The aim of this thesis is to investigate the mechanisms behind dynamic fragmentation. This phenomenon occurs in a material when a blast or impact loading nucleates multiple cracks, whose propagation and coalescence break the specimen into fragments. Although since the beginning of the last century this topic has been well studied in many fields ranging from engineering to astrophysics, its complexity is still keeping researchers far from a complete understanding of it. Analytical approaches are challenging and sometimes unfeasible, while experiments are limited in scale and are hard to realize due to the extreme rapidity of the phenomenon. In this context, numerical methods constitute a useful tool to provide insights and complement the traditional models. Among the existing techniques, the finite-element method with dynamic insertion of cohesive elements represents an excellent compromise between performance and realistic modeling. The first topic of the thesis is the prediction of residual velocities of fragments. Even in tensile fragmentation, their relative velocity difference leads to impacts, redistributing the kinetic energy in the system. This event is studied in an elementary setup: a quasi-1D ceramic bar is subjected to a constant blast tensile loading until failure. With this simple model, it is possible to identify the link between the elastic waves and the different relative velocities of the fragments, that cause impacts. This aspect highlights the importance of including a realistic reproduction of contact in the numerical models. Another topic is the connection between the shape of a 3D ceramic specimen and its fragmentation patterns, in particular concerning the mass and shape distributions of the fragments. For this purpose extremely large meshes are needed and an optimization of the code is necessary. The best strategy is to extend the algorithms to work in parallel in order to take advantage of the most modern clusters available at EPFL. This accomplishment, together with the analysis and solution of a numerical instability that can affect the method, results in the realization of a powerful numerical tool for large 2D and 3D dynamic fragmentation problems. The last subject treated in this thesis is the influence of eigenstresses on the dynamic fragmentation of glass. The plates made of this material can be thermally treated in order to obtain compression residual stresses along the surfaces, that are balanced by tensile residual stresses in the interior. Therefore the flexural strength is increased but, whenever a crack reaches the tensile region, it becomes unstable and the plate quickly breaks into fragments. In the past, researchers tried to predict both analytically and experimentally the number of fragments as function of the residual stress magnitude and the plate thickness. However the available models are partially inaccurate and in contradiction with each other. Thanks to the parallel implementation of the dynamic insertion of cohesive elements, now also numerical simulations are a valid tool to explore the underlying physics. Their usage permits to easily monitor the evolution of potential, dissipated and kinetic energies over time, highlighting the flaws of the existing analytical approaches as well as providing more information than experiments. A new mathematical expression is proposed to accurately predict the number of fragments in function of the plate thickness for high values of residual stress.