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

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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.