On the Increase in Signal Depth due to High-Order Effects in Micro- and Nanosized Deformable Conductors

With regard to the transmission of a thermomechanical signal on extremely short temporal and spatial scales, which represents an issue particularly important dealing with micro- and nanosized electromechanical systems, it is well known that the so-called non-Fourier effects become not negligible. In addition, it has to be considered that the interaction among multiple energy carriers has, as a direct consequence, the involvement of high-order terms in the time-differential formulation of the dual-phase lag heat conduction constitutive equation linking the heat flux vector with the temperature variation gradient. Accepting that the deformations caused by the temperature variations are small enough to be modeled under the assumptions typical of the linear thermoelasticity, in the present article we take into account the highest Taylor expansion orders able to guarantee (under appropriate assumptions) stability conditions, thermodynamic consistency, and at the same time the existence of an influence domain of the external data linked to the energy transmission as thermal waves. To this aim, a cylindrical domain filled by an anisotropic and inhomogeneous thermoelastic material is investigated, although the results obtained will be independent from the considered geometry: for such a reason, we will be able to consider as illustrative examples some simulations referred to single-layer graphene and to show how the expansion orders selected strongly influence the domain of influence depth.