Formulation of anisotropic damage in quasi-brittle materials and structures based on discrete element simulation

Quasi-brittle materials, commonly found in civil engineering structures, tend to degrade when submitted to mechanical loadings. This degradation leads to a loss in mechanical properties and can induce anisotropy of the material behavior, which depends on the loading direction. Predicting this degradation and its impact on the material is essential to guarantee the integrity of structures and the safety of users. This problem is at the heart of this work, which aims to formulate a (macroscopic) anisotropic damage model for quasi-brittle materials in 2D. To this end, a dataset of effective elasticity tensors is generated by "virtual'' testing. A (mesoscopic) area element of the material is represented by a discrete beam-particle model, which provides an explicit description of micro-cracking. The evolution of the element's effective elasticity tensor is measured for various loadings (some of which are multiaxial and non-proportional). The analysis of the measured tensors by calculating distances to symmetry classes shows that a tensor variable of order two or higher is needed to describe micro-cracking. To facilitate the formulation of the state model, a formula for reconstructing the elasticity tensor from its covariants and an associated damage variable, both derived from previous work, are recalled. Based on these tools and the generated dataset, a model of the effective elasticity tensor as a function of the damage variable, i.e. a state model, is proposed and evaluated. For evolution modeling, the criterion function of the area element is determined and calibrated by "virtual'' testing. Finally, a (preliminary) non-standard evolution model is proposed after an analysis of the damage evolution in the dataset.