Modified Continuum Mechanics Modeling on Size-Dependent Properties of Piezoelectric Nanomaterials: A Review

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.

Local gradient Bernoulli–Euler beam model for dielectrics: effect of local mass displacement on coupled fields

“…Equations (20) and (21), along with the boundary and jump conditions (22), constitute the stationary boundary-value problems for linear local gradient electroelasticity. Note that the proposed variational approach can be the theoretical basis for numerical studies of surface and size effects in dielectric bodies with complex shapes.…”

“…It is worth remarking that the theory of dielectrics with the electric field gradient is equivalent to the theory of dielectric media with electric quadrupoles proposed by Kafadar [18]. Trends in the development of the mentioned higher-grade theories of dielectrics are highlighted in review papers [19][20][21] and books [13,22,23]. Note that non-classical theories have found various applications in plasticity [2] and electro-thermo-elasticity [24], as well as in mechanics of nano-sized elastic solids [25,26] and other structures [27].…”

Multi-phase-field method for surface tension induced elasticity

“…Recalling the definition of the free energy functional F , and the elastic and interface free energy densities, Eqs. (9) and (11), one obtains from Eq. (13b) at mechanical equilibrium,…”

Strain-Gradient Bar-Elastic Substrate Model with Surface-Energy Effect: Virtual-Force Approach

“…Their superior mechanical properties have attracted a wide spectrum of novel applications in modern science and technology [ 1 ]. Examples of novel devices employing small-sized structures are biosensors [ 2 ], piezoelectric actuators [ 3 ], nanosensors [ 4 ], and gyroscopes [ 5 ]. Profound understanding and characterizing mechanical properties of small-sized structures are critical to rational design procedure and performance assessment of these devices during their service life.…”