A semianalytical approach for determining the nonclassical mechanical properties of materials

In this article, a semianalytical approach for demonstrating elastic waves' propagation in nanostructures has been presented based on the modified couple-stress theory including acceleration gradients (MCST-AG). Using the experimental results and atomic simulations, the static and dynamic length scales were calculated for several materials, zinc oxide (ZnO), silicon (Si), silicon carbide (SiC), indium antimonide (InSb), and diamond. To evaluate the predicted static and dynamic length scales as well as the presented model, the natural frequencies of a beam in addition to the phase velocity and group velocity of Si were studied and compared with the available static length scales, estimated using strain-gradient theory without considering acceleration gradients (SGT). These three criteria, natural frequency, phase velocity, and group velocity, show that the presented model is dynamically stable even for larger wavevector values. Furthermore, it is explained why the previous works, which all are based on the SGT, predicted very small values for the static length scale in the longitudinal direction comparing the static length scale in the transverse directions.