Localization of Deformation in Anisotropic Granular Materials Utilizing the Microstructure Tensor

Abstract

The shear band formation and orientation in anisotropic granular materials have been studied. The anisotropy is described by making use of the microstructure tensor that complies with principles of continuum mechanics and expresses the anisotropy in a coordinate-invariance form. Further studies are conducted, based on bifurcation analysis, to investigate the conditions for the initiation and orientation of the shear band in anisotropic granular materials. The role of parameters describing the material anisotropy in shear band formation is examined. The main focus of this study is to relate principal values and directions of the microstructure tensor with the condition of localization of the deformation into a shear band. In particular, the influence of eigenvalues and eigenvectors of the microstructure tensor have been studied based on the classical theory of plasticity.