The simulation of the damage process is a challenge for researchers nowadays. In ductile materials, the continuum damage mechanics is based on the plasticity framework, but quasi-fragile materials have some characteristic phenomena such as localization and size effects, among others, that cannot be taken into account with this approach. The discrete element method has demonstrated considerable success in simulating the damage process in this kind of material. One of the advantages of this approach consists of capturing the transition between continuum and cracked regions in a natural way. In the first part of this work, extensive validation of the proposed numerical method is done, where fissures are introduced in a lattice structure. The variations of the mechanical properties are evaluated and compared to the analytical responses based on continuum damage theory. In the second part, an application considering the damaging process due to cyclic load history simulates a fatigue process with special attention on the transition between the continuum to macro-cracks nucleation. Finally, in the framework of quasi-brittle materials, a discussion about the performance of this approach in quantifying damage is presented.

损伤过程的模拟是当今研究人员面临的挑战。在延性材料中，连续介质损伤力学基于塑性框架，但准脆性材料具有一些特征现象，例如局部化和尺寸效应等，这种方法无法考虑。离散元方法在模拟此类材料的损伤过程方面取得了相当大的成功。这种方法的优点之一包括以自然的方式捕捉连续区和裂纹区域之间的过渡。在这项工作的第一部分，对所提出的数值方法进行了广泛的验证，其中在晶格结构中引入了裂缝。机械性能的变化被评估并与基于连续损伤理论的分析响应进行比较。在第二部分中，考虑由于循环载荷历史造成的破坏过程的应用程序模拟了疲劳过程，特别关注连续体到宏观裂纹形核之间的过渡。最后，在准脆性材料的框架内，讨论了这种方法在量化损伤方面的性能。