Premium
Analysis of Gold Microbeams with Higher Order Continuum Theories
Author(s) -
Kandaz Murat,
Dal Hüsnü,
Ünlü Mehmet
Publication year - 2017
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201710180
Subject(s) - microbeam , length scale , microelectromechanical systems , continuum mechanics , timoshenko beam theory , elasticity (physics) , continuum hypothesis , finite element method , classical mechanics , beam (structure) , bernoulli's principle , physics , theoretical physics , statistical physics , mechanics , optics , quantum mechanics , thermodynamics
Microbeams are building blocks for many microstructures as well as microelectromechanical systems (MEMS) and cannot accurately be modelled by classical continuum theories due to size effects based on their micro‐scale. These size effects can be taken into account by the so‐called higher order continuum theories. Modified Strain Gradient Theory (MSGT) and Modified Couple Stress Theory (MCST) are two commonly used theories, which extend the classical local continuum theories of grade one with the introduction of additional length scale parameters. In this contribution, the variational problem governing the elasticity of higher order beam formulation and the finite element implementation based upon, are briefly introduced. To this end, well known Euler‐Bernoulli beam formulation assumptions are used. The size effect for gold‐micro beams is demonstrated and the length scale parameters of gold microbeams for MSGT and MCST 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 microbeam structures developed for MEMS applications, which reveals the necessity of the use of higher order theories at these length scales. Advantages and drawbacks of these theories are also identified. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)