A combined Lattice-Boltzmann-finite element approach to modeling unsaturated poroelastic behavior of heterogeneous media

Abstract : In this paper, we propose a procedure combining Lattice-Boltzmann and finite element simulations to model the effects of capillary pressure in porous microstructures. Starting from an explicit geometry of the microstructure, the Lattice-Boltzmann method is used to simulate the condensation from vapor phase to liquid and predict the geometry of capillary liquid films and liquid phases for arbitrary geometry of the solid skeleton. Then, a procedure is provided to prescribe surface tension and pressure due to the capillary liquid films and liquid phases. The solid skeleton can deform elastically under the action of the liquid and its deformation can be captured using the finite element method. Finally, a procedure to extract the shrinkage strain and the effective macroscopic behavior of the material, taking into account the explicit geometry of the microstructure and of the liquid capillary phases for a given saturation is described. Several numerical examples are provided to validate the methodology and show its potential.