Abstract
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.
Highlights
IntroductionDue to their small sizes, micro- and nano-mechanical systems (M/NEMS) hold tremendous promise for novel, versatile and very sensitive devices for different applications ranging from mass detection [1,2] to frequency synthesis [3,4,5,6], including bio- [7,8], force [9] and light detection [10,11]
Due to their small sizes, micro- and nano-mechanical systems (M/NEMS) hold tremendous promise for novel, versatile and very sensitive devices for different applications ranging from mass detection [1,2] to frequency synthesis [3,4,5,6], including bio- [7,8], force [9] and light detection [10,11].In addition to being incredibly sensitive, they show a very low power consumption, and a very small footprint, which is beneficial for miniaturization
In this paper we focus on the study of this alleged Young’s modulus size dependence, we first give an overview of the state of the art about experimental measurement of the Young’s modulus, we present the typical theories used to explain this size effect and we apply them to the selected cases from the literature, concluding that none of the theories alone can predict the size dependence for all samples
Summary
Due to their small sizes, micro- and nano-mechanical systems (M/NEMS) hold tremendous promise for novel, versatile and very sensitive devices for different applications ranging from mass detection [1,2] to frequency synthesis [3,4,5,6], including bio- [7,8], force [9] and light detection [10,11]. Among the different properties that arise when reducing the size of the any device we can find changes in resistivity [16,17], magnetic frustration [18], thermal conductivity [19], and mechanical properties This latter case includes anomalous behavior of nonlinear response [20] and the quality factor [21], the appearance of nonlinear damping [22], and the variation of the Young’s modulus. At the micro/nanoscale researchers have observed that the behavior of mechanical structures cannot be explained using macroscopic theory and a constant value of the Young’s modulus It is different from the bulk value, but it is size-dependent in most cases. We propose a combined model which considers the residual stress in the material, the microstructure of the bulk and the surface properties of M/NEMS
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