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A one-dimensional continuum with microstructure for single-wall carbon nanotubes bifurcation analysis. (English) Zbl 1332.74007
Summary: 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 S. S. Antman [Nonlinear problems of elasticity. 2nd, revised and extended ed. New York, NY: Springer (2005; Zbl 1098.74001)] and P. Podio-Guidugli [J. Elasticity 12, 3–17 (1982; Zbl 0491.73050)] 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.

MSC:
74B20 Nonlinear elasticity
74M25 Micromechanics of solids
74H60 Dynamical bifurcation of solutions to dynamical problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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