Correlation and shear bands in a plastically deformed granular medium

Abstract

Recent experiments (Le Bouil et al., Phys. Rev. Lett., 2014, 112, 246001) have analyzed the statistics of local deformation in a granular solid undergoing plastic deformation. Experiments report strongly anisotropic correlation between events, with a characteristic angle that was interpreted using elasticity theory and the concept of Eshelby transformations with dilation; interestingly, the shear bands that characterize macroscopic failure occur at an angle that is different from the one observed in microscopic correlations. Here, we interpret this behavior using a mesoscale elastoplastic model of solid flow that incorporates a local Mohr-Coulomb failure criterion. This differs from the interpretation of Le Bouil et al., which is based on purely elastic considerations ignoring the potential role of local friction on deformation patterns. We show that the angle observed in the microscopic correlations can be understood by combining the elastic interactions associated with Eshelby transformation with the local failure criterion. At large strains, we also induce permanent shear bands at an angle that is different from the one observed in the correlation pattern. We interpret this angle as the one that leads to the maximal instability of slip lines.

Deformation and flow of amorphous solids: Insights from elastoplastic models

“…An additional concern could be raised as regards the use of a global one-step minimization, whereas plastic events occur sequentially and the elastic deformation field in the material evolves during the process. Nevertheless, in a similar endeavor, Karimi and Barrat (2018) rationalized the observed deviation between the direction of the macroscopic shear band in a deformed granular medium and that of the microscopic correlations between rearrangements. The authors contended that the former direction is the direction of maximal instability with respect to the Mohr-Coulomb failure criterion, rather than that of maximal increase of the shear stress.…”

From plastic flow to brittle fracture: Role of microscopic friction in amorphous solids

“…This view was also validated within the context of a continuum damage model and Mohr-Coulomb plasticity that weakly frictional systems favor more scattered damage distributions [13]. In a more recent study [14], in the framework of a standard elasto-plastic model [15], the permanent localization phenomenon in granular flow was rationalized via an emergent weakening mechanism that was attributed to a compromise between elastic-type couplings among small-scale events and the pressuresensitivity in local yielding thresholds. Recent granular experiments have analyzed the anisotropic structure of the mesoscopic patterns within the context of linear elasticity and the concept of shear transformations accompanied with local dilatancy [6].…”

Comment on tc-2020-354

“…11, and also in Dansereau et al, 2019). Note that the Poisson ratio also affects the amount of shear and normal stress concentration associated with a local discontinuity in material properties (Karimi and Barrat, 2018). The fact that the fracture angle is not affected by the changes in Poisson ratio thus indicates that the stress concentration and propagation of the fracture in space is mainly controlled by the stress correction rather than by the relaxation of material properties with damage.…”