The aim of this contribution is to propose an energy damage criterion for Cohesive Zone Models (CZM) within the context of Non-linear Thermodynamics of Irreversible Processes (TIP). The material under consideration is an isotropic elastic material that is prone to damage during isothermal transformations. The damage is considered to be the only irreversible effect that occurs during the deformation process and is assumed to be fully dissipative. After selecting a separation law and a damage state variable, it is demonstrated that the damage evolution law can be derived from the energy balance. Based on this finding, a CZM is developed for a given choice of traction-separation law and damage state variable, and the accuracy of its numerical predictions is evaluated using an experimental bending test. The damage, elastic, and dissipated energy fields around the crack path are displayed during this rupture test. Finally, a numerical simulation of a Brazilian test is performed in which there is no pre-existing crack in the specimen, and the evolution of the dissipated energy fields is plotted until the specimen reaches total failure