A conductive device to form electrical connections on the surface of a structure made of composite material. The device includes a thin interface layer having a face via which the device is fixed to the surface of the structure made of composite material. A conductive metal element is placed on the face of the interface layer opposite the face making contact with the surface of the structure. The conductive element is configured to be able to undergo tensile and compressive stresses without damage. A protective layer is configured to protect the conductive element from attack from the environment surrounding the structure. These various elements are arranged relative to one another such that the length of the conductive element can vary as a function of temperature variations independently of the amplitude of the variations undergone by the structure on which the device is mounted.