A two-phase composite in simple shear: Effective mechanical anisotropy development and localization potential

We present a combined shape and mechanical anisotropy evolution model for a two-phase inclusion-bearing rock subject to large deformation. A single elliptical inclusion embedded in a homogeneous but anisotropic matrix is used to represent a simplified shape evolution enforced on all inclusions. The mechanical anisotropy develops due to the alignment of elongated inclusions. The effective anisotropy is quantified using the differential effective medium (DEM) approach. The model can be run for any deformation path and an arbitrary viscosity ratio between the inclusion and host phase. We focus on the case of simple shear and weak inclusions. The shape evolution of the representative inclusion is largely insensitive to the anisotropy development and to parameter variations in the studied range. An initial hardening stage is observed up to a shear strain of gamma = 1 irrespective of the inclusion fraction. The hardening is followed by a softening stage related to the developing anisotropy and its progressive rotation toward the shear direction. The traction needed to maintain a constant shear rate exhibits a fivefold drop at gamma = 5 in the limiting case of an inviscid inclusion. Numerical simulations show that our analytical model provides a good approximation to the actual evolution of a two-phase inclusion-host composite. However, the inclusions develop complex sigmoidal shapes resulting in the formation of an S-C fabric. We attribute the observed drop in the effective normal viscosity to this structural development. We study the localization potential in a rock column bearing varying fraction of inclusions. In the inviscid inclusion case, a strain jump from gamma = 3 to gamma = 100 is observed for a change of the inclusion fraction from 20% to 33%.