Simultaneous Thermal and Electrical Cloaking Via Level-Set-Based Topology Optimization With Isotropic Materials

Abstract Cloaks are devices designed to conceal objects from detection. With the advancement of metamaterials, there is an increasing interest in developing multi-functional cloaks rather than single-functional ones to cater to various application scenarios. This paper proposes to design simultaneous thermal and electrical cloaking devices via a level-set-based shape and topology optimization scheme. Unlike popular methods such as coordinate transformation and scattering cancellation, which are vulnerable to high material anisotropy, the proposed method only employs naturally occurring bulk materials, which can greatly facilitate physical realization. The bifunctional cloak is achieved by reproducing the reference temperature and electrical potential fields in the evaluation domain through the optimal layout of two thermally and electrically conductive materials in the design domain. Due to the clear boundary characteristic of the level-set formulation, no filtering schemes are required to render a “0-1” design as opposed to density-based counterparts. The feasibility and validity of the proposed method are demonstrated through a number of numerical examples with parallel or orthogonal inflow direction combinations. The dependency of the optimization results on the initial designs is also briefly investigated. Despite exhibiting a notable reliance on the initial guesses, the objective functions based on least square error are sufficiently small to be considered an effective cloak. This work has the potential to spark broader exploration into meta-devices carrying multiple functionalities.