In this paper a one-dimensional continuum endowed with polynomial nonlinear hyperelastic constitutive functions is used in order to capture the necking and the kinking arising in carbon nanotubes. In view of some preceding works by Antman and Podio-Guidugli these 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 eigenmode are determined by solving a standard eigenvalue problem. The slopes of the trivial and the bifurcated equilibrium curves at the critical point are also determined and shown.
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