Micromechanical modelling of the anisotropic viscoelasticity of granular materials: statistical homogenization

Abstract

Granular materials can exhibit a viscoelastic behaviour resulting from a) the viscoelastic character of the material the grains are made of, b) the presence of a viscous or viscoelastic fluid between particles. The micromechanical modelling of the behaviour of such materials considering a statistical homogenization approach is performed in this paper. Several homogenization schemes are first reviewed. The main differences between these schemes lie in the way statistical distributions of local variables are related to the global variables. Once the viscoelastic contact law is chosen (based on physical considerations), the overall behaviour can be derived. The later is shown to be dependent on the wave velocity. Furthermore, an anisotropic behaviour is obtained if a description of the interparticle contact distribution is included. The respective influence of wave velocity and contact distribution anisotropy is determined. The relevance of this approach is shown in the last section of this paper through a comparison with experimental results on bituminous concrete.

Anisotropic elastic theory of preloaded granular media

“…Equations ( 9), (10) constitute our central result and describe the response of a preloaded granular medium to an incremental strain. If the medium is statistically isotropic (µ = ρ/4π constant), we recover standard isotropic elasticity, with Lamé coefficients λ L = ρD 2 (k − k ⊥ )/15 and µ L = ρD 2 (k /15+k ⊥ /10), in agreement with the results of Chang and Gao [23,26]. In particular, if the Poisson ratio ν g of the grain constitutive material is positive, that of the preloaded granular medium, ν = ν g /(10 − 6ν g ), lies between 0 and 1/14.…”

“…In the present work, our starting point is the well-established elastic theory of inter-grain contacts [24,25]; on this basis, we construct a specific macroscopic elastic theory [26] that encodes the texture of the granular network. We consider a preloaded granular medium [27] and small applied incremental stresses, so that the corresponding elastic response be linear.…”

Statistical homogenization for assemblies of elliptical grains: effect of the aspect ratio and particle orientation

“…Different types of contact laws have been successfully introduced in the general concept of statistical homogenization and compared with experimental or numerical results: linear elasticity (Cambou et al, 1995;Chang and Liao, 1994), Hertz-Mindlin nonlinear elasticity , linear viscoelasticity (Emeriault and Claquin, 2000) or friction laws .…”