Flow patterns around rigid inclusions in a multiple inclusion system undergoing bulk simple shear deformation

During deformation of an inclusion-matrix system, the velocity fields around individual inclusions mutually interfere with one another. Such interacting inclusions rotate at slower rates than non-interacting, single inclusions. This paper presents a theoretical model that describes the flow pattern of matrix (viscous) material around interacting rigid inclusions of spherical shape in bulk simple shear deformation. Numerical simulations based on the velocity functions reveal that the volume concentration of inclusions is a crucial parameter controlling the flow pattern around rotating inclusions under interacting conditions. At low volume concentrations (ρv<0.01, where ρv=(a/b)3, 2a: inclusion diameter and 2b: mean inter-inclusion distance) the flow is characterized by an eye-shaped separatrix, which, with increase in volume concentration (ρv>0.1), transforms into a pattern with a bow-tie shaped separatrix. At a large volume concentration (ρv=0.4) the separatrix assumes the geometry of a super-ellipse. We also present numerical models that illustrate the influence of volume concentration on the (1) nature of strain distribution, (2) distortion patterns of passive foliations ,and (3) mantle structures around inclusions in an interacting state. Based on this theory, it is shown that the rotational retardation of the inclusions slightly enhances the bulk viscosity of the inclusion-matrix system.