Spatial repartition of local plastic processes in different creep regimes in a granular material

Granular packings under constant shear stress display below the Coulomb limit, a logarithmic creep dynamics. However the addition of small stress modulations induces a linear creep regime characterized by an effective viscous response. Using Diffusing Wave Spectroscopy, we investigate the relation between creep and local plastic events spatial distribution (“hot-spots”) contributing to the plastic yield. The study is done in the two regimes, i.e. with and without mechanical activation. The hot-spot dynamics is related to the material effective fluidity. We show that far from the threshold, a local visco-elastic rheology coupled to an ageing of the fluidity parameter, is able to render the essential spatio-temporal features of the observed creep dynamics. Introduction. – Granular packings are often seen as rigid below a limit corresponding to a critical ratio between shear stress and normal stress (Coulomb threshold) [1]. However, the existence of a clear-cut transition between a solid-like and liquid-like behaviour is currently strongly challenged [2–5]. In the presence of a shear band (i.e. a fluid zone dwelling somewhere in the packing) different authors brought evidences for mechanically activated creeping processes taking place in remote regions, below the Coulomb threshold [2, 3]. This behaviour led to nonlocal rheological relations proposed to extend the standard local constitutive relations for granular flows [6–9]. For granular packing sheared in all of its parts below the Coulomb limit, dynamical processes leading to a logarithmic creep occurs [4, 5, 10]. Interestingly, this creeping dynamics can be mapped onto a simple visco-elastic model initially designed to render the phenomenology of yield stress fluids displaying ageing in the solid phase [11]. The model is centred on a dynamical equation for a fluidity parameter representing an effective visco-elastic relaxation. This phenomenological parameter was directly related to the occurrence of mesoscopic plastic events called ”hot spots” [5]. In the vicinity of the dynamical threshold, these events combine to provide large scale plastic yields [5,12]. Recently, we have shown that providing a tiny stress modulation around a nominal shear stress, the creep dynamics changes from a logarithmic to a linear behaviour [13]. The physical interpretation stems from the combination of memory effects and non-linearities, leading to a ”secular” accumulation of tiny effects, meaning that the creep dynamics is revealed at a time scale much larger than the modulation. We call this behaviour “rectified creep” in the following as the interpretation of this regime is different from an Eyring-like activated process. As the ingredients at the origin of this rectified creep are generic for a large class of soft glassy materials, this effect should be seen in other yield stress fluids displaying creep [14–17]. In this paper, using a spatially resolved multiple scattering technique [18], we monitor the spatial distribution of hot-spots during the two creep regimes. In parallel, a spatially resolved visco-elastic model is solved assuming a direct relation between the hot-spots production rate and the local fluidity value. The numerical solution is compared to the experiments. Interpretation of the results in the framework of a local rheological model is provided. Methods. – The experimental set-up is shown in fig. 1a. It consists in a cylindrical shear cell (Radius R = 5cm, height H = 10cm) filled with glass beads of density ρ = 2500 kg/m and mean diameter d = 200 μm (rms polydispersity ∆d = 30 μm). A well defined packing fraction Φ = 0.605 ± 0.005 is obtaining using an air