From Microscopic To Macroscopic Second Order Work In Granular Assemblies

Author(s)
F. Darve, F. Donze, F. Nicot, L. Sibille
Publisher
Elsevier
Source
Mechanics of Materials
Keywords
Granular material, Homogenization, Love formula, Micro Structure, Second-Order Work
Year
2007

It is now well established that for non-associated materials such as geomaterials, a broad domain exists, strictly within the plastic limit, where different failure modes can coexist. In particular, material instability as defined by Hill [Hill, R., 1958. A general theory of uniqueness and stability in elastic–plastic solids. J. Mech. Phys. Solids, 6, 236–249], related to the vanishing of the second-order work, can potentially occur. In this paper, we focus on granular materials and establish from theoretical considerations that the macroscopic second-order work on the assembly scale is related to the microscopic second-order work computed on each contact. This question is examined from a multi-scale approach, and the relation between macroscopic and microscopic second-order works is brought to light using a micro-mechanically based model. Finally, these theoretical results are confirmed from numerical simulations based on a discrete element method.

Keywords: Homogenization, Granular material, Love formula, Micro-structure, Second-order work

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