Precursors of inertial transitions in granular materials: search for a consistent definition for the mesoscopic second-order work

  • Clerc, Adriane (INSA Lyon, LaMCoS, Villeurbanne)
  • Wautier, Antoine (INRAE, RECOVER, Aix-en-Provence)
  • Bonelli, Stéphane (INRAE, RECOVER, Aix-en-Provence)
  • Nicot, François (Université Savoie Mont Blanc, ISTerre)

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From snow avalanches to industrial storage, the mechanical stability of granular material is a subject of great interest. Inertial transition is a form of mechanical instability caused by the transition from a quasi-static to an inertial regime. In continuum mechanics framework, this type of instability is well captured based on Hill’s sufficient condition for stability [2]. It has been demonstrated that the vanishing of the internal second-order work of the system (W_2=Δσ:Δε) for some incremental loading directions is the signature of a possible inertial transition for the material state considered [4][3]. The complexity of the granular media behaviour comes from their discrete nature. It can be considered as continuous at the macroscopic scale, but discrete at the grain scale. The continuum behaviour emerges from the coupling between grain interactions and local geometrical arrangements. The mesoscale, often represented by grain loops in 2D granular materials [5] is an intermediate scale that enable to link the macroscale to the microscale. In this paper, we propose to define the second-order work at the mesoscale to anticipate instabilities such as burst of kinetic energies. This involves a wise choice of a mesoscopic stress definition. With a criterion based on the energy balance, we propose a formulation of a mesoscopic second-order work that can be used as a precursor of mechanical instabilities. This provides a unique opportunity to investigate local mesostructured features responsible for the triggering of the inertial transitions in granular materials [1]. [1] Clerc, A., Wautier, A., Bonelli, S., & Nicot, F.: Meso-scale signatures of inertial transitions in granular materials. Granular Matter, 23(2), 28 (2021) [2] Hill, R. A general theory of uniqueness and stability in elastic-plastic solids. Journal of the Mechanics and Physics of Solids, 6(3), 236-249 (1958) [3] Nicot, F., Kruyt, N. P., Millet, O.: On Hill's lemma in continuum mechanics. Acta Mechanica, 228(2), 1581–1596 (2017) [4] Wan, R., Pinheiro, M., Daouadji, A., Jrad, M., & Darve, F.: Diffuse instabilities with transition to localization in loose granular materials. International Journal for Numerical and Analytical Methods in Geomechanics, 37(10), 1292-1311 (2013) [5] Zhu, H., Nicot, F., Darve, F.: Meso-structure evolution in a 2D granular material during biaxial loading. Granul. Matter, 18(1), 3 (2016)