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Analytical solutions for the elastic properties of a variety of binary nanotubes with arbitrary chirality are obtained through the study of systematic molecular mechanics. This molecular mechanics model is first extended to chiral binary nanotubes by introducing an additional out-of-plane inversion term into the so-called stick-spiral model, which results from the polar bonds and the buckling of binary graphitic crystals. The closed-form expressions for the longitudinal and circumferential Young’s modulus and Poisson’s ratio of chiral binary nanotubes are derived as functions of the tube diameter. The obtained inversion force constants are negative for all types of binary nanotubes, and the predicted tube stiffness is lower than that by the former stick-spiral model without consideration of the inversion term, reflecting the softening effect of the buckling on the elastic properties of binary nanotubes. The obtained properties are shown to be comparable to available density functional theory calculated results and to be chirality and size sensitive. The developed model and explicit solutions provide a systematic understanding of the mechanical performance of binary nanotubes consisting of III–V and II–VI group elements.

We report on a first-principles study of a novel band modulation in zigzag double-walled boron nitride nanotubes (DBNNTs) by applying radial strain and coupled external electric field. We show that the band alignment between the inner and outer walls of the DBNNTs can be tuned from type I to type II with increasing radial strain, accompanied with a direct to indirect band gap transition and a substantial gap reduction. The band gap can be further significantly reduced by applying a transverse electric field. The coupling of electric field with the radial strain makes the field-induced gap reduction being anisotropic and more remarkable than that in undeformed DBNNTs. In particular, the gap variation induced by electric field perpendicular to the radial strain is the most remarkable among all the modulations. These tunable properties by electromechanical coupling in DBNNTs will greatly enrich their versatile applications in future nanoelectronics.

Through detailed three-dimensional (3D) finite ele- ment (FE) calculations, the out-of-plane constraints Tz along embedded center-elliptical cracks in mode I elastic plates are studied. The distributions of Tz are obtained near the crack front with aspect ratios (a/c) of 0.2, 0.4, 0.5, 0.6, 0.8 and 1.0. Tz decreases from an approximate value of Poisson ratio ν at the crack tip to zero with increasing normalized radial distances (r/a) in the normal plane of the crack front line, and increases gradually when the elliptical parameter angle φ changes from 0 ◦ to 90 ◦ at the same r/a. With a/c rising to 1.0, Tz is getting nearly independent of φ and is only related to r/a. Based on the present FE calculations for Tz, empirical formulas for Tz are obtained to describe the 3D distribution of Tz for embedded center-elliptical cracks using the least squares method in the range of 0.2 ≤ a/c ≤ 1.0. These Tz results together with the corresponding stress intensity fac- tor K are well suitable for the analysis of the 3D embedded center-elliptical crack front field, and a two-parameter K -Tz principle is proposed.