ANALYSIS OF GOLD MICRO-BEAMS WITH MODIFIED STRAIN GRADIENT THEORY

Year 2017, Volume: 18 Issue: 3, 663 - 681, 30.09.2017

Hüsnü Dal

https://doi.org/10.18038/aubtda.273867

Abstract

Micro-beams are building blocks
for many micro- and nano-structures as well as
micro-electro-mechanical systems (MEMS) 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 micro-beams 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
form 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 NEMS and MEMS applications, which reveals
the necessity of the use of higher order theories at these length
scales.

Keywords

gold micro-beams, modified strain gradient theory, higher order elasticity, size effect, MEMS devices

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