Summary The combined finite‐discrete element method (FDEM) was originally developed for fracture and fragmentation of brittle materials, more specifically for cementitious and rock‐like materials. In this work, a combination of a discrete crack and plastic deformation has been combined and applied to FDEM simulation of fracture. The deformation is described using a FDEM‐specific mechanistic approach with plastic deformation being formulated in material embedded coordinate systems leading to multiplicative decomposition and plastic flow, that is, resolved in stretch space; this is combined with the FDEM fracture and fragmentation criteria. The result and main novelty of the present work is a robust framework for simulation of large strain solid deformation combined with a multiplicative decomposition‐based model that simultaneously involves elasticity, plasticity, and fracture.