Mixed Arlequin method for multiscale poromechanics problems

Abstract

An Arlequin poromechanics model is introduced to simulate the hydro-mechanical coupling effects of fluid-infiltrated porous media across different spatial scales within a concurrent computational framework. A two-field poromechanics problem is first recast as the twofold saddle point of an incremental energy functional. We then introduce Lagrange multipliers and compatibility energy functionals to enforce the weak compatibility of hydro-mechanical responses in the overlapped domain. To examine the numerical stability of this hydromechanical Arlequin model, we derive a necessary condition for stability, the twofold inf-sup condition for multi-field problems, and establish a modified inf-sup test formulated in the product space of the solution field. We verify the implementation of the Arlequin poromechanics model through benchmark problems covering the entire range of drainage conditions. Through these numerical examples, we demonstrate the performance, robustness, and numerical stability of the Arlequin poromechanics model. Copyright (C) 2016 John Wiley & Sons, Ltd.