Within the framework of dissipative systems with time-independent behavior, the study of the evolution of delaminated structures modeled by frames of plates is considered via a global energetic analysis. Assuming the current equilibrium state is known, the governing rate problem for the instantaneous delamination is formulated as either a system of local equations or as a global variational inequality. This global formulation enables to study stability and non-bifurcation of the evolution of a delaminated structure under quasi-static loading, corresponding to the statement of existence and uniqueness criteria for the rate solution. Two analytical applications to simple structures are presented.