A numerical study of one-dimensional compression of granular materials. II. Elastic moduli, stresses and microstructure

Mohamed Hassan Khalili (1) , Jean-Noël Roux (1) , Jean-Michel Pereira (1) , Sébastien Brisard (1) , Michel Bornert (1)

1 navier umr 8205 - Laboratoire Navier

The elastic moduli of a transversely isotropic model granular material, made of slightly polydis-perse elastic-frictional spherical beads, in equilibrium along a one dimensional (oedometric) compression path, as described in the companion paper [1], are investigated by numerical simulations. The relations of the five independent moduli to stresses, density, coordination number, fabric and force anisotropies are studied for different internal material states along the oedometric loading path. It is observed that elastic moduli, like in isotropic packs, are primarily determined by the coordination number, with anomalously small shear moduli in poorly coordinated systems, whatever their density. Such states also exhibit faster increasing moduli in compression, and larger off-diagonal moduli and Poisson ratios. Anisotropy affects the longitudinal moduli, C11 in the axial direction, and C22 in the transverse directions, and the shear modulus in the transverse plane, C44, more than the shear modulus in a plane containing the axial direction, C55. The results are compared to available experiments on anisotropic bead packs, revealing, despite likely differences in internal states, a very similar range of stiffness level (linked to coordination), and semi-quantitative agreement as regards the influence of anisotropy. Effective Medium Theory (the Voigt approach) provides quite inaccurate predictions of the moduli. It also significantly underestimates ratios C11/C22 (varying between 1 and 2.2) and C55/C44 (varying from 1 to 1.6), which characterize elastic anisotropy, except in relatively weakly anisotropic states. The bulk modulus for isotropic compression and the compliance corresponding to stress increments proportional to the previous stress values are the only elastic coefficients to be correctly estimated by available predictive relations. We discuss the influences of fabric and force anisotropies onto elastic anisotropy, showing in particular that the former dominates in sample series that are directly assembled in anisotropic configurations and keep a roughly constant lateral to axial stress ratio under compression.

Domaines: Mécanique des matériaux [physics.class-ph]; Matériaux et structures en mécanique [physics.class-ph]; Mécanique [physics]

Mohamed Hassan Khalili, Jean-Noël Roux, Jean-Michel Pereira, Sébastien Brisard, Michel Bornert. A numerical study of one-dimensional compression of granular materials. II. Elastic moduli, stresses and microstructure. Physical Review E , 2017, ⟨10.1103/PhysRevE.95.032908⟩. ⟨hal-01497638⟩