Journal
SENSORS
Volume 15, Issue 11, Pages 28543-28562Publisher
MDPI
DOI: 10.3390/s151128543
Keywords
size effect; Young's modulus; residual stress; couple stress; grain boundary; surface elasticity; surface stress; length scale parameter
Funding
- Swiss National Science Foundation [PP00P2-144695]
- European Commission [PCIG14-GA-2013-631801]
- Swiss National Science Foundation (SNF) [PP00P2_144695] Funding Source: Swiss National Science Foundation (SNF)
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Experiments on micro- and nano-mechanical systems (M/NEMS) have shown that their behavior under bending loads departs in many cases from the classical predictions using Euler-Bernoulli theory and Hooke's law. This anomalous response has usually been seen as a dependence of the material properties on 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.
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