A One-Dimensional Beam Model for Single-Wall Carbon Nano Tube Column Buckling

In this paper a one-dimensional continuum endowed with polynomial nonlinear hyperelastic constitutive functions is used in order to capture the necking and the Brazier effect arising in carbon nano tubes. In view of some preceding works by Antman and Podio-Guidugli this phenomena are seen as cases of bifurcation from a trivial nonlinear equilibrium path. The bifurcation analysis is performed by means of the asymptotic method. For a sample case, the bifurcation point and the eignemode are determined by solving a standard eigenvalue problem. The slopes of the trivial and the bifurcated equilibrium curves at the critical point are determined and also shown