### Monday, 11 October 2004 - 1:00 PM

### This presentation is part of : Graduate Student Competition

### Upscaling of Fluid Flow in Porous Shape Memory Alloys

**Peter Popov**^{1}, Dimitris C. Lagoudas^{1}, and Oleg Iliev^{2}. (1) Texas A&M University, College Station, TX 77843, (2) Fraunhofer Institut fuer Techno- und Wirtschaftsmathematik, Kaiserslautern, D-67657, Germany
In this work the problem of fluid flow in deformable porous media is studied. The stationary fluid-structure interaction (FSI) problem is formulated in terms of incompressible Newtonian fluid and a deformable solid. Both linearized elastic solids and nonlinear hysteretic materials such as Shape Memory Alloys (SMAs) are considered. The flow is assumed to be at very low Reynolds number and is described by the Stokes equations. The strains in the solid are assumed small but no restrictions are applied on the magnitude of the displacements leading to a strongly coupled, nonlinear, FSI problem. The FSI problem is then solved numerically by an iterative procedure, which sequentially solves fluid and solid sub-problems. Each of the two sub-problems is discretized by finite elements and the fluid-structure coupling is reduced to an interface boundary condition. A three-dimensional constitutive model for SMAs is used to resolve the material response of the solid. Several numerical examples are presented including simulations of SMA flow regulator devices. Further, effective properties for the permeability of long deformable channels are computed. Comparisons are made with an analytical result, which is available for a linearized, elastic, solid.

P.Popov: PhD Student D.C. Lagoudas: Student's Advisor

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