Mixed Arlequin method for multiscale poromechanics problems

Abstract

Summary 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 hydro‐mechanical 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 © 2016 John Wiley & Sons, Ltd.

A configurational force for adaptive re-meshing of gradient-enhanced poromechanics problems with history-dependent variables

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“…As such, it is convenient for considering the energy flux of the apparent solid skeleton along the trajectory of the solid skeleton. The energy of the apparent solid skeleton therefore reads [62][63][64],…”

“…More general discussion on the specific form of plastic work for other types of materials can be found in, for instance, Ortiz and Stainier [67], Weinberg et al [68], Mosler and Bruhns [69], Miehe et al [17] but is out of the scope of this study. Next, the fluid contribution of the free energy W fluid takes the following form (cf., [23,64,70]),…”

“…In addition to contributions of the free energy described above (12), the coupling between the local and micromorphic internal variables and gradient dependence of the plastic flow introduced via the micromorphic internal variable also constitutes energy. As a result, the resultant regularized energy-dissipation functional for the apparent solid skeleton reads (cf., [16,64,71]),…”

An Adaptive Reduced-Dimensional Discrete Element Model for Dynamic Responses of Granular Materials With High-Frequency Noises

“…In dynamic particulate mechanics simulations, high-frequency modes may lead to the spurious numerical results and also cause stability and convergence issues in explicit scheme (Deokar et al, 2017). In the case where concurrent multiscale coupling takes place in a handshake domain, the high frequent component may destabilize the numerical simulations and must be eliminated in the transition zone (Badia et al, 2007;Chamoin et al, 2010;Sun et al, 2017;Sun and Mota, 2014). Hence, the numerical dissipation approach is frequently introduced to the explicit time integration algorithms in order to damp out the spurious oscillations occurring in high-frequency domain.…”