Tempered glass panes are subjected to high eigenstresses that induce a state of compression along the surfaces and a state of tension in the inner part. Whenever a crack reaches the tensile region, it rapidly propagates and branches in all directions driven by the eigenstress. These mechanisms induce dynamic fragmentation. The present work contains a numerical investigation of this phenomenon on panes with different thicknesses, using massively parallel simulation based on FEM with the dynamic insertion of cohesive elements. Simulations are first validated by comparing the obtained number of fragments with experimental data. Then, the resulting energy fields are examined and they show that the dissipated energy is significantly underestimated by the existing analytical models. Finally, an extended analytical model that includes the influence of the plate thickness is proposed to correctly estimate the number of fragments for high eigenstresses.