Modeling and analysis of microtubules based on a modified couple stress theory

Based on a modified couple stress theory, a new Timoshenko beam model is established to address the size effect of microtubules (MTs) in this paper. The bending equation and the buckling equation are derived from the minimum total potential energy principle. Results obtained from the present model show that length dependence of MTs is related not only to shear effect but also to size effect, and the size effect is coupled in the shear effect, which means that the phenomenon of length dependence will disappear when the shear effect is neglected. Moreover, when very long MTs are considered, the persistence lengths are related to the internal material length scale parameter, which is different from the conclusions obtained from the classical and previous nonlocal beam models. The effect of the internal material length scale parameter on the buckling wavelength, the buckling growth rate and the buckling amplitude of the MTs is also discussed in this paper, and a comparison between present and previous results is presented.