Dual-function thermoelastic cloak based on coordinate transformation theory

Abstract

• Transformation theory is extended to thermoelastic framework for dual-function cloak design. • Two transformation schemes with asymmetric or symmetric elastic tensors are given. • Invisibility of different cloaks is validated by FEM and observed in both temperature and displacement fields. In past years, various cloaks have attracted the attention of many scientists but they usually remain confined to a single function. Cloaks combining multiple functions, however, are desirable. In this paper, we design thermoelastic cloaks with dual functionality by the coordinate transformation technique. The transformation of the thermoelastic wave equations for cloaking and explicit expressions for the required material parameters are established. Symmetrization of the elastic tensor is applied using Norris’ gauge matrix to emphasize the feasibility of the designs. Two different operating conditions, transient elastic wave propagation and steady heat transfer, are adopted in numerical calculations for the designed cloaks. It is shown that, on one hand, from the perspective of observer, whether the cloak is symmetrized or not, its external response is identical and invisibility is reliable. On the other hand, it is destined that the symmetrization of the cloak would be accompanied by the increase of internal displacement, which may need to be paid attention to in the actual design. In addition, the temperature effects of both cloaks are consistent. The work in this paper may pave a way toward the realization of thermoelastic cloaks, thus broadening the research scope for metamaterials.