Analysis of two-dimensional displacement fluctuations in granular media

Univ. Grenoble Alpes, Grenoble INP, CNRS, 3SR, F-38000, Grenoble, France

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Published online: 1 December 2025

Abstract

The discrete nature of granular materials imposes significant limitations on equivalent continuum based formulations of their mechanical behavior. In densely packed granular assemblies, the trajectories of the particles diverge from the streamlines predicted by continuum mechanics, due to the mutual volume exclusion among particles. Such steric exclusion obliges grains to deviate from affine displacements, resulting into displacement fluctuations. During quasistatic loading of a granular assembly, structured vortex patterns emerge, fused with high magnitude noise. Although the origins of this phenomenon are different from those behind turbulence in fluids, these patterns present striking similarities to vortex shape. The present work analyses and interprets experimentally measured granular fluctuations within a two-dimensional granular assembly by means of statistics. A cyclic isochoric test is conducted using the 1γ2ε shearing device at Laboratoire 3SR and the two-dimensional displacement field is obtained by Digital Image Correlation. The PDFs of the horizontal and vertical fluctuation vector components provide the essential trends to remove unstable granular movement that is caused by equilibrium loss. Moreover, the statistical isotropy of the fluctuations vector field is investigated via the expansion of the PDF to function of vectors. The results confirm that the displacement fluctuations in granular media are strongly dependent on the observation frequency.