This article is devoted to the comprehension, the prediction and the numerical simulation of dynamic fracture for a wide variety of materials and structures. The main contribution concerns the prediction of the entire fracture process from crack initiation, growth, propagation, and final rupture, to post fracture behavior such as unilateral contact and dry friction interactions between created fragments after fracture. The new Non Smooth Fracture Dynamics (NSFD) approach presented in this paper is thus based on three main features: a) a surface-volumetric multibody approach using mixed boundary conditions between each volumetric finite elements and/or rigid bodies, b) the development of a generic formulation of the cohesive zone models dedicated to a wide variety of materials and physical phenomena, and incorporating unilateral contact and Coulomb's dry friction and c) a specific nonsmooth dynamical framework based on measure differential inclusions and an associated implicit time--integration scheme allowing the numerical treatment of nonsmooth events such as impacts due to unilateral constraints.