Phase-field modeling of drying-induced cracks: Choice of coupling and study of homogeneous and localized damage

Phase-field modeling has already proved to be a suitable framework to predict the initiation and propagation of drying cracks in variably saturated porous media. In this paper, we focus on some fundamental modeling aspects which have not yet been given sufficient attention. In the first part, different formulations for the total energy, characterized by different choices for the coupling between the damage and the poro-mechanical fields, are evaluated based on their ability to lead to qualitatively reasonable predictions for two benchmark cases of free and restrained desiccation. In the second part, for a selected energy formulation, we conduct the variational analysis of the quasi-static damage evolution. Hereby, we focus on restrained desiccation under a given capillary pressure distribution, resulting from the solution of Richards equation with either flux-driven or pressure-driven boundary conditions. Extending the analysis in Sicsic et al. (2014) to the present case, we show that the damage evolution follows first a fundamental branch without localization, and then bifurcates into another branch with damage localization, which leads to the initiation of periodic cracks. The analysis enables the computation of the drying crack spacing as a function of material and loading parameters.