A comparative study of modified strain gradient theory and modified couple stress theory for gold microbeams

Abstract

Microbeams are common structures encountered in micro- and nano-electromechanical systems. Their mechanical response cannot be modelled by local theories of continuum mechanics due to size effect, which becomes more pronounced as the structural length scale approaches the microstructural length scale. The size effect can be circumvented by higher-order continuum theories. In this study, Euler–Bernoulli microbeams are analysed with modified strain gradient theory (MSGT) and modified couple stress theory (MCST). The weak forms for the numerical implementation are obtained by using variational methods. Then, the set of algebraic equations for the finite element method are derived. As a novel aspect, the performance of MSGT and MCST is compared and the length scale parameters of these theories are identified for gold microbeams from the existing experimental results in the literature. With the help of the identified parameters, the cut-off point for the applicability of the classical beam theories for gold microbeams is assessed. The study suggests use of higher-order theories for the state-of-the-art gold microbeam structures having thickness $$t<30\,\upmu {\hbox {m}}$$ .