Abstract
Piezoelectric nanomaterials (PNs) are attractive for applications including sensing, actuating, energy harvesting, among others in nano-electro-mechanical-systems (NEMS) because of their excellent electromechanical coupling, mechanical and physical properties. However, the properties of PNs do not coincide with their bulk counterparts and depend on the particular size. A large amount of efforts have been devoted to studying the size-dependent properties of PNs by using experimental characterization, atomistic simulation and continuum mechanics modeling with the consideration of the scale features of the nanomaterials. This paper reviews the recent progresses and achievements in the research on the continuum mechanics modeling of the size-dependent mechanical and physical properties of PNs. We start from the fundamentals of the modified continuum mechanics models for PNs, including the theories of surface piezoelectricity, flexoelectricity and non-local piezoelectricity, with the introduction of the modified piezoelectric beam and plate models particularly for nanostructured piezoelectric materials with certain configurations. Then, we give a review on the investigation of the size-dependent properties of PNs by using the modified continuum mechanics models, such as the electromechanical coupling, bending, vibration, buckling, wave propagation and dynamic characteristics. Finally, analytical modeling and analysis of nanoscale actuators and energy harvesters based on piezoelectric nanostructures are presented.
Highlights
Piezoelectricity represents the capability of some materials to convert mechanical energy into electrical energy and vice versa
Strain gradient induced flexoelectricity, which is a more universal and diverse electromechanical coupling effect in comparison with piezoelectricity, is expected to contribute to the size-dependent properties of Piezoelectric nanomaterials (PNs) and explain the unusual ferroelectric properties of materials such as the unusual domain structure and domain wall observed at the nanoscale
In order to capture the size-dependent properties of nanomaterials, higher-order continuum mechanics theories such as polarization gradient theory [66], strain gradient theory [78], non-local theory [48], micropolar theory [79] and couple stress theory [80,81,82] have been employed in the literature
Summary
Piezoelectricity represents the capability of some materials to convert mechanical energy into electrical energy and vice versa. Strain gradient (or nonuniform deformation) induced flexoelectricity, which is a more universal and diverse electromechanical coupling effect in comparison with piezoelectricity, is expected to contribute to the size-dependent properties of PNs and explain the unusual ferroelectric properties of materials such as the unusual domain structure and domain wall observed at the nanoscale. With the consideration of surface effects or flexoelectricity, a number of modified continuum models have been established to explore the mechanical, physical, and electromechanical coupling properties of PNs. Extended from the non-local elasticity [48], a non-local piezoelectricity theory has been developed to analyze the mechanical behaviors of PNs. A review of these theories as well as the size-dependent electromechanical coupling, bending, vibration, buckling, wave propagation and dynamic characteristics of PNs are reviewed . The applications of nanostructured piezoelectric materials as actuators and energy harvesters will be discussed
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