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The fracture energy dissipated by a crack growing in a compositematerial can be influenced by different material parameters which are affected by themanufacturing process. In case of brittle composite materials, failure mechanisms likedebonding of the matrix-fiber interface or fiber breakage can result in crack deflectionand hence in the improvement of the damage tolerance of the material. While somematerial parameters affect dissipative processes during crack growth, others influencethe crack path. Concerning simulations of crack growth the cohesive element methodprovides a framework to model the fracture considering strength, stiffness and failureenergy in an integrated manner. Combination with the discontinuous Galerkin methodallows to investigate the influence of different cohesive parameters and crack paths onthe fracture energy dissipation to optimize the toughness of the considered composite.