|
We study the initial stages and the finite strain evolution of the behavior of a rigid circular inclusion embedded in an anisotropic matrix subjected to anisotropy parallel simple shear. The model is two dimensional, plane strain, and linear viscous materials are assumed. The initial instantaneous flow stages are studied with an analytical solution that is based on Willis (1964). The finite strain evolution of the inclusion and the structural development are studied with a finite element method model. This model also allows for studying the effect of explicitly layered host material and the correspondence to effective anisotropic approximations and sheds light on the issue of upscaling versus resolving layered medium.
Investigated aspects include the inclusion motion, flow field rearrangement and structural development in the host. Our results show that matrix anisotropy has a first order effect on the motion of a rigid heterogeneity subject to shear and the development of structures around it. We are able to demonstrate that this is the case for even weakly anisotropic hosts if the total inclusion rotation is considered. Strong anisotropy leads to substantially reduced rotation rates once a shear strain magnitude of 2 is reached. This effect and related developments in the structural development in the matrix may yield finite strain structures that appear to be the result of substantially lower strains. Furthermore, perturbation flow ranges are much larger in anisotropic material and therefore boundary effects and flow confinement and interaction distances much larger, which also have to be considered when interpreting natural structures. The comparison of layered and anisotropic hosts reveals that the effective approach is good when inclusion motion is considered. However, the detailed structural evolution in a layered matrix, e.g. development of rootless folds, thickening of strong layers, deformation localization in weak layers, and break in orthotropic symmetry, can only be studied if the layers are explicitly resolved.
|
