attached to a lipid membrane to correlate the filamentous actin architecture with its viscoelastic properties. The system is composed of a supported 1-palmitoyl-2-oleoyl- sn-glycero-3-phosphocholine bilayer doped with the receptor lipid phosphatidylinositol(4,5)-bisphosphate (PtdIns(4,5)P2) to which a constitutively active mutant of ezrin, which is a direct membrane-cytoskeleton linker, is bound. The formation of the MAC on the supported lipid bilayer is analyzed as a function of increasing PtdIns(4,5)P2/ezrin pinning points, revealing an increase in the intersections between actin filaments, that is, the node density of the MAC. Bead tracking microrheology on the membrane-attached actin network provides information about its viscoelastic properties. The results show that ezrin serves as a dynamic cross-linker for the actin cortex attached to the lipid bilayer and that the stiffness of the network is influenced by the pinning point density, relating the plateau storage modulus G0 to the node density of the MAC.

Athermal rheology of weakly attractive soft particles.

We study the rheology of a soft particulate system where the interparticle interactions are weakly attractive. Using extensive molecular dynamics simulations, we scan across a wide range of packing fractions (ϕ), attraction strengths (u), and imposed shear rates (γ[over ̇]). In striking contrast to repulsive systems, we find that at small shear rates generically a fragile isostatic solid is formed even if we go to ϕ≪ϕ_{J}. Further, with increasing shear rates, even at these low ϕ, nonmonotonic flow curves occur which lead to the formation of persistent shear bands in large enough systems. By tuning the damping parameter, we also show that inertia plays an important role in this process. Furthermore, we observe enhanced particle dynamics in the attraction-dominated regime as well as a pronounced anisotropy of velocity and diffusion constant, which we take as precursors to the formation of shear bands. At low enough ϕ, we also observe structural changes via the interplay of low shear rates and attraction with the formation of microclusters and voids. Finally, we characterize the properties of the emergent shear bands, and thereby, we find surprisingly small mobility of these bands, leading to prohibitively long time scales and extensive history effects in ramping experiments.

Thermalized connectivity networks of jammed packings.

Jammed packings of repulsive elastic spheres have emerged as a rich model system within which the elastic properties of disordered glassy materials may be elucidated. Most of the work on these packings has focused on the case of vanishing temperature. Here, we explore the elastic properties of the associated connectivity network for finite temperatures, ignoring the breaking of bonds and the formation of new ones. Using extensive Monte Carlo simulations, we find that, as the temperature is increased, the resulting spring network shrinks and exhibits a rapidly softening bulk modulus via a cusp. Moreover, the shear modulus stiffens in a fixed volume ensemble but not in a fixed pressure ensemble. These counter-intuitive behaviors may be understood from the characteristic spectrum of soft modes near isostaticity, which resembles the spectrum of a rod near its buckling instability. Our results suggest a generic mechanism for negative thermal expansion coefficients in marginal solids. We discuss some consequences of bond breaking and an apparent analogy between thermalization and shear.

Viscoelasticity of reversibly crosslinked networks of semiflexible polymers.

We present a theoretical framework for the linear and nonlinear viscoelastic properties of reversibly crosslinked networks of semiflexible polymers. In contrast to affine models where network strain couples to the polymer end-to-end distance, in our model strain rather serves to locally distort the network structure. This induces bending modes in the polymer filaments, the properties of which are slaved to the surrounding network structure. Specifically, we investigate the frequency-dependent linear rheology, in particular in combination with crosslink binding-unbinding processes. We also develop schematic extensions to describe the nonlinear response during creep measurements as well as during constant strain-rate ramps.

Rheological chaos of frictional grains.

A two-dimensional dense fluid of frictional grains is shown to exhibit time-chaotic, spatially heterogeneous flow in a range of stress values, σ, chosen in the unstable region of s-shaped flow curves. Stress-controlled simulations reveal a phase diagram with reentrant stationary flow for small and large stress σ. In between, no steady flow state can be reached, instead the system either jams or displays time-dependent heterogeneous strain rates γ(r,t). The results of simulations are in agreement with the stability analysis of a simple hydrodynamic model, coupling stress and microstructure which we tentatively associate with the frictional contact network.

Transition from a Linear to a Harmonic Potential in Collective Dynamics of a Multifilament Actin Bundle.

Attractive depletion forces between rodlike particles in highly crowded environments have been shown through recent modeling and experimental approaches to induce different structural and dynamic signatures depending on relative orientation between rods. For example, it has been demonstrated that the axial attraction between two parallel rods yields a linear energy potential corresponding to a constant contractile force of 0.1 pN. Here, we extend pairwise, depletion-induced interactions to a multifilament level with actin bundles, and find contractile forces up to 3 pN. Forces generated due to bundle relaxation were not constant, but displayed a harmonic potential and decayed exponentially with a mean decay time of 3.4 s. Through an analytical model, we explain these different fundamental dynamics as an emergent, collective phenomenon stemming from the additive, pairwise interactions of filaments within a bundle.

Free volume under shear.

Using an athermal quasistatic simulation protocol, we study the distribution of free volumes in sheared hard-particle packings close to, but below, the random-close packing threshold. We show that under shear, and independent of volume fraction, the free volumes develop features similar to close-packed systems - particles self-organize in a manner as to mimick the isotropically jammed state. We compare athermally sheared packings with thermalized packings and show that thermalization leads to an erasure of these structural features. The temporal evolution in particular the opening-up and the closing of free-volume patches is associated with the single-particle dynamics, showing a crossover from ballistic to diffusive behavior.

Jamming of frictional particles: a nonequilibrium first-order phase transition.

We propose a phase diagram for the shear flow of dry granular particles in two dimensions based on simulations and a phenomenological Landau theory for a nonequilibrium first-order phase transition. Our approach incorporates both frictional as well as frictionless particles. The most important feature of the frictional phase diagram is reentrant flow and a critical jamming point at finite stress. In the frictionless limit the regime of reentrance vanishes and the jamming transition is continuous with a critical point at zero stress. The jamming phase diagrams derived from the model agree with the experiments of Bi et al. [Nature (London) 480, 355 (2011)] and brings together previously conflicting numerical results.

Rheology near jamming: the influence of lubrication forces.

We study, by computer simulations, the roles of different dissipation forces in the rheological properties of highly dense particle-laden flows. In particular, we are interested in the close-packing limit (jamming) and the question of whether "universal" observables can be identified that do not depend on the details of the dissipation model. To this end, we define a simplified lubrication force and systematically vary the range h(c) of this interaction. For fixed h(c) a crossover is seen from a Newtonian flow regime at small strain rates to inertia-dominated flow at larger strain rates. The same crossover is observed as a function of the lubrication range h(c). At the same time, but only at high densities close to jamming, single-particle velocities as well as local density distributions are unaffected by changes in the lubrication range--they are candidates for universal behavior. At densities away from jamming, this invariance is lost: short-range lubrication forces lead to pronounced particle clustering, while longer-ranged lubrication does not. These findings highlight the importance of "geometric" packing constraints for particle motion--independent of the specific dissipation model. With the free volume vanishing at random close packing, particle motion is more and more constrained by the ever smaller amount of free space. On the other hand, macroscopic rheological observables as well as higher-order correlation functions retain the variability of the underlying dissipation model.

Elasto-plastic response of reversibly crosslinked biopolymer bundles.

We study the response of F-actin bundles to driving forces through a simple analytical model. We consider two filaments connected by reversibly bound crosslinks and driven by an external force. Two failure modes under load can be defined. Brittle failure is observed when crosslinks suddenly and collectively unbind, leading to catastrophic loss of bundle integrity. During ductile failure, on the other hand, bundle integrity is maintained, however at the cost of crosslink reorganization and defect formation. We present phase diagrams for the onset of failure, highlighting the importance of the crosslink stiffness for these processes. Crossing the phase boundaries, force-deflection curves display (frequency-dependent) hysteresis loops, reflecting the first-order character of the failure processes. We evidence how the introduction of defects can lead to complex elasto-plastic relaxation processes, once the force is switched off. Depending on, both the time-scale for defect motion and the crosslink stiffness, bundles can remain in a quasi-permanent plastically deformed state for a very long time.

Impact of attractive interactions on the rheology of dense athermal particles.

Using numerical simulations, the rheological response of an athermal assembly of soft particles with tunable attractive interactions is studied in the vicinity of jamming. At small attractions, a fragile solid develops and a finite yield stress is measured. Moreover, the measured flow curves have unstable regimes, which lead to persistent shear banding. These features are rationalized by establishing a link between the rheology and the interparticle connectivity, which also provides a minimal model to describe the flow curves.

(Ir)reversibility in dense granular systems driven by oscillating forces.

We use computer simulations to study highly dense systems of granular particles that are driven by oscillating forces. We implement different dissipation mechanisms that are used to extract the injected energy. In particular, the action of a simple local Stokes' drag is compared with non-linear and history-dependent frictional forces that act either between particle pairs or between particles and an external container wall. The Stokes' drag leads to particle motion that is periodic with the driving force, even at high densities around close packing where particles undergo frequent collisions. With the introduction of inter-particle frictional forces this "interacting absorbing state" is destroyed and particles start to diffuse around. By reducing the density of the material we go through another transition to a "non-interacting" absorbing state, where particles independently follow the force-induced oscillations without collisions. In the system with particle-wall frictional interactions this transition has signs of a discontinuous phase transition. It is accompanied by a diverging relaxation time, but not by a vanishing order parameter, which rather jumps to zero at the transition.

Shear thickening in granular suspensions: interparticle friction and dynamically correlated clusters.

We consider the shear rheology of concentrated suspensions of non-Brownian frictional particles. The key result of our study is the emergence of a pronounced shear-thickening regime, where frictionless particles would normally undergo shear thinning. We can clarify that shear thickening in our simulations is due to enhanced energy dissipation via frictional interparticle forces. Moreover, we evidence the formation of dynamically correlated particle clusters of size ξ, which contribute to shear thickening via an increase in viscous dissipation. A scaling argument gives for the associated viscosity η(v)~ξ(2), which is in very good agreement with the data.

Melting a granular glass by cooling.

Driven granular systems readily form glassy phases at high particle volume fractions and low driving amplitudes. We use computer simulations of a driven granular glass to evidence a reentrance melting transition into a fluid state, which, contrary to intuition, occurs by reducing the amplitude of the driving. This transition is accompanied by anomalous particle dynamics and superdiffusive behavior on intermediate time scales. We highlight the special role played by frictional interactions, which help particles to escape their glassy cages. Such an effect is in striking contrast to what friction is expected to do: reduce particle mobility by making them stick.

Shear flow of non-Brownian suspensions close to jamming.

The dynamical mechanisms controlling the rheology of dense suspensions close to jamming are investigated numerically, using simplified models for the relevant dissipative forces. We show that the velocity fluctuations control the dissipation rate and therefore the effective viscosity of the suspension. These fluctuations are similar in quasi-static simulations and for finite strain rate calculations with various damping schemes. We conclude that the statistical properties of grain trajectories-in particular the critical exponent of velocity fluctuations with respect to volume fraction φ-only weakly depend on the dissipation mechanism. Rather they are determined by steric effects, which are the main driving forces in the quasistatic simulations. The critical exponent of the suspension viscosity with respect to φ can then be deduced, and is consistent with experimental data.