Nonlocal Euler-Bernoulli beam theories with material nonlinearity and their application to single-walled carbon nanotubes

Abstract Although the small-scale effect and the material nonlinearity significantly impact the mechanical properties of nanobeams, their combined effects have not attracted researchers’ attention. In the present paper, we propose two new nonlinear nonlocal Euler-Bernoulli theories to model nanobeam’s mechanical properties corresponding to extensible or inextensible locus. Two new theories consider the material nonlinearity and the small-scale effect induced by the nonlocal effect. The new models are used to analyze the static bending and the forced vibration for single-walled carbon nanotubes (SWCNTs). The results indicate that the material nonlinearity and the nonlocal effect significantly impact SWCNT’s mechanical properties. Therefore, neglecting the two factors may cause qualitative mistakes.