Connecting statistical mechanics and granular materials: a novel experimental validation of the Tsallis-Bukman scale law in two dimensions

Outgoint grant / short term visitor project

The research project concerns the understanding of the mechanisms of deformation in the steady state of granular media using the tools of statistical mechanics and the scaling law of Constantino Tsallis1.

In the first part of the project, constant volume cyclic shear experiments with rotation of the main deformation axes using the 1γ2ε experimental device of the 3SR laboratory will be conducted. The 1γ2ε device (Figure 1), unique in the world, was initially designed to perform this type of test. A few tests were carried out in the past but with a low number of cycles (2 at most) and on granular media for which the measurements were carried out at the macroscopic scale2 or for a very low number of particles (300)3. Since 1997, the 1γ2ε device has lost this unique ability to perform complex loading tests. A software development is necessary to be able to do this type of test again.

The idea if to perform shear tests by imposing a continuous rotation of the main axes of deformation, at constant volume, on samples with a large number of particles (about 6000) coupled with kinematic measurements of all particles throughout the tests with the digital image correlation technique.


In the second part of the project, the kinematic data (displacement and rotation of the particles) obtained will then be analysed using statistical mechanics tools. The final objective will be, on the basis of controlled experiments, to study the displacement fluctuations of particles (deviation of the particle displacement from the imposed affine kinematic field - the origin of plasticity at the grain scale) and to see to what extent the scaling law formulated in 2D and predicted by C. Tsallis is verified for experimental granular assemblies - which would be a world first.


Fig. 1: During the deformation process of the granular medium, photographs allow the complete kinematics of all the particles in the sample to be followed using the digital image correlation technique4.

This project involves a collaboration between the laboratory 3SR, the Federal Center for Technological Education of Minas Gerais (CEFET MG, Brazil), and the Brazilian Center for Research in Physics


1 C. Tsallis, Introduction to Nonextensive Statistical Mechanics : Approaching a Complex World, ed. 2022.

2 H. Joer, J. Lanier, J. Desrues, E. Flavigny, Geotechnical Testing Journal, 15(2), 129-137, 1992

3 F. Calvetti, G. Combe, J. Lanier, Mechanics of Cohesive Frictional Materials, 2 (2), pp 121-163, 1997

4 V. Richefeu, G. Combe, Strain, 56(6), e12362, 2020




GESC - Grupo de Estudos em Sistemas Complexos - Physics Department (CEFET-MG, Belo Horizonte - Brazil)


Centro Brasileiro de Pesquisas Físicas (Rio - Brazil)


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