Mathematical Sciences: Analysis and Numerical Modeling of Wave Phenomena in Composite Materials

复合材料的时间相关问题的一个困难来源是以观测频率或时间的形式存在额外的长度尺度。该项目的目标是获得复合材料对时变载荷响应的令人信服的描述，并得出有效介质理论，给出响应的宏观描述。在这项持续研究的这一阶段，重点将放在复合材料中应力场和位移场与边界的相互作用预计会很强的情况上。感兴趣的是边界层型现象的描述，以及它们对复合材料宏观行为的影响。所使用的工具将结合渐近分析、偏微分方程的解析方法和数值实验。最终的目标是得到复合结构中波传播和振动的精确和有效的可计算模型。复合材料现在是常见的建筑材料，特别是在高科技应用中，因此了解其力学性能是很重要的。这个研究项目的目标是建立在复合材料力学性能的知识库上，特别强调它们的动态行为。

One source of difficulty for time dependent problems for composites is the presence of an additional length scale in the form of frequency or time of observation. The goal of this project is to obtain a cogent description of the response of composites to time-dependent loadings and to arrive at effective medium theories which give a macroscopic description of the response. In this phase of this continuing research, the emphasis will be on those cases where the interaction of the stress and displacement field in the composite with the boundary is expected to be strong. Of interest is the description of boundary layer-type phenomena, and their influence on the macroscopic behavior of the composite. The tools used will be a combination of asymptotic analysis, analytical methods for partial differential equations, and numerical experimentation. The eventual goal is to arrive at accurate and efficiently computable models of wave propagation in, and vibration of, composite structures. Composite materials are now commonplace building materials, especially in high-tech applications, therefore it is important to know their mechanical properties. The goal of this research project is to build on the knowledge-base on the mechanical properties of composites, with particular emphasis on their dynamic behavior.