Various descriptors have been introduced to describe and predict the anisotropy of granular materials. Among many, common descriptors often related to the microstructure of granular materials, are typically based on the particles orientation, the void spaces and the contact force. In addition, the evolution of anisotropy, also called the induced anisotropy, is primarily related to the stress state. At least, such a relation is more desirable for practical purposes when the original state and the stress path are known. Since experimental measurements on the evolution of anisotropy are very difficult, often accompanied by errors, the widely accepted and practically applied DEM simulation has been implemented in this work to study the intensity and trends of induced anisotropy captured by the void-based and contact-based fabrics due to axial loading. The coaxiality of various descriptors with the stress tensor along with the evolution of the anisotropy of the granular materials have been studied and compared based on some available experimental data on renowned sands. Results indicated that contact-based descriptors are closely coaxial with the stress tensor while the void-based descriptor is orthogonal, i.e. a particular type of coaxiality. A linear mapping from the contact-based descriptors to the stress tensor has been conducted to clarify their relationship and evaluate if they can estimate the anisotropy with sufficient accuracy.