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A new model is proposed for two-dimensional simulation of the concrete fracture in compression. The model generated by using the Voronoi diagram method and with considering random shape and distribution of full graded aggregates at the mesoscopic level. The aggregates modeled by combining irregular polygons, which then is placed into the concrete with no intersection between them. By this new modeling approach, the simulation of high-strength concretes with possible aggregates fracture is also feasible. After generation of the geometrical model, a coupled explicit discrete element method and a modified rigid body spring model have been used for solution. In this method, all the neighboring elements are connected by springs. The mortar springs have Elasto-plastic behavior and considering normal concrete, the aggregate springs behave only elastically without any fracture. The proposed model can accurately predict the mechanical behavior of concrete under compression for small and large deformations both descriptively and quantitatively