Evolution of the effective moduli for anisotropic granular materials during pure shear

We analyze the behavior of a frictionless dense granular packing sheared at constant volume. Goal is to predict the evolution of the effective moduli along the loading path. Because of the structural anisotropy that develops in the system, volumetric and deviatoric stresses and strains are cross coupled via four distinct quantities, the classical bulk and shear moduli and two anisotropy moduli. Here, by means of numerical simulation, we apply small perturbations to various equilibrium states that previously experienced different pure shear strains and investigate the effect of the microstructure (2^nd rank fabric tensor) on the elastic bulk response. Besides the expected dependence of the bulk modulus on the isotropic fabric, we find that both the isotropic density of contacts and the (deviatoric) orientational anisotropy affect the anisotropy moduli. Interestingly, the shear modulus of the material depends also on the actual stress state, along with the (isotropic and anisotropic) contact configuration.