Design of elastic metamaterials via topology optimization

Abstract

Artificially structured materials, known as metamaterials, have been widely explored for manipulating waves thanks to their unconventional properties beyond those found in natural materials. Unlike natural materials whose properties are determined by their chemical constituents, the physical properties of metamaterials depend largely on the internal structures of their building blocks, and thus by designing the internal structures, various properties/functionalities can be achieved. In the past two decades, many designs have been proposed, resulting in a range of materials with a variety of exotic properties, for example, negative refraction, super-resolution imaging, etc. However for practical applications, in addition to the desired properties, various design requirements and constraints such as broadband performance, robustness, multiple functionalities and tunability are needed. The conventional physical-guided design approach often leads to suboptimal solutions for design problems with multiple requirements. This thesis work aims to develop inverse design approaches based on topology optimization for systematic design of elastic metamaterials with multiple design objectives. A set of novel elastic metamaterials/metasurfaces with robust performance and multi-functionalities has been designed and verified numerically and/or experimentally. Firstly, a two-step topology optimization scheme is proposed for dispersion engineering of hyperbolic elastic metamaterials over a broad frequency range. The scheme is formulated based on the physical nature of the hyperbolic dispersion and is solved by a typical gradient optimizer. By manipulating the dispersion band structure, non-resonant hyperbolic metamaterials have been successfully designed. Novel features/applications such as negative refraction, wave partial focusing and super-resolution imaging have been numerically demonstrated. The optimized designs outperform the traditional designs in terms of working frequency bandwidth. Furthermore, polarization-dependent transmission has been found in the designed metamaterial, which is a unique feature due to the optimization scheme developed. The proposed two-step scheme is also applicable for general dispersion engineering of metamaterials. Secondly, a general design framework based on topology optimization is proposed for the design of elastic metasurfaces with multiple requirements/functionalities. The proposed design framework has been applied to design elastic metasurfaces with high-energy transmission and robust performance. Multifunctional metasurfaces that can simultaneously control longitudinal and shear wave have been designed and realized for the first time. Furthermore, multi-frequency metasurfaces that can realize different wave manipulation at different wave frequencies have also been designed. Such metasurfaces can serve as tunable materials that can switch wave control mode simply by changing operation frequencies. Compared with the existing tunable metamaterials, our metasurfaces are passive and do not need any control/actuation schemes, and thus are much easy to implement. Another application of the designed multi-frequency metasurfaces is to use them as demultiplexers, which is useful in a range of practical applications such as structural health monitoring and vibration control.

Date of Award	2019
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology