Analysis of Gold Micro-Beams With Modified Strain Gradient Theory

Abstract

Micro-beams are building blocks for many micro-and nano-electro-mechanical systems (MEMS/NEMS) and cannot accurately be modeled by classical continuum theories due to significant size effects at the length scales associated with these structures. Size effects can be taken into account by the so-called higher-order continuum theories. In this study, Euler-Bernoulli microbeams are analyzed with the Modified Strain Gradient Theory (MSGT), which extends the classical local continuum theories of grade one with the introduction of three additional length scale parameters. In this contribution, finite element implementation is briefly demonstrated by using Galerkin discretization techniques for Euler-Bernoulli beams. The size effect for gold-micro beams is demonstrated and the length scale parameters of gold micro-beams for MSGT are identified from the existing experimental data from literature for the first time. As a novel aspect, significant size effect is demonstrated for the length-scales associated with the state of the art gold micro-beam structures developed for MEMS and NEMS applications, which reveals the necessity of the use of higher-order theories at these length scales.

Analysis of Gold Microbeams with Higher Order Continuum Theories

“…The length scale parameters yielding the minimum error for macroscopic elastic modulus of gold i.e. E=80 GPa are found as l 0 =3.60 µm for MSGT and l 2 =6.75 µm for MCST [5,6]. As the increment of length scale parameter variation is 0.05 µm in the analysis, the results are correct with an accuracy of ± 0.025 µm.…”

A Quasi 3D Modified Strain Gradient Formulation for Static Bending of Functionally Graded Micro beams Resting on Winkler-Pasternak Elastic Foundation

“…MSGT formulation has been gained more attention recently and has been widely employed by researchers. Dal [16] analyzed Euler-Bernoulli micro gold beams and demonstrated the accuracy of the results by comparing to the existing experiment tests. Ashoori and Mahmoodi [17] presented a geometric nonlinear formulation for analysis of thick plates.…”