Granular materials consist of dense pack of solid grains and a pore-filling element such as a fluid or a solid matrix. The grains interact via elastic repulsion, friction, adhesion and other surface forces. External loading leads to grain deformations as well as cooperative particle rearrangements. The particle deformations are of particular importance in many industry applications and research subjects, such as powder metallurgy and soil mechanics. The response of granular materials to external loading is complex, especially in case when failure occurs: the mode of the failure can be diffuse or localized, and the development of specimen pattern can be drastically different when the specimen can no longer sustain external loading. In this thesis, a thorough numerical analysis based on a discrete element method is carried out to investigate the macroscopic and microscopic behavior of granular materials when a failure occurs. The numerical simulations include the vanishing of the second-order work instability criterion to detect failure. Furthermore, it is proved that the vanishing of second-order work coincides with the change from a quasi-static regime to a dynamic regime in the response of the specimen. Then, microstructure evolution is investigated. Evolution of force-chains and grain-loops are investigated during the deformation process until reaching the failure. The second-order work is once again taken into account to elucidate the local aspect that governs the failure, taking place at the particle scale. The collapse of the discrete specimen when it turns from quasi-static to dynamic regime is accompanied with a burst in kinetic energy. This rise of kinetic energy occurs when the internal stress cannot balance with the external loading when a small perturbation is added to the boundary, resulting in a difference between the internal and external second-order works of the system. The mesostructures have a symbiosis relationship with each other and their evolution decides the macroscopic behavior of the discrete system. The distribution of the collapse of force-chain correlates with the vanishing of the second-order work at the grain scale. The mesostructures play an important role in the instability of granular media. The second-order work can be used as an effective criterion to detect the instability of the system on both the macroscale and microscale (grain scale).