It is assumed in this paper that energy dissipation is a two-phase phenomenon. During the pre-localization stage, dissipation is a continuous process. After localization, it is lumped in surfaces of zero volume. To describe this process, it is proposed a new formulation called extended damage mechanics. The new framework incorporates the additional terms of lumped energy dissipation into a weak form of the damage evolution law. The variational formulation allowing for this approach characterizes the solution as a non-cooperative equilibrium point. This concept is also named after its inventor, the mathematician John Forbes Nash, as Nash point. Finally, numerical implementation of the extended damage mechanics is performed to describe the objectivity of the numerical simulations with respect to the finite element meshes in some practical cases of solids and structures.