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

Abstract

Abstract. 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.

The role of force chains in granular materials: from statics to dynamics

“…The evolution of grain clusters and force chains governs the stress evolution as well as the microstructure evolution of granular materials. Particularly, it has been proven in 2D quasistatic conditions that the buckling of force chains is related to the death of clusters composed of three particles and generation of clusters composed of six or beyond number of particles (Arévalo et al, 2010;Tordesillas et al, 2014;Zhu et al, under review;Zhu et al, in press for the journal of Granular Matter). In 3D dynamic impact cases, the microstructure of grain clusters that surround force chains will be much more complex than in 2D cases.…”

“…In the following quasi-static biaxial test, δt equals to 1 s, θ b is set to 1 • . This value has been commonly used in literature in cases of simulations dealing with quasi-static loading, see Tordesillas (2007), Tordesillas et al (2011Tordesillas et al ( , 2014 …”

“…The failure of force chains is characterised by the buckling of force chains. The definition of force chain buckling (Tordesillas et al, 2014) is based on geometry variation of chain particles: suppose at a time t, a three-chain-particle segment exists; at time t + δt, a buckling event has occurred if ( Figure 2…”

“…Particularly, the buckling of force chains leads to unjamming and shear bands in granular materials (Tordesillas, 2007;Zhu et al, under review). In addition, Tordesillas et al (2014) showed that the mechanical response of a dense granular material subjected to indentation by a rigid flat punch is closely related to force chains and surrounding grain clusters. However, the role of force chains in granular materials is not totally pointed out.…”

On the kinematics and dynamics of crystal‐rich systems

“…During deformation the force chains migrate as percolating networks on a time scale approximately the inverse of the shear rate, where force is discontinuously transmitted by abandoning existing force chains and the recruitment of particles that were previously spectators into new chains, with the continuous rotation of the branch vectors (see Figures and ). In the quasi‐static regime this process is phenomenologically a buckling of the force chain [ Cundall and Strack , ; Guo , ; Tordesillas , ; Tordesillas et al ., ; Tordesillas et al ., ]. However, for this buckling to occur it requires a rearrangement of particles in the region surrounding the force chain, as controlled by the interplay between steric constraints and the local void ratio.…”