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.
Highlights
Plasticity is an important mechanical property in a wide variety of amorphous systems such as dense colloidal glasses, foams, emulsions, and fine-grained granular packings
A commonly accepted picture that supports this universal character is that the bulk plastic response emerges from a collective dynamics that is not specific to the particle, but rather results from interactions mediated by the universal laws of linear elasticity
This emergent dynamics is characterized by plastic events or shear transformations that are localized in space and time, but have long-range elastic-type consequences[5]
Summary
Plasticity is an important mechanical property in a wide variety of amorphous systems such as dense colloidal glasses, foams, emulsions, and fine-grained granular packings It is formally defined as intense unrecoverable (shear) deformations that the material undergoes beyond its elastic limit without any crushing or crumbling. In systems in which thermal fluctuations are irrelevant (which will be the case of the granular systems considered in this work), rearrangements are initially activated by external deformation, but further instability may be triggered and propagated due to non-local interactions In this framework, propagation of plasticity is a dynamical process which, once the characteristics of the shear transformations and the elastic properties of the medium are known, depends only on the dissipation mechanism[6,7]. This preferential direction (with respect to the principal axis of the local shear event) is the one along which a shear band should form in a system deformed at constant volume (in particular incompressible), as it corresponds to the direction of maximum macroscopic shear stress
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