Considerable effort has been made to study the piezoelectric effect on the nanoscale, which serves as a physical basis for a wide range of smart nanodevices and nanoelectronics. This paper reviews recent progress in the research on the piezoelectric properties and electromechanical effects of piezoelectric nanomaterials (PNs). The review begins with an introduction to existing PNs which exhibit a diverse range of atomic structures and configurations. The nanoscale measurement of their effective piezoelectric coefficients (EPCs) is summarised with an emphasis on the major factors determining the piezoelectric properties of PNs. The paper concludes with a review of the electromechanical theories that are able to capture the small-scale effects on PNs, which include the surface piezoelectricity, flexoelectricity and Eringen's nonlocal theory. In contrast to the classical theories, two types of EPCs are defined, which were found to be size-dependent and loading condition-selective.

This paper discusses the fundamental issues of the elastic properties and effective wall thickness of single-walled carbon nanotubes (SWCNTs). It provides an in-depth analysis based on the rationale of the nanoscale-to-macroscale deformation relationship of SWCNTs and carries out a critical assessment of the diverse theoretical predictions in the literature. It was found that the in-plane stiffness of SWCNTs is a mechanics quantity that has been consistently reflected by the majority of the existing models. However, a further systematic study is necessary to clarify the dilemma of the wall thickness of SWCNTs.

This paper examines applicability and limitations of simplified models of elastic cylindrical shells for carbon nanotubes. The simplified models examined here include Donnell equations and simplified Flugge equations characterized by an uncoupled single equation for radial deflection. These simplified elastic shell equations are used to study static buckling and free vibration of carbon nanotubes, with detailed comparison to exact Flugge equations of cylindrical shells. It is shown that all three elastic shell models are in excellent agreement (with relative errors less than 5%) with recent molecular dynamics simulations for radial breathing vibration modes of carbon nanotubes, while reasonable agreements for various buckling problems have been reported previously for Donnell equations. For general cases of buckling and vibration, the results show that the simplified Flugge model, which retains mathematical simplicity of Donnell model, is consistently in better agreement with exact Flugge equations than Donnell model, and has a significantly enlarged range of applicability for carbon nanotubes. In particular, the simplified Flugge model is applicable for carbon nanotubes (with relative errors around 10% or less) in almost all cases of physical interest, including some important cases in which Donnell model results in much larger errors. These results are significant for further application of elastic shell models to carbon nanotubes because simplified shell models, characterized by a single uncoupled equation for radial deflection, are particularly useful for multiwall carbon nanotubes of large number of layers.

In view of the fact that microtubules exhibit strong anisotropic elastic properties, an orthotropic elastic shell model for microtubules is developed to study buckling behavior of microtubules. The predicted critical pressure is found to agree well with recent unexplained experimental data on pressure-induced buckling of microtubules [Needleman et al., Phys. Rev. Lett. 93, 198104 (2004); Biophys. J. 89, 3410 (2005)] which are lower than that predicted by the isotropic shell model by four orders of magnitude. General buckling behavior of microtubules under axial compression or radial pressure is studied. The results show that the isotropic shell model greatly overestimates the bucking loads of microtubules, except columnlike axially compressed buckling of long microtubules (of length-to-diameter ratio larger than, say, 150). In particular, the present results also offer a plausible explanation for the length dependency of flexibility of microtubules reported in the literature.