# A semianalytical approach for determining the nonclassical mechanical properties of materials

## TL;DR

This paper introduces a semianalytical model incorporating acceleration gradients to determine nonclassical elastic properties of nanostructures, validated through experimental data and atomic simulations across various materials.

## Contribution

It presents a novel semianalytical approach that includes acceleration gradients in the modified couple-stress theory for better prediction of elastic wave behavior in nanomaterials.

## Key findings

- Model accurately predicts natural frequencies and wave velocities.
- Static and dynamic length scales are validated against experimental data.
- Model shows stability for larger wavevector values.

## Abstract

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. 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. 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 strain-gradient theory without acceleration gradients, predicted very small values for the static length scale in the longitudinal direction rather than the static length scale in the transverse directions.

---
Source: https://tomesphere.com/paper/1706.06559