The rheology of dense granular flows is studied numerically in a shear cell controlled at constant pressure and shear stress, confined between two granular shear flows. We show that a liquid state can be achieved even far below the yield stress, whose flow can be described with the same rheology as above the yield stress. A nonlocal constitutive relation is derived from dimensional analysis through a gradient expansion and calibrated using the spatial relaxation of velocity profiles observed under homogeneous stresses. Both for frictional and frictionless grains, the relaxation length is found to diverge as the inverse square root of the distance to the yield point, on both sides of that point.

Soft solids with tunable mechanical response are at the core of new material technologies, but a crucial limit for applications is their progressive aging over time, which dramatically affects their functionalities. The generally accepted paradigm is that such aging is gradual and its origin is in slower than exponential microscopic dynamics, akin to the ones in supercooled liquids or glasses. Nevertheless, time- and space-resolved measurements have provided contrasting evidence: dynamics faster than exponential, intermittency and abrupt structural changes. Here we use 3D computer simulations of a microscopic model to reveal that the timescales governing stress relaxation, respectively, through thermal fluctuations and elastic recovery are key for the aging dynamics. When thermal fluctuations are too weak, stress heterogeneities frozen-in upon solidification can still partially relax through elastically driven fluctuations. Such fluctuations are intermittent, because of strong correlations that persist over the timescale of experiments or simulations, leading to faster than exponential dynamics.

Abstract. The rheology of dense granular flows is studied numerically in a shear cell controlled at constant pressure and shear stress, confined between two granular shear flows. We show that a liquid state can be achieved even far below the yield stress, whose flow can be described with the same rheology as above the yield stress. A non-local constitutive relation is derived from dimensional analysis through a gradient expansion and calibrated using the spatial relaxation of velocity profiles observed under homogeneous stresses. Both for frictional and frictionless grains, the relaxation length is found to diverge as the inverse square root of the distance to the yield point, on both sides of that point. We also make use of a micro-rheometer to determine the influence of a distant shear band on the local rheological behaviour. Finally, we compare various approaches based on different non-local constitutive relations and choices for the fluidity parameter. We emphasise that, to discriminate between the different approaches proposed in the literature, one has to go beyond the predictions derived from linearisation around a uniform stress profile, such as that obtained in a simple shear cell. We argue that future tests can be based on the nature of the chosen fluidity parameter, and the related boundary conditions, as well as the hypothesis made to derive the models and the dynamical mechanisms underlying their dynamics.

The structural complexity of soft gels is at the origin of a versatile mechanical response that allows for large deformation, controlled elastic recovery, and toughness in the same material. A limit to exploiting the potential of such materials is the insufficient fundamental understanding of the microstructural origin of the bulk mechanical properties. Here we investigate the role of the network topology in a model gel through 3D numerical simulations. Our study links the topology of the network organization in space to its nonlinear rheological response preceding yielding and damage: our analysis elucidates how the network connectivity alone could be used to modify the gel mechanics at large strains, from strain-softening to hardening and even to a brittle response. These findings provide new insight for smart material design and for understanding the nontrivial mechanical response of a potentially wide range of technologically relevant materials.

Rigidity percolation (RP) occurs when mechanical stability emerges in disordered networks as constraints or components are added. Here we discuss RP with structural correlations, an effect ignored in classical theories albeit relevant to many liquid-to-amorphous-solid transitions, such as colloidal gelation, which are due to attractive interactions and aggregation. Using a lattice model, we show that structural correlations shift RP to lower volume fractions. Through molecular dynamics simulations, we show that increasing attraction in colloidal gelation increases structural correlation and thus lowers the RP transition, agreeing with experiments. Hence colloidal gelation can be understood as a RP transition, but occurs at volume fractions far below values predicted by the classical RP, due to attractive interactions which induce structural correlation. arXiv:1807.08858v1 [cond-mat.soft]

α-Actinin-4 (ACTN4) bundles and cross-links actin filaments to confer mechanical resilience to the reconstituted actin network. How this resilience is built and dynamically regulated in the podocyte, and the cause of its failure in ACTN4 mutation-associated focal segmental glomerulosclerosis (FSGS), remains poorly defined. Using primary podocytes isolated from wild-type (WT) and FSGS-causing point mutant Actn4 knockin mice, we report responses to periodic stretch. While WT cells largely maintained their F-actin cytoskeleton and contraction, mutant cells developed extensive and irrecoverable reductions in these same properties. This difference was attributable to both actin material changes and a more spatially correlated intracellular stress in mutant cells. When stretched cells were further challenged using a cell adhesion assay, mutant cells were more likely to detach. Together, these data suggest a mechanism for mutant podocyte dysfunction and loss in FSGS-it is a direct consequence of mechanical responses of a cytoskeleton that is brittle.

International audienc

It has been conjectured by Bagnold [1] that an assembly of hard non-deformable spheres could behave as a compressible medium when slowly sheared, as the average density of such a system effectively depends on the confining pressure. Here we use discrete element simulations to show the existence of transverse and sagittal waves associated to this dynamical compressibility. For this purpose, we study the resonance of these waves in a linear Couette cell and compare the results with those predicted from a continuum local constitutive relation.Acoustics in granular media is a rapidly developing field that is attractive both from the fundamental point of view and for its applications in material science, soil mechanics and geophysics [2,3]. It provides a unique tool to probe the mechanical response of such materials, to detect heterogeneities, aging or avalanche precursors. In the static case, grain elasticity is the only restoring force; elastic waves present most of the known behaviors of mechanical waves: velocity dispersion, non-linearity associated to contact geometry, scattering associated to disorder, anisotropy, aging, mode coupling, wave-guiding in the presence of macroscopic heterogeneities, fragility, etc [3][4][5][6][7][8]. Recent studies [9][10][11] have focused on the failure of the mean field description of elasticity when approaching the jamming transition separating the solid-like from the liquid-like regime. The importance of non-affine displacements in this limit was revealed by the structure of the vibration spectrum, which exhibits an anomalous excess of low frequency 'soft' modes [12][13][14]. In the following we wish instead to investigate wave propagation on the liquid side of the jamming transition.Wave propagation in granular shear flows have never been studied for itself. It has been revealed indirectly by instabilities, in situations where acoustic waves are spontaneously emitted during a dense granular flow (see [2] for a review): when sufficiently dry, avalanches flowing at the surface of a dune produce a loud sound known as the 'song of dunes ' [15-18]; vibrations are also produced during the discharge of a granular flow from a silo or any elongated tube [19]; soft mono-disperse particles flowing on an inclined plane near the angle of repose exhibit spontaneous oscillations at the resonant frequency of elastic waves [20,21]. These phenomena have mostly been associated to the elastic deformations of the grains. However, Bagnold [1] and followers [2,16,18] have hypothesized the existence of vibrations driven by the coupling between normal stress and shear rate.In this Letter we theoretically demonstrate the existence of such waves in dense slow shear flows of hard non-deformable grains. We show that these waves are due to a compressibility of dynamical origin, whose scaling with the volume fraction φ is related to the non-affine cooperative motion of the grains. The dispersion relation presents three branches, two of which becoming nondissipative when approaching the jamming point. Our a...