Conference: Homogenization and Materials Science

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An International Conference, "Homogenization and Materials Science", inhonor of the late Professor Ulrich Hornung of Bundeswehr University Munich,Germany, will take place at the University of Akron, Akron, Ohio, duringSeptember 15 - 17, 2000. The purpose of this interdisciplinary conferenceis to bring together researchers from interacting areas of MaterialsScience. In particular special focus will be paid to the latest scientificand industrial developments concerning homogenization theory and methods.Homogenization is a powerful mathematical tool for solving, both static (effectiveproperties) and dynamic (wave propagation, transport equations) problems ininhomogeneous materials with periodic and random microstructure. Thisincludes prediction of mechanical and dielectrical properties ofcomposites, shape memory materials, materials undergoing phasetransitions, and polymeric composites. Solutions of these problems provideguidance in the design of new materials possessing the specific properties required by modern technological needs. The conference shall address both modeling and computational aspects of these problems. This conference will bringtogether the leading scientists from Europe and the U.S. who are working onhomogenization problems and applications in materials science.Modern electronic and mechanical devices require materials with specificproperties in their design. For example, the automotive industry seekslightweight yet very strong materials. Such materials do not necessarilyoccur naturally. Hence, these materials must be engineered from existingresources. One approach is to form a composite material. A compositematerial is made from a blend of other materials. Fundamental questions inthe design of composites are (1) what materials should be used to form thecomposite, (2) how much of each material should be used in the composite,and (3) how should the materials be combined to form the composite? In thelatter case the geometric patterns of the combined materials (think ofplywood) play an important role. Materials scientists and engineers try toanswer the above keeping in mind the specific properties required from theresulting composite. Practical experience and trial and error approachesare common means of obtaining answers. Within the past two decades manynew tools have been developed by the applied mathematics community to helpanswer these questions. These tools fall under the heading of what iscalled homogenization theory. One reason for holding this conference willbe to highlight the use of these new tools. A second purpose of theproposed conference will be to highlight the formulation and solution ofnew homogenization problems arising in materials design. For example, onearea that may further benefit from the utilization of homogenization toolsis polymer-based composites. Hence, the conference should help answer twoquestions: (1) what should be the future directions in homogenizationtheory based upon the current needs of modern technology (in short, whichproblems should be solved), and (2) what is the best way of utilizing newlydeveloped mathematical tools to solve these problems in order to enhancethe use of homogenization methods in materials design? These questionswill be answered through both speaker presentations and a panel discussion,which will summarize the current state of the subject and future trends.