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The process of damage in quasi-brittle materials is characterized by loss of isotropy for certain load levels. The strain localization, the cooperative effect between damaged regions and the avalanche of ruptures are particular features in measuring the damage in this kind of material. The mentioned features create different forms of energy dissipation, which are not easy to represent with a continuous approach. In the present work, a version of the lattice discrete element method (LDEM) is employed. In this method the fracture and fragmentation are taken into account in a natural manner, since the bars that reached their limit strength during the process are disabled of the system, respecting the energy balance. It is possible to introduce heterogeneity in the model considering the material properties as random fields with spatial Weibull probability distribution and known correlation length. The aim of the present paper is to describe the implementation, in the context of this version of the LDEM, of three classical indexes used to measure the level of damage: a scalar index, and a second- and a fourth-order tensorial index. A simple uniaxial tensile test is used to illustrate the implementation. A discussion about the advantages of applying this tool to analyse the damage evolution in quasi-brittle structures and the possibility to link these indexes with other forms of measurement of damage evolution, such as acoustic emission data, also are commented.

The damage process in quasi‐brittle materials is characterized by the evolution of a micro‐crack field, followed by the joining of micro‐cracks, stress localization and crack instability. In network models, masses are lumped at nodal points which are interconnected by one‐dimensional elements with a bilinear constitutive relation, considering the energy consistency during the simulated process. In order to replicate the material imperfections, to render a realistic behaviour in damage localization, the model has not only random elastic and rupture properties, but also a geometric perturbation. In the present paper 2D plates with different levels of brittleness are simulated. The numerical results are presented in terms of global stress vs strain diagram, final network configuration, energy balance during the process and as geometric damage evolution. Therefore, the predictive potential of the lattice discrete element model to capture fracture processes in quasi‐brittle materials is demonstrated.