The Discrete Element Method (DEM) is increasingly used to study the failure behavior of rock. Despite DEM's intrinsic capability to capture the mechanical behavior of discontinua, there remains several open questions that include the numerical modelling of the meso-fracture evolution and behavior of brittle rock bodies. A Cohesive Fracture Model (CFM) designed explicitly for polyhedral shaped DEM particles is proposed for the simulation of the fracture and behavior of brittle rock bodies. A rock body is discretized into a series of rigid polyhedral blocks which are bonded along the boundary faces along the normal and shear directions. A cohesive criterion dictates the normal and shear break strengths of the bonds for the CFM. The computational efficiency of the CFM for polyhedral shaped DEM simulations is enhanced by parallelization over multiple graphical processing units (GPUs) in the Blaze-DEM framework. A series of numerical and laboratory tests are conducted. For marble, these include three-point bending and uniaxial tests to investigate the relationship between the meso-mechanical parameters and macro-mechanical behavior. Following a sensitivity analysis of the meso-mechanical parameters, an inversion procedure is established to estimate the numerical meso-mechanical parameters of the CFM model. Two different failure modes for different rocks are proposed. (C) 2020 Elsevier B.V. All rights reserved.