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Parallels are drawn between the response of a discrete strut on a linear elastic foundation and force-chain buckling in a constrained granular medium. Both systems buckle initially into periodic shapes, with wavelengths that depend on relative resistances to lateral displacement, and curvature in the buckled shape. Under increasing end shortening, the classical structural model evolves to a localized form extending over a finite number of contributing links. By analogy, it is conjectured that the granular model of force-chain buckling might follow much the same evolutionary route into a shear band.

SUMMARYThe evolution of internal structure plays a pivotal role in the macroscopic response of granular materials to applied loads. A case in point is the so-called 'stress-dilatancy relation', a cornerstone of Soil Mechanics. Numerous attempts have been made to unravel the connection between stress-dilatancy and the evolution of fabric and contact forces in a deforming granular medium. We re-examine this connection in light of the recent findings on force chain evolution, in particular, that of collective force chain failure by buckling. This study is focussed on two-dimensional deformation of dense granular assemblies. Analysis of individual and collective force chain bucklings is undertaken using data from a discrete element simulation. It is shown that the kinematics of force chain buckling lead to significant levels of local dilatation being developed in the buckling force chain particles and their confining first-ring neighbors. Findings from the simulation are used to guide the development of a lattice model of collective, localized force chain buckling. Consideration of the statics and kinematics of this process yields a new stress-dilatancy relation. The physics of buckling, even at its simplest form, introduces a richness into the stress-dilatancy formulation in a way that preserves the essential aspects of fabric evolution, specifically the buckling mode.

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