About RVE size objectivity of multiscale analysis of porous media

Abstract

This study proposes a multi-scale model formulation for saturated porous media, centered on the concept of the Representative Volume Element (RVE). The linkage between scales is established by enforcing the equivalence of the total virtual power per unit volume at the larger scale with its corresponding volume-averaged counterpart at the smaller length scale, both derived from the general theory of poromechanics. By employing the Principle of Multiscale Virtual Power (PMVP) along with appropriate constraints on micro-scale displacements and pore pressures, a robust variational theory is established. This variational framework allows us to derive the micro-scale balance equations and obtain homogenization relations between the relevant macro-and micro-scale quantities. The formulation can be implemented using the finite element squared (FE2) strategy through spatial discretization and standard time integration methods for time evolution. The theoretical evidence presented in this work reveal a pathological inconsistency in the objectivity of the macro scale response with respect to the RVE size, also observed in existing literature. This incongruity is often addressed by assuming infinitely small micro-scale dimensions or by neglecting dynamic terms causing the size effect. The primary contribution of this work is to offer an alternative solution to the aforementioned issue, aiming to restore the fundamental concept of RVE. To achieve this, a conveniently fine-scale constitutive approach is proposed, introducing usefull adjustments in the micro-scale pore pressure field expansion.