Hawaii Pacific University, USA
Dr. Lee’s major research interest is mathematical modeling in practical problems, broadly encompassed in Solid Mechanics, Acoustics and Fluid Dynamics. In the topic of Solid Mechanics, a classical theory, Hashin-Shtrikman variational principle, and its reformulations are applied to various heterogeneous particulate composites, such as rocket propellants, granular media etc., that are from either computer simulation or micro-tomographic images. Optimized numerical tools have been developed to capture better morphological information of the materials. The current material of interest is Liquid Crystal Elastomer (LCE). In the research topic of Acoustics, the source of aircraft noise in turbulent flow region near the nozzle tip was identified based on the underlying physics of sound generation mechanism. It possibly brings a better understanding of noise control devices when the study is applied to different nozzle configurations. In Fluid Dynamics, Rayleigh-Taylor instability which occurs when a dense, heavy fluid is accelerated by a light fluid, penetrating into the other, followed by the development of a complex mixing layer, was studied. Closure models of averaged interfacial quantities were proposed and validated based on direct numerical simulations.
Generalized Hashin-Shtrikman variational principle with di_erent order of statistics is used to compute a rigorous approximation on the macroscopic e_ective elastic moduli for composite materials with di_erent internal structures. For this purpose, the statisti- cal and morphological features of the material are directly extracted from simulated or tomographic images and applied to the model. An interesting application with Liquid Crystal Elastomer (LCE) network composites will be introduced by coupling the model with piezoelectricity.