ABSTRACT
Stress-strain curves as displayed on fig. 1 should express a macroscopic, quasistatic constitutive law. Sample to sample fluctuations should regress in the large system limit, and the results should be independent on dynamical parameters such as inertia, viscous dissipation, and strain rate, summarized in dimensionless parameters ξ and I . Fig. 2 is indicative of sample to sample fluctuations with 4000 beads. One may notice the very good reproducibility of the curve between A samples in the initial rapidly growing part. We checked that differences between samples decreased for increasing N . As to the influence of dynamical parameters, fig. 3 shows that the quasistatic limit is correctly approached for I ≤ 10−3, a quite satisfactory result, given that usual laboratory tests with ˙a ∼ 10−5 correspond to I ≤ 10−8. In previous 2D simulations with disks (Roux & Combe 2002), sample to sample fluctuations were shown to regress as N−1/2.
