While coarse graining techniques have largely improved over the past decades, the question of the treatment of material interfaces remains a critical challenge. The work presented proposes to use field defect mechanics  in addition to a non-local treatment of elastic behavior, in the lineage of Eringen, in order to model the dynamic evolution of material interfaces at the nano-scale. In this approach, material interfaces are represented by their interfacial defect content, formally represented with dislocation and/or disclination fields. Near interfacial defect, the local elastic behavior of the material is seen to depart from that of the macroscopic one thereby providing a driving force for both stabilization and migration of interfacial defects. The mechanical framework is applied to both the cases of bicrystals and polycrystals. It is shown that the model proposed can successfully reproduce key features of dislocation/grain boundary interactions, of grain boundary migration etc.