Study on the size dependent effective Young modulus by EPI method based on modified couple stress theory

Various experimental and theoretical researches have been shown the size-dependence behavior of the effective Young modulus (EYM) in the micron and sub-micron scales. One of the most accurate methods is the electrostatic pull-in instability (EPI) method that is based on the bending of the classical beam under the electrostatic force. In this paper, the modified couple stress theory (MCST) is employed to calculate the EYM of silicon nanocantilevers. The MCST compensates the inability of the classical continuum mechanic to predicting the size-dependent behavior of the nano-scale structures. Next, as a case study the EYM of silicon nanocantilevers have been calculated and results compared with classical EPI. The governing equation is solved by the Galerkin method and obtained results show significant size-dependent behavior in the EYM. From the other hand, a new value for the material length scale parameter is introduced based on the dimension of the crystal or grain size of the material.