# Are granular materials simple? An experimental study of strain gradient effects and localization

## TL;DR

This experimental study investigates how shear stress in granular materials depends on strain gradients, revealing non-linear responses and various localization patterns, with implications for understanding material behavior under non-uniform deformation.

## Contribution

The paper provides the first detailed experimental analysis of how first and second strain gradients influence shear stress and localization in granular materials using DEM simulations.

## Key findings

- Shearing stress depends on both first and second strain gradients.
- Responses to strain and its gradients are incrementally non-linear.
- Multiple localization patterns, including microbands and shear bands, are observed.

## Abstract

Experiments test the dependence of shearing stress on the first two gradients of shear strain. The tests were conducted by direct numerical simulation using the Discrete Element Method (DEM) on a large two-dimensional (2D) assembly of circular disks. The assembly was coerced into non-uniformly deformed shapes by applying body forces to the material region. The tests show that shearing stress is affected by both the first and second gradients of shear strain, and the measured responses to strain and its gradients are all incrementally non-linear. The dilation rate is unaffected by strain gradients. Particle rotations, although highly erratic, are, on average, consistent with the mean-field rotation and unaffected by strain gradients. In independent unconstrained tests, the material was sheared without body forces so that localization could freely occur. Three localization patterns were observed: microbands at very small strains; non-persistent shear bands at moderate strains; and persistent bands at large strains. The observed features of microbands and shear bands are consistent with the measured influences of shearing strain and its first two derivatives.