Damage index proposals applied to quasi-brittle materials simulated using the lattice discrete element method

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.