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.
