@article{ly_ito_banks_jolly_reitich_2001, title={Dynamic simulation of the temporal response of microstructure formation in magnetorheological fluids}, volume={15}, ISSN={["0217-9792"]}, DOI={10.1142/s0217979201005416}, abstractNote={ Efficient numerical simulations of microstructure development in magnetorheological (MR) fluids are conducted. The simulations, which are based upon a fast multipole algorithm, treat the magnetic inclusions as two-dimensional continuum magnetic entities. The development of microstructure is quantified by computing and recording the time evolution of the effective permeability of the composite fluid. Such a principle has been previously exploited for the experimental measurements of microstructure development [Jolly, Bender and Mathers, ERMR'97, Yonezawa, Japan 1997]. As was observed experimentally, numerical simulations reveal the evolution of microstructure to be multimodal in nature. Unlike the experiments, the numerical simulations afford us the ability to observe the physical mechanisms associated with various modes. }, number={6-7}, journal={INTERNATIONAL JOURNAL OF MODERN PHYSICS B}, author={Ly, HV and Ito, K and Banks, HT and Jolly, MR and Reitich, F}, year={2001}, month={Mar}, pages={894–903} }
 @article{lee_reitich_jolly_banks_2001, title={Piecewise linear model for field-responsive fluids}, volume={37}, ISSN={["1941-0069"]}, DOI={10.1109/20.914377}, abstractNote={The Frohlich-Kennelly model provides a constitutive law for saturation that is field dependent and has been widely used for studying nonlinear properties for a variety of electric and magnetic applications. Under the Frohlich-Kennelly model, saturation begins to occupy the entire conducting domain even at low-moderate applied fields, in this paper, we first present a new nonlinear constitutive law for field-responsive fluids that depends on the local fields and allows regions where the fields have not reached a critical value to remain unsaturated. We then study numerically the nonlinear saturated model and compare the results to the Frohlich-Kennelly model and experiments performed at the Lord Corporation, Cary, NC.}, number={1}, journal={IEEE TRANSACTIONS ON MAGNETICS}, author={Lee, CH and Reitich, F and Jolly, MR and Banks, HT}, year={2001}, month={Jan}, pages={558–560} }
 @article{simon_reitich_jolly_ito_banks_2001, title={The effective magnetic properties of magnetorheological fluids}, volume={33}, ISSN={["0895-7177"]}, DOI={10.1016/S0895-7177(00)00244-2}, abstractNote={Magnetorheological (MR) fluids represent a class of smart materials whose rheological properties change in response to the application of a magnetic field. These fluids typically consist of small (μm) magnetizable particles dispersed in a nonmagnetic carrier fluid that generally contains additives such as surfactants and antiwear agents [1]. Due to such additives, there is an outer nonmagnetic layer on the particles that keeps them from touching. The goal of this paper is to study the effective magnetic behavior of an MR composite as a function of the interparticle distance. To this end, we present and employ a model for the effective magnetic properties of MR fluids with periodic microstructure that is based on the theory of homogenization. Finally, we discuss an interpolating formula for the effective permeability of MR fluids as an extension of the work of Keller [2] and Doyle [3].}, number={1-3}, journal={MATHEMATICAL AND COMPUTER MODELLING}, author={Simon, TM and Reitich, F and Jolly, MR and Ito, K and Banks, HT}, year={2001}, pages={273–284} }
 @article{simon_ito_banks_reitich_jolly_1999, title={Estimation of the effective permeability in magnetorheological fluids}, volume={10}, ISSN={["1045-389X"]}, DOI={10.1106/6KW6-7V12-NRQ3-BW6V}, abstractNote={ Magnetorheological (MR) fluids constitute examples of controllable ("smart") fluids, whose Theological properties vary in response to an applied magnetic field. These fluids typically consist of micron-sized, magnetizable particles dispersed in a nonpermeable carrier fluid. The essential characteristic of MR fluids is that they may be continuously and reversibly varied from a state of free flowing liquids in the absence of an applied magnetic field to that of stiff semi-solids in a moderate field. Understanding the magnetic properties of MR fluids is crucial to the design of MR fluid-based devices and it also provides valuable insight into the character of the microstructure responsible for their field-dependent rheology. Prediction of the overall magnetic properties of MR composites is a challenging task, however, due to the highly nonlinear and strongly spatially variable nature of the magnetization of the constituents. In this paper we propose a model for this behavior that is based on the mathematical theory of homogenization. We derive effective equations that govern the magnetic response of (periodically arranged) particle-chains through magnetic saturation. Comparisons of numerical results for these equations with experimental data show good agreement which suggests that our approach could be useful in the design of improved MR fluids. }, number={11}, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, author={Simon, TM and Ito, K and Banks, HT and Reitich, F and Jolly, MR}, year={1999}, month={Nov}, pages={872–879} }
 @article{ly_reitich_jolly_banks_ito_1999, title={Simulations of particle dynamics in magnetorheological fluids}, volume={155}, ISSN={["1090-2716"]}, DOI={10.1006/jcph.1999.6335}, abstractNote={We present particle dynamics simulations for the response of magnetorheological (MR) fluids upon application of a magnetic field. The particles motion is considered to be governed by magnetic, hydrodynamic, and repulsive interactions. Fluid-particle interactions are accounted for via Stokes' drag while inter-particle repulsions are modeled through approximate hard-sphere rejections. In accordance with their greater significance, on the other hand (linear) magnetic interactions are fully simulated. The time evolution is considered to be magnetically quasi-static and magnetostatic forces are derived from the solution of (steady) Maxwell's equations, recomputed at each instant in time. For this we use a potential theoretic formulation where the boundary integral equations are solved with a fast multipole approach. We show that the resulting numerical codes can be effectively used to study a number of experimental observables such as effective magnetic permeabilities and response time-scales which are of crucial importance in the design of MR fluids.}, number={1}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Ly, HV and Reitich, E and Jolly, MR and Banks, HT and Ito, K}, year={1999}, month={Oct}, pages={160–177} }