A Phase Field Arlequin Model for Resolving Nonlocal Hydromechanical Effects of Porous Media Across Time and Spatial Scales

Columbia University, New York NY

Investigators

Abstract

Porous media are common to engineered and natural systems. This class of materials includes amongst others bone, sand, rock and concrete. Understanding how the microscopic defects and flaws of porous media evolve is of great importance for predicting large-scale response. This award supports fundamental research on predicting and analyzing mechanical behaviors of fluid infiltrating porous media. Emphasis is placed on problems that involve strong near- and far-field interactions, such as hydraulic fracture operations and preventing re-activation of faults. The framework will adaptively activate material models of different levels of sophistication based on the need to extract small-scale information. This adaptive nature leads to highly efficient simulations where all CPU time and computational resources are wisely allocated for the most important hydro-mechanical events in the most important region at the most critical time. As a result, this highly efficient model will help industries and engineers predicting material failures more accurately and faster and therefore benefit to the US economy and society. The research is fully integrated with education activities that use 3D printers to demonstrate the fundamental physics of porous media. Outreach activities at the underprivileged school district will help broaden participation of underrepresented groups in research and positively impact engineering education. This award supports research on a new phase-field based, adaptive Arlequin multiscale model for poromechanics. While classic Arlequin method uses partition of unity on energy functional to couple small- and large-scale models in a fixed domain of interest, this new work will allow fine-scale region to enlarge, shrink or vanished via an evolving phase field. The fact that phase field has finite thickness will be exploited to seamlessly create evolving transition zone between fine- and coarse-scale models. The coupled numerical model will be implemented in an operator-splitting scheme where displacement, Darcy's velocity, pore pressure and the phase fields are updated asynchronously. By overcoming the computational barrier due to coupling effect across length scale, the concurrent multiscale model will provide fresh insight in understanding the fundamental role of pore-fluid in the formation of localized band, cracks propagations in porous media with defects, flaws and other small-scale geometrical features.