Adaptive design and adaptive finite element verification of bifunctional layer-wise cloak metamaterials for thermal and electrical insulation

In this paper, a bifunctional metamaterial device with thermal and insulating functions is designed by utilizing the principles of transformational thermodynamics and transformational electrostatics in combination with the adaptive finite element method. Our main idea in designing this stealth material is to first derive the ideal stealth material parameters (typically represented as a function matrix) that vary with spatial position through the principles of transformation thermotics and transformation electrostatics. We recognize that there are significant differences in the rate of variation of these parameters in space. Based on the actual characteristics of the material parameters, we perform adaptive layered design according to the magnitude of their spatial variation rates. In regions where the parameters change drastically, finer layering is employed, while in areas with relatively gentle parameter variations, coarser layering is used. This method aims to enhance the manufacturability of stealth devices, enabling the design of dual-functional electrothermal stealth devices in a more efficient manner In order to verify the feasibility of this approach, an adaptive finite element method has been used to numerically simulate the proposed device. The numerical results validate the rationality of the adaptive layering design strategy proposed in this paper and suggest a reasonable scheme for the actual fabrication of the material.