Correlation and shear bands in a plastically deformed granular medium

TL;DR

This paper investigates the microscopic and macroscopic shear band formation in plastically deformed granular media using a mesoscale elastoplastic model, linking local correlations to failure angles and shear band orientations.

Contribution

It introduces a mesoscale elastoplastic model with Mohr-Coulomb failure criterion to explain correlation angles and shear band orientations in granular deformation.

Findings

Microscopic correlations align with elastic interactions and failure criteria.

Permanent shear bands form at angles of maximal instability.

Correlation angles differ from macroscopic shear band angles.

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. 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.