Biphysical undetectable concentrators manipulating both heat flux and direct current via topology optimization.

Recent remarkable developments in metamaterials and metadevices manipulating diffusive processes, such as thermal and electrical conduction, have enabled the control of multiple phenomena and the development of multifunctional devices. However, only either multiphysics operations or multiple functionalities are usually implemented on single metadevices. In this paper, we describe a method for the optimal design of metadevices that achieves both cloaking and focusing in the control of both heat flux and direct current by a single device, i.e., biphysical-bifunctional metadevices having four capabilities. Our design scheme performs well in terms of providing cloaking and focusing bifunctionality. Additionally, it assumes bulk natural materials without the use of metamaterials, which improves the manufacturability of the designed metadevices. Moreover, multidirectional metad evices are optimally designed for thermal-electrical conductions transmitted from multiple directions or from heat and voltage sources at various locations.