The present paper deals with a gradient damage modeling framework for the case of general shell structures. The particularity of this formulation is that, as for the balance of linear momentum, the damage evolution is also governed by a boundary value problem. In a first step, the generalized standard formalism of continuum thermodynamics is developed for the particular case of continuum damage mechanics. A model is presented that fulfils the requirements of irreversible processes. Then, in a second step, the model is adapted to shell kinematics in terms of the twodimensional mid-surface. On the numerical side, we discuss the problem of numerically integrating this coupled problem and its implementation within the context of the finite element method. For the spatial discretization, a node-based approach is performed for the damage field that is related to a staggered global solution procedure. Here the popular four-nodes shell finite element is used for illustrative purposes. Finally, a set of simulations highlights the efficiency of the proposed framework.