Micro-mechanism of stress-dilatancy anisotropy in granular materials: Affine and nonaffine deformation

Abstract

The stress-induced dilatancy anisotropy is an important kinematic response in granular materials and is very complex due to the stochastic motion of particles. In this study, the local stress-dilatancy relationship is investigated referring to the local contact force and relative displacement in a certain contact direction. The micromechanism of this anisotropy is investigated from the view of affine and nonaffine approaches based on DEM simulation. Numerical results indicate that the local nonaffine dilatancy/contraction tendency is opposite with that of local affine deformation in macroscopic compression and extension direction, which mainly stems from the counteraction effect between the normal components of affine and nonaffine displacements. The local stress-dilatancy of affine and nonaffine components is linear and orientation-dependent, which results in the nonlinear character of macroscopic stress-dilatancy. By establishing an analytical relation of stress-dilatancy, the local affine/nonaffine dilatancy is decomposed into the component of stress-induced dilatancy synchronized with the local stress anisotropy; and the component of stress-induced dilatancy asynchronized with the local stress anisotropy. The former is related to the unchanged isotropic microstructure, and the latter attributes to the anisotropic microstructure. Besides, the contribution of nonsliding contacts to nonaffine dilatancy is larger than that of sliding contacts even for the case of relatively higher sliding ratio, which indicates that the heterogeneous deformation attributes not only to the friction dissipation, but to the blocked energy at micro contacts in granular materials.