Size Effects on Mechanical Properties of Micro/Nano Structures

TL;DR

This paper reviews and compares five theories explaining size-dependent mechanical behavior in micro/nano structures, proposing a simplified combined model of Couple Stress and Surface Elasticity theories that accurately predicts nanoscale properties.

Contribution

It introduces a simplified two-parameter model combining CST and SET that fits experimental data and predicts size effects in M/NEMS structures.

Findings

The combined CST and SET model accurately fits experimental data.

The model provides a practical tool for predicting nanoscale mechanical properties.

Comparison of theories clarifies the origins of size effects in micro/nano systems.

Abstract

Experiments on Micro- and Nano-mechanical systems (M/NEMS) have shown that their behavior upon bending loads departs in many cases from the classical predictions using Euler-Bernoulli theory and Hooke law. This anomalous response has usually been seen as a dependence of the material properties with the size of the structure, in particular thickness. A theoretical model that allows for quantitative understanding and prediction of this size effect is important for the design of M/NEMS. In this paper, we summarize and analyze the five theories that can be found in the literature: Grain Boundary Theory (GBT), Surface Stress Theory (SST), Residual Stress Theory (RST), Couple Stress Theory (CST) and Surface Elasticity Theory (SET). By comparing these theories with experimental data we propose a simplified model combination of CST and SET that properly fits all considered cases, therefore delivering a simple (two parameters) model that can be used to predict the mechanical properties at the nanoscale.