Conference: Homogenization and Materials Science

University Of Akron, Akron OH

Investigators

Abstract

An International Conference, "Homogenization and Materials Science", in honor of the late Professor Ulrich Hornung of Bundeswehr University Munich, Germany, will take place at the University of Akron, Akron, Ohio, during September 15 - 17, 2000. The purpose of this interdisciplinary conference is to bring together researchers from interacting areas of Materials Science. In particular special focus will be paid to the latest scientific and industrial developments concerning homogenization theory and methods. Homogenization is a powerful mathematical tool for solving, both static (effective properties) and dynamic (wave propagation, transport equations) problems in inhomogeneous materials with periodic and random microstructure. This includes prediction of mechanical and dielectrical properties of composites, shape memory materials, materials undergoing phase transitions, and polymeric composites. Solutions of these problems provide guidance 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 bring together the leading scientists from Europe and the U.S. who are working on homogenization problems and applications in materials science. Modern electronic and mechanical devices require materials with specific properties in their design. For example, the automotive industry seeks lightweight yet very strong materials. Such materials do not necessarily occur naturally. Hence, these materials must be engineered from existing resources. One approach is to form a composite material. A composite material is made from a blend of other materials. Fundamental questions in the design of composites are (1) what materials should be used to form the composite, (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 the latter case the geometric patterns of the combined materials (think of plywood) play an important role. Materials scientists and engineers try to answer the above keeping in mind the specific properties required from the resulting composite. Practical experience and trial and error approaches are common means of obtaining answers. Within the past two decades many new tools have been developed by the applied mathematics community to help answer these questions. These tools fall under the heading of what is called homogenization theory. One reason for holding this conference will be to highlight the use of these new tools. A second purpose of the proposed conference will be to highlight the formulation and solution of new homogenization problems arising in materials design. For example, one area that may further benefit from the utilization of homogenization tools is polymer-based composites. Hence, the conference should help answer two questions: (1) what should be the future directions in homogenization theory based upon the current needs of modern technology (in short, which problems should be solved), and (2) what is the best way of utilizing newly developed mathematical tools to solve these problems in order to enhance the use of homogenization methods in materials design? These questions will be answered through both speaker presentations and a panel discussion, which will summarize the current state of the subject and future trends.