Force chain and contact cycle evolution in a dense granular material under shallow penetration

The mechanical response of a dense granular material submitted to indentation by a rigid flat punch is examined. The resultant deformation is viewed as a process of self-organisation. Four aspects of the mechanical response (i.e. indentation resistance, failure, Reynolds' dilatancy, the undeforming dead zone) are explored with respect to the linear and cyclic structural building blocks of granular media self-organisation: force chains and contact network cycles. Formation and breaking of 3-cycle contacts preferentially occur around and close to the punch uncovering a dilation zone. This zone encapsulates (i) most of the indentation resistance and is populated by force chains consisting of six or more particles, (ii) all buckling force chains, and (iii) a central, near-triangular, undeforming cluster of grains beneath the punch face. Force chain buckling is confined to the zone's outer regions, beneath the corners and to the sides of the punch where surface material heave forms. Grain rearrangements here involve the creation of 6-, 7-, and 8-cycles -in contrast with Reynolds' postulated cubic packing rearrangements (i.e. 3-cycles opening up to form 4-cycles). In between these intensely dilatant regions lies a compacted triangular grain cluster which moves in near-rigid body with the punch when jammed, but this dead zone unjams and deforms in the failure regimes when adjacent force chains buckle. The long force chains preferentially percolate from the punch face, through the dead zone, fanning downwards and outwards into the material.