This study proposes a technique to predict the effect of wear on the dynamics of structures with contact interfaces and the evolution of contact interface using a coupled static and dynamic multiharmonic balance (MHBM) method. A multiscale approach is implemented, namely slow-scale for wear phenomena and fast-scale for the non-linear dynamic response. The wear is computed using wear energy approach and adaptive wear logic. The technique is applied to a tuned shrouded bladed disk on a single sector using cyclic symmetry property to predict the evolution of wear at the shroud contact interface and the corresponding change in dynamic response