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Systematic numerical simulations of model dense granular materials inmonotonous, quasistatic deformation reveal the existence of two differentr\'egimes. In the first one, the macroscopic strains stem from the deformationof contacts. The motion can be calculated by purely static means, withoutinertia, stress controlled or strain rate controlled simulations yieldidentical smooth rheological curves for a same sample. In the second r\'egime,strains are essentially due to instabilities of the contact network, theapproach to the limits of large samples and of small strain rates isconsiderably slower and the material is more sensitive to perturbations. Theseresults are discussed and related to experiments : measurements of elasticmoduli with very small strain increments, and slow deformation (creep) underconstant stress.

Discrete numerical simulation, quasistatic deformation and the origins of strain in granular materials