A Surface Energy Density-Based Theory of Nanoelastic Dynamics and Its Application in the Scattering of P-Wave by a Cylindrical Nanocavity

The scattering of elastic waves in nanoporous materials is inevitably influenced by the surface effect of nanopores. In order to investigate such a dynamic problem with surface effect of nanomaterials, a new theory of nanoelastic dynamics is proposed, in which both the effect of surface free energy and the effect of surface inertia force are included. With the new theory, a scattering of plane compressional waves (P-wave) by a cylindrical nanocavity is analyzed, and the corresponding dynamic stress concentration factor (DSCF) around the nanocavity is analytically solved. It is found that, when the size of cavity is at a nanoscale, the surface energy effect leads to a reduction of the maximum DSCF comparing with the classical counterpart without surface effect, while the surface inertial effect enlarges the maximum DSCF. The surface inertial effect gradually becomes dominant over the surface energy effect with an increasing incident wave frequency. Although both kinds of surface effects tend to vanish with an increasing cavity radius, the surface inertial effect can exist in a submicron-sized cavity if the wave frequency is sufficiently high. All these results should be of guiding value not only for an optimal design of porous structure possessing a better dynamic load bearing capacity but also for the non-destructive detection of nano-defects.