MODELING AND COMPUTATION OF THE OVERALL MAGNETIC AND RHEOLOGICAL PROPERTIES OF MAGNETORHEOLOGICAL FLUIDS: A joint Lord Corp.--CRSC proposal submitted to NSF author Mark R. Jolly & Beth C. Munoz Advanced Technologies Research Group Lord Corporation Thomas Lord Research Center 405 Gregson Drive Cary, NC 27511-7900 Fernando Reitich, H. Thomas Banks & Kazufumi Ito Department of Mathematics and CRSC Box 8205 North Carolina State University Raleigh, NC 27695--8205 PROJECT SUMMARY This project deals with the mathematical modeling, analysis and computations of the magnetic and rheological characteristics of ``smart'' fluids. It has recently been demonstrated that many of the classical obstacles for the development of industrially viable controllable devices based on fluids can be overcome with the use of appropriate magnetorheological (MR) suspensions. Indeed, the successful synthesis of MR fluids with low power demand, high achievable yield stresses, short response times and low sensitivity to impurities has allowed the Lord Corporation, Cary, North Carolina, to become the first ---and, so far, the only--- company to develop a variety of commercial dampers and brakes that operate on MR materials (see, for instance, www.mrfluid.com). Attempts at optimizing the macroscopic characteristics of such products are still out of reach, however, due to the expense involved in a thorough experimental investigation of their properties and the lack of accurate and efficient predictive mathematical models and computational tools. It is the goal of this project to advance the present capabilities in these latter areas. For this, the PI's will appeal to newly developed techniques in the mathematical theory of nonlinear homogenization to investigate the overall (nonlinear) magnetic and (small deformation) rheological response of MR fluids. The investigation will include numerical and analytical calculations of effective permeabilities and storage modul i for realistic microgeometries, as well as a study of their dependence on important design variables such as particle size (volume fraction and size distribution) and shape. The proposed analysis will also involve the derivation of tight bounds on the effective properties, applicable to rather general microstructures,by means of a method recently introduced by the PI in the context of shape--memory polycrystalline alloys. In every case, the research group intends to take advantage of Lord's local facilities to periodically validate the models through appropriate physical experimentation. This project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).
