Division of Applied Mathematics
Department of Mathematics and Computer Science
The University of Akron
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Conference SummaryWithin the past two decades many new tools have been developed by the applied mathematics community for homogenization and related topics. However, materials scientists often use old tools, such as mixing rules, effective medium, etc. for characterizing inhomogeneous materials. It is now time to bridge the gap between the two communities, since applied mathematicians have developed tools which can be used to answer practical problems in the design of new materials in university and industrial labs. For example, using nonlinear homogenization the difference between shape memory behavior of single crystals and polycrystals has been explained. Further, homogenization methods have been used in the study and design of piezoceramic composites, materials characterized by zero and negative Poisson's ratio, and materials characterized by zero and negative thermal expansion coefficients. In the latter case homogenization successfully predicted geometric patterns which have been used to create such materials. Thus, one reason for holding this conference will be to highlight the use of these new tools. Secondly, homogenization theory is currently in a transition phase, changing its focus from abstract mathematical PDE and probabilistic issues to solving important practical problems in materials science and mechanics of composites. Hence, a second purpose of the conference will be to highlight the formulation and solution of new homogenization problems arising in materials design in academic labs, government labs, and industry. For example, one area which may further benefit from the utilization of homogenization tools is polymer based composites. The University of Akron together with Akron area industrial base forms a cetner for world leadership in polymers. Hence, it is especially appropriate to host the meeting at The University of Akron and to bring homogenization tools to work for polymer needs. For this reason we have invited one University of Akron polymer scientist to speak about problems in the design of polymeric composites. Hence, this conference should answer two questions: (1) which problems should be solved and (2) what is the best way of utilizing newly developed mathematical tools to solve these problems. 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. These answers will especially benefit the junior researchers and graduate students working in this area. List of Tentative Topics
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Questions and Comments: Click here to contact the organizing committee.
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