Conference: Homogenization and Materials Science

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.