An efficient monolithic multiscale numerical manifold model for fully coupled nonlinear saturated porous media

This paper presents an efficient monolithic computational homogenization model for transient nonlinear hydro-mechanical analysis within the framework of Numerical Manifold Method (NMM). The proposed model is on the same theoretical basis as the FE2 method. The scale transitions are achieved through the extended Hill-Mandel theorem so that the microscopic fluid and solid dynamic effects are fully incorporated. The two-scale simulations are solved in a monolithic manner and the microscopic problems of all macroscopic integration points are decoupled from each other to prevent size of the system of equations from soaring to exceedingly large. By conveying microscale unbalanced forces and tangent operators to the macroscale level, the micro- and macroscale problems are solved in the same Newton loop such that unnecessary microscopic iterations based on estimated macroscopic variables in the conventional nested homogenization m are avoided. By solving benchmark numerical examples, the proposed model proves to be capable of capturing transient hydro-mechanical responses accurately. Moreover, in contrast to the conventional nested homogenization model, the proposed model saves around 40% of computational costs for nonlinear hydro-mechanical analysis. Using the framework of numerical manifold, the presented model can be easily extended to multiscale analyses involving complex boundaries, interfaces and fractures.