Predicting gradient damage and frictional effects in quasi-brittle materials with asymptotic homogenization – MicroDamage

This project aims at developing accurate models to predict the mechanical behavior of quasi-brittle materials like concrete and rocks. These materials undergo irreversible deformations due to the nucleation, growth, and coalescence of microcracks. Effective macroscopic elasto-plastic gradient damage models are often used to predict these behaviors but remain empirical and require parameter tuning. Starting from a periodic array of microcracks in an isotropic matrix, micromechanics-based homogenization methods bridge the gap between the microscopic behavior and macroscopic models. Early works in this direction rely on simplifying assumptions, such as isolated microcracks or periodic boundary conditions, which limit their predictive accuracy, particularly in capturing gradient effects due to spatially varying microcrack patterns. I aim at expanding asymptotic homogenization methods, used in purely periodic microstructures, to quasi-periodic microstructures. This will allow the resulting model to account for varying crack lengths and orientations, improving the accuracy of predictions. The ultimate goal is to include sliding along microcrack lips in the asymptotic approach to derive an effective elasto-plastic gradient damage model, which incorporates the effects of microstructure evolution on the macroscopic behavior. The methodology involves using a two-scale expansion approach, where the displacement field is split into macroscopic and microscopic contributions. The latter will be obtained by solving a series of boundary value problems on unit cells with varying microcrack lengths and orientations. The resulting effective model will be implemented using finite element methods and tested under various loading conditions. It will then be validated by comparing its predictions with full-scale simulations of the materials’ microstructure.