This work aims to propose a new damaging beam-lattice model using the Discrete Element Method paradigm dedicated to the simulation of quasi-brittle fracture under complex loadings. Enrichment of the elastic Euler–Bernoulli beam link, inspired by the cohesive zone models, is proposed to provide a damageable behavior in mixed mode and contribution of frictional behavior is not considered in this first version of the damage model. The tensile contribution on the beam link is taken into account from the first order elongation of the beam while all other contributions, i.e. bending, shear, and torsion are considered from the second-order elongation of the beam. These orders of elongation refer to beam theory, where the first elongation is induced by a force normal to the cross-section and the second is the elongation of the curvilinear length of the beam resulting from shear, bending and torsion loads. As these two kinematics do not correspond to the conventional modes I, II, and III, a deep checking step of the model is undertaken. First, mixed-mode testing on a single beam is performed to monitor the energy components dissipated in each mode and to ensure that energy dissipated in mixed mode exhibits a monotonic evolution between boundary values related to pure modes. Based on this first verification, a tensile test and a compression one are simulated on a cylinder specimen to evaluate the model capabilities to qualitatively describe the well-known characteristics of quasi-brittle fracture such as failure facies, unilateral effect, and the ratio between the compression and tensile strength. Finally, the model is used to simulate a complex crack propagation test coming from the recent international Carpiuc benchmark.< Réduire