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In the present work, we propose the incorporation of a bilinear softening constitutive law in a purely linear elastic discrete model previously developed by the authors. The new model includes information of the fracture energy for the constitutive law. Three numerical examples of dynamic crack propagation are provided to demonstrate the effectiveness and robustness of the modification proposed. The obtained results are presented in terms of the crack path, the crack speed ,and the dissipated energy. These results are compared with those obtained with a previous discrete model developed by the authors and other numerical results published by other researchers. Final comments on the performance of the new model are carried out.