Second-order computational homogenization for bridging poromechanical scales under large deformations

We introduce a second-order computational homogenization procedure designed to address heterogeneous poromechanical media. Our approach relies on the method of multiscale virtual power, a variational multiscale method that extends the Hill–Mandel principle of macro-homogeneity. Constraints on displacement and pore pressure fields are managed using periodic and second-order minimally constrained fluctuating spaces. Numerical comparisons reveal that first-order models fail to accurately represent nonzero net fluid flow and volume changes at the micro-scale. In contrast, our second-order approach effectively captures nonuniform fluid flow across representative volume element boundaries, in agreement with results from direct numerical simulations. Our findings indicate that the classical first-order expansion of the pressure field is inadequate for poromechanical homogenization in cases involving micro-scale volume changes, such as swelling or contraction. The proposed second-order approach not only overcomes these limitations but also proves effective in cases where the principle of separation of scales is not strictly upheld.