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

多孔介质在工程和自然系统中很常见。这类材料包括骨头、沙子、岩石和混凝土。了解多孔介质的微观缺陷和缺陷是如何演化的，对于预测大规模响应具有重要意义。该奖项支持预测和分析流体渗透多孔介质力学行为的基础研究。重点是涉及强近场和远场相互作用的问题，例如水力压裂作业和防止断层重新激活。该框架将根据提取小规模信息的需要，自适应地激活不同复杂程度的材料模型。这种自适应特性导致了高效的模拟，其中所有CPU时间和计算资源都被明智地分配给最重要的流体力学事件在最重要的区域在最关键的时间。因此，这种高效的模型将帮助行业和工程师更准确、更快地预测材料失效，从而有利于美国经济和社会。该研究与使用3D打印机演示多孔介质基本物理的教育活动完全结合在一起。在贫困学区开展的外展活动将有助于扩大弱势群体在研究中的参与，并对工程教育产生积极影响。该奖项支持一种新的基于相场的自适应Arlequin多孔力学多尺度模型的研究。经典的Arlequin方法使用能量泛函上的统一分割来耦合固定兴趣域中的小型和大型模型，而这项新工作将允许精细尺度区域通过不断发展的相场来扩大，缩小或消失。将利用相场厚度有限的事实，无缝地创建精细和粗尺度模型之间的演化过渡区。耦合数值模型将采用算子分裂格式实现，其中位移、达西速度、孔隙压力和相场将异步更新。通过克服跨长度尺度耦合效应的计算障碍，并行多尺度模型将为理解孔隙流体在具有缺陷、缺陷和其他小尺度几何特征的多孔介质中局部带形成、裂纹扩展等方面的基本作用提供新的视角。

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.