This paper is concerned with the modeling and simulation of the evolution of fretting wear of interacting solids submitted to cyclic loading and possibly undergoing large mechanical transformations. A Lagrangian formalism of the virtual work principle integrating significant worn volumes from the interacting solids is given. An extension of the Archard's wear model to the large transformations framework is developed and explained. Variational large transformations Lagrangian hybrid contact wear formulations are then derived. Wear explicit and wear implicit solution methodologies are described. A delocalized Archard's law is introduced to bound the wear of a structure under a corner or an edge of contact. Further, we resort to the multimodel Arlequin framework to capture efficiently wear concentrations as well as significant material removal due to wear, while enhancing the modeling flexibility and reducing the simulation costs of wear of structures, particularly thin ones. Our global methodology is assessed by some didactic numerical tests.