University-Industry Cooperative Research Programs: Modelingand Computation of the Overall Magnetic and Rheological Properties of Magnetorheological Fluids

磁流变液的整体磁和流变特性的建模和解释：联合Lord公司-- CRSC提案提交给NSF作者Mark R. Jolly Beth C穆尼奥斯 先进技术研究组 洛德公司托马斯洛德研究中心405 Gregson Drive卡里，NC 27511-7900 Fernando Reitich，H.托马斯班克斯伊藤和文 数学系和CRSC Box 8205 北卡罗来纳州州立大学罗利，NC 27695--8205 项目摘要 该项目涉及“智能”流体的磁特性和流变特性的数学建模、分析和计算。 最近已经证明，许多经典的障碍，为发展工业上可行的可控设备的基础上的流体可以克服与使用适当的磁流变（MR）悬浮液。实际上，具有低功率需求、高可实现的屈服应力、短响应时间和对杂质的低敏感性的MR流体的成功合成已经使得位于北卡罗来纳州的卡里的Lord公司成为第一家--并且迄今为止唯一一家--开发出多种在MR材料上操作的商业阻尼器和制动器的公司（例如，参见http://www.mrfluid.com）。 然而，由于对其性质进行彻底的实验研究所涉及的费用以及缺乏准确有效的预测数学模型和计算工具，因此优化此类产品的宏观特性的尝试仍然遥不可及。 本项目的目标是提高后几个领域的现有能力。为此，PI的将呼吁新开发的技术在数学理论的非线性均匀化研究的整体（非线性）磁和（小变形）流变响应的MR流体。调查将包括数值和分析计算的有效渗透率和存储modul i为现实的微观几何形状，以及它们的依赖于重要的设计变量，如颗粒尺寸（体积分数和尺寸分布）和形状的研究。拟议的分析还将涉及推导的有效属性，适用于相当一般的微观结构，通过最近介绍的PI的形状记忆多晶合金的上下文中的方法。在每一种情况下，研究小组都打算利用洛德的当地设施，通过适当的物理实验定期验证模型。 该项目由MPS多学科活动办公室（OMA）和数学科学部（DMS）共同支持。

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, http://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).