dc electric cloak concentrator via topology optimization

We succeeded in simultaneously cloaking and concentrating direct current in a conducting material through topology optimization based on a level-set method. To design structures that perform these functions simultaneously, optimal topology is explored for improving two objective functions that govern separately the cloaking and concentration of current. Our design scheme, i.e., the topology optimization of a direct-current electric cloak concentrator, provides this bifunctionality well despite simple, common bulk materials being used to make up the structures. The materials also rigorously obey the electric conduction equation in contrast to the approximated artificial materials, so-called metamaterials, of other design schemes. The structural features needed for this simultaneous bifunctionality are found by adopting level-set method to generate material domains and clear structural interfaces. Furthermore, robust performances of the bifunctional structures against fluctuations in electrical conductivity was achieved by improving the fitness incorporating multiple objective functions. Additionally, the influence of the size of the current-concentrating domain on the performances of the optimal configuration is investigated.