Iterative upscaling of fluid flows in nonlinear deformable porous media

该项目的目标是开发流体在形状变化、非弹性、多孔介质中流动的数值升级模型，该模型能够在压力和温度变化下恢复形状。目前，孔隙弹性介质的成熟模型只能应用于线性、弹性、多孔固体。此外，平均流体压力和固体位移等宏观参数受到各种限制。该研究的一个关键科学贡献是在微观尺度上模拟流体流动和固体变形之间的非线性耦合，这是由于固体的非弹性行为和大孔隙水平位移造成的。该项目将重点研究流体在不同类型三维孔隙几何形状和不同宏观参数（如温度、压力和排量）下的流动情况。均质化方法将用于识别描述有效介质的宏观方程和放大参数。由于精细尺度下流固耦合问题的复杂性和形状记忆固体的复杂非线性响应，我们将不尝试推导封闭形式的宏观方程。相反，将开发一种高效、易于并行的混合多尺度有限元模型（HMFEM），该模型通过将精细尺度信息直接构建到粗尺度计算网格中来绕过明确的均匀化步骤。该数值升级方法将应用于具有SMA（形状记忆合金）矩阵的可变磁导率滤波器的分析，作为所提出方法的演示。本文还将对数值模拟进行实验验证。多孔SMA（形状记忆合金）基体使得器件具有变化的、温度和/或应力相关的孔隙度，而不需要移动部件和主动控制机制。该项目将扩大我们对这种介质中紧密耦合多物理现象的理解。只有对这些可变形多孔介质中的流体流动进行精确的数学建模和数值模拟，才能设计出适用于过滤器、催化转化器、分离器和微流体传感器的新型温度和压力控制流量调节器。该项目还将为升级强耦合流固相互作用问题提供良好的理论理解，扩展当前复杂设备的工程分析和设计方法。虽然我们专注于sma，但sma包括标准塑料材料，并且代表了更广泛的形状改变材料，如磁性sma，形状记忆聚合物和铁电材料。因此，这项工作将直接适用于更一般的非弹性、温度相关材料。

The objective of this project is to develop numerical upscaling models for fluid flow through shape changing, inelastic, porous media, capable of shape recovery under pressure and temperature variations. Currently, the well-established models for poro-elastic media can only be applied to linear, elastic, porous solids. Moreover, macroscopic parameters such as average fluid pressure, and solid displacements are subject to various limitations. A key scientific contribution of the proposed research is modeling of the nonlinear coupling at the microscale between the fluid flow and solid deformation, due to both inelastic behavior of the solid and large pore-level displacements. The project will focus on fluid flow in various types of 3D pore geometries and different macroscopic parameters such as temperature, pressure and displacements. The homogenization method will be used to identify macroscopic equations and upscaled parameters which describe the effective media. Due to the complexity of the coupled fluid-structure interaction problem at the fine scale and the complex nonlinear response shape memory solids we will not attempt do derive closed form macroscopic equations. Instead, an efficient, easily parallelizable, Hybrid Multiscale Finite Element Model (HMFEM) which bypasses the explicit homogenization step by building fine-scale information directly into a coarse-scale computational grid will be developed. This numerical upscaling method will be applied to the analysis of a variable permeability filter with an SMA (Shape Memory Alloy) matrix, as a demonstration of the proposed methodology. Experimental verification of the numerical simulations will also be carried out.A porous SMA (Shape Memory Alloy) matrix makes possible devices with changing, temperature and/or stress dependent, porosity without the need for moving parts and active control mechanisms. The project will expand our understanding of tightly coupled multiphyics phenomena in such media. Design of novel temperature and pressure-controlled flow regulators with applications to filters, catalytic converters, separators and microfluidic sensors can only become possible with accurate mathematical modeling and numerical simulations of fluid flow in such deformable porous media. The project will also provide a sound theoretical understanding of upscaling strongly coupled fluid-structure interaction problems, extending current methods for engineering analysis and design of complex devices. While we focus on SMAs, SMAs encompass standard plastic materials and are representative of a broader class of shape changing materials such as Magnetic SMAs, Shape Memory Polymers and Ferroelectric materials. As a result, this work will be directly applicable to a more general class of inelastic, temperature-dependent materials.