Topology Optimization of Anisotropic Elastic Metamaterials for Anomalous Reflection and Mode Converting

Abstract

Metamaterials are artificially engineered materials for realizing material properties that do not exist in nature. They are being used in various disciplines, but in this study, we are mainly concerned with the design of metamaterials for tailoring wave characteristics. Wave characteristics are affected by the shape of the unit cell of the metamaterial, the size of which is smaller than the wavelength of interest. By elaborately designing the shape and arrangement of the heterogeneous body constituting the unit cell, unique material properties, such as negative, zero, and infinite material properties can be obtained. Recently, there have been studies to systematically design a metamaterial unit cell by topology optimization. In this study, we propose a topology optimization formulation to design anisotropic metamaterials. This technique can effectively design the desired metamaterial microstructure for specific tailoring of wave characteristics without any baseline design.<br/> The specific design problems considered in this work are a mode converter for converting a longitudinal wave into a transverse wave and a metasurface for reflecting a vertically incident elastic wave into various reflection angles by controlling a wavefront. To design and evaluate the performance of each metamaterial, specific wave characteristics are unitized