As sea ice extent decreases in the Arctic, surface ocean waves have more time and space to develop and grow, exposing the marginal ice zone (MIZ) to more frequent and more energetic wave events. Waves can fragment the ice cover over tens of kilometres, and the prospect of increasing wave activity has sparked recent interest in the interactions between wave-induced sea ice fragmentation and lateral melting. The impact of this fragmentation on sea ice dynamics, however, remains mostly unknown, although it is thought that fragmented sea ice experiences less resistance to deformation than pack ice. Here, we introduce a new coupled framework involving the spectral wave model WAVE-WATCH III and the sea ice model neXtSIM, which includes a Maxwell elasto-brittle rheology. This rheological framework enables the model to efficiently track and keep a "memory" of the level of sea ice damage. We propose that the level of sea ice damage increases when wave-induced fragmentation occurs. We used this coupled modelling system to investigate the potential impact of such a local mechanism on sea ice kinematics. Focusing on the Barents Sea, we found that the internal stress decrease of sea ice resulting from its fragmentation by waves resulted in a more dynamical MIZ, particularly in areas where sea ice is compact. Sea ice drift is enhanced for both on-ice and office wind conditions. Our results stress the importance of considering wave-sea-ice interactions for forecast applications. They also suggest that waves likely modulate the area of sea ice that is advected away from the pack by the ocean, potentially contributing to the observed past, current and future sea ice cover decline in the Arctic.