Analysis of Gold Microbeams with Higher Order Continuum Theories

Kandaz, Murat
Dal, Hüsnü
Ünlü, Mehmet
Microbeams are building blocks for many micro and nanostructures as well as microelectromechanical systems (MEMS) and cannot accurately be modelled by classical continuum theories due to size effects due to 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 micro-beams 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 micro-beam structures developed for NEMS and 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 discussed comparatively
Citation Formats
M. Kandaz, H. Dal, and M. Ünlü, “Analysis of Gold Microbeams with Higher Order Continuum Theories,” presented at the 88th Annual Meeting of the International Association of Applied Mathematics and Mechanics (6 - 10 Mart 2017), Weimar, Almanya, 2017, Accessed: 00, 2021. [Online]. Available: