Conference: Homogenization and Materials Science

为纪念德国慕尼黑联邦国防军大学已故教授Ulrich Hornung，将于2000年9月15日至17日在俄亥俄州阿克伦的阿克伦大学举行“均匀化与材料科学”国际会议。 这个跨学科会议的目的是汇集来自材料科学相互作用领域的研究人员。 特别是将特别关注有关均匀化理论和方法的最新科学和工业发展。均匀化是一个强大的数学工具，用于解决具有周期性和随机微观结构的非均匀材料的静态（有效性质）和动态（波传播，输运方程）问题。这包括复合材料、形状记忆材料、相变材料和聚合物复合材料的机械和介电性能的预测。这些问题的解决方案为设计具有现代技术需求所要求的特定性能的新材料提供了指导。会议将讨论这些问题的建模和计算方面。本次会议将汇集来自欧洲和美国的顶尖科学家，他们致力于研究材料科学中的均匀化问题和应用。现代电子和机械设备在设计中需要具有特定性能的材料。 例如，汽车工业寻求强度小但非常坚固的材料。 这些物质不一定是天然存在的。 因此，这些材料必须从现有资源中进行设计。 一种方法是形成复合材料。 复合材料是由其他材料混合而成的。 复合材料设计中的基本问题是（1）应该使用什么材料来形成复合材料，（2）每种材料在复合材料中应该使用多少，以及（3）这些材料应该如何组合以形成复合材料。 在后一种情况下，组合材料的几何图案（想想胶合板）起着重要的作用。 材料科学家和工程师试图回答上述问题，同时牢记合成材料所需的特定性能。 实践经验和试错法是获得答案的常用方法。 在过去的二十年里，应用数学界开发了许多新的工具来帮助解决这些问题。 这些工具属于所谓的同质化理论的范畴。 举办这次会议的原因之一就是强调这些新工具的使用。 会议的第二个目的将是强调材料设计中出现的新的均匀化问题的制定和解决方案。 例如，一个可能进一步受益于均质化工具的领域是聚合物基复合材料。 因此，这次会议应该有助于回答两个问题：（1）基于现代技术的当前需求，均匀化理论的未来方向应该是什么（简而言之，应该解决哪些问题），以及（2）为了提高均匀化方法在材料设计中的应用，利用新开发的数学工具来解决这些问题的最佳方法是什么？ 这些问题将通过演讲者的演讲和小组讨论来回答，小组讨论将总结该主题的当前状态和未来趋势。

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.