Limitations of poromechanical first-order computational homogenization for the representation of micro-scale volume changes

Poromechanical computational homogenization models relate the behavior of a macro-scale poroelastic continuum to phenomena occurring at smaller (and also poroelastic) spatial scales. This paper presents a comprehensive analysis of classical micro-scale boundary conditions for the pore pressure field, namely Taylor boundary condition (TBC-p), linear boundary condition (LBC-p), periodic boundary condition (PBC-p) and uniform boundary flux (UBF-p), in terms of their accuracy in representing primary (pore pressure) and dual (relative fluid velocity) fields in finite-strain multiscale poromechanical problems. A specific benchmark problem was formulated to investigate the performance of these approaches in scenarios where the rate of the volumetric Jacobian is nonzero, a condition of significant physical interest, especially in contexts such as swelling. Numerical results show that the UBF-p and PBC-p approaches effectively capture the behavior of direct numerical simulation (DNS) during the early time steps. However, deviations from the expected behavior occur when the representative volume element (RVE) undergoes significant volume changes. It is concluded that the observed limitations are due to the first-order nature of the multiscale model. This study highlights the need for more sophisticated computational homogenization poromechanical models that can accurately capture the complex interplay between fluid flow and deformation at different length scales. Second-order computational homogenization models can be alternatives to overcome the limitations of first-order multiscale poromechanical models by enriching the information coming from the macro-scale and relaxing the constraints on the fluid flow at the RVE boundaries.