A rigid circular inclusion in an anisotropic host subject to simple shear

The solution for velocity and rate of deformation in an incompressible, homogeneously anisotropic viscous host embedding a cylindrical rigid inclusion subjected to a far-field shearing parallel to the anisotropy direction is presented. The rotation rate of the inclusion is equal to half the ambient shear rate independently of the anisotropy factor. The flow in the matrix localizes into conjugate shear bands sub-parallel to the anisotropy directions as the anisotropy factor increases. The presented anisotropic analytical solution, which neglects the bending stiffness, approximates the flow in a layered medium in the limit of infinitely thin layers. An initially planar layering is deflected adjacent to the inclusion and fold trains propagate into the host with progressing deformation. Numerical simulations show that the structural development leads to a decrease in the inclusion rotation rate and eventually to inclusion stagnation at high strains. The fold shapes become more angular and the fold trains reach further out into the host as the anisotropy factor is increased. Increasing the layering thickness (up to only 9 layers intercepting the inclusion) has no significant effect on how the layer inclusion rotation rate evolves with strain. A coarse layering in the host leads to a strongly reduced outreach of the fold trains and the absence of tight folds. The analytical solution, which is derived for a planar anisotropy in the host, can be employed to approximate the structural development for a weakly anisotropic host or small deformation. Structural development of an anisotropic medium plays a major role in determining the system behavior for large deformation.