Classical Piezoelectric Theory Research Articles

Size-dependent electromechanical responses of a bilayer piezoelectric microbeam

On the basis of the couple stress piezoelectric theory including flexoelectric effects, a size-dependent model of a bilayer microbeam consisting of a piezoelectric material layer and an elastic layer has been established. The governing equations along with the boundary conditions of the microbeam model have been obtained from variation principle. The microbeam bending problems have been solved to analyse the electromechanical coupling responses to the applied concentrated force and voltage. Numerical results show that whether under the concentrated force or the voltage, the influence of flexoelectric effects on the equivalent piezoelectric response is larger than that of rotation gradient elastic effects when the size of the microbeam is much larger than the material length scale parameters. However, with the continuous decrease of the beam characteristic size scale, rotation gradient elastic effects have a stronger impact on the electromechanical responses than flexoelectric effects, which leads to a rapid decrease of the equivalent piezoelectric responses. The result also shows that the contribution of flexoelectric effects on the equivalent piezoelectric response increases when the beam size diminishes, which leads to a significant surge of the electromechanical responses compared to the model under the classical piezoelectric theory.

The direct piezoelectric effect in the globular protein lysozyme

Here, we present experimental evidence of the direct piezoelectric effect in the globular protein, lysozyme. Piezoelectric materials are employed in many actuating and sensing applications because they can convert mechanical energy into electrical energy and vice versa. Although originally studied in inorganic materials, several biological materials including amino acids and bone, also exhibit piezoelectricity. The exact mechanisms supporting biological piezoelectricity are not known, nor is it known whether biological piezoelectricity conforms strictly to the criteria of classical piezoelectricity. The observation of piezoelectricity in protein crystals presented here links biological piezoelectricity with the classical theory of piezoelectricity. We quantify the direct piezoelectric effect in monoclinic and tetragonal aggregate films of lysozyme using conventional techniques based on the Berlincourt Method. The largest piezoelectric effect measured in a crystalline aggregate film of lysozyme was approximately 6.5 pC N−1. These findings raise fundamental questions as to the possible physiological significance of piezoelectricity in lysozyme and the potential for technical applications.

A description of piezoelectric effect in non‐polar materials taking into account the quadrupole moments

A method of the description of piezoelectric effect in non‐polar materials is suggested. This method is based on the model of unit cell possessing a non‐zero quadrupole moment and the zero dipole moment. The suggested theory contains several additional material tensors. A comparison of the suggested theory with the classical theory of piezoelectricity is carried out. The structure of the additional material tensors is determined for the crystal lattice with the hexagonal crystal symmetry of quartz. An analysis of dispersion relations is carried out. This analysis reveals that the quadrupole moment tensor has a qualitative influence on the behavior of solution. Namely, the quadrupole moments cause rather the redistribution of energy between the waves of different type than the wave damping. A method of determination of the additional material moduli is suggested. The method consists in using the dispersion relations containing the unknown material moduli and the experimental data on attenuation factor versus frequency.

Size-dependent piezoelectricity: A 2D finite element formulation for electric field-mean curvature coupling in dielectrics

The classical theory of piezoelectricity defines linear size-independent electromechanical response in non-centrosymmetric dielectrics that involves coupling between the electric field and the mechanical strains. However, with the continuing push to develop novel micro- and nano-scale materials, structures and devices, there is a need to refine and explore size-dependent electro-mechanical coupling phenomena, which have been observed in experiments on centrosymmetric dielectrics. Here a finite element variational formulation is developed based upon a recent consistent size-dependent theory that incorporates the interactions between the electric field and the mechanical mean curvatures in dielectrics, including those with centrosymmetric structure. The underlying formulation is theoretically consistent in several important aspects. In particular, the electric field equations are consistent with Maxwell's equations, while the mechanical field equations are based upon the recent consistent couple stress theory, involving skew-symmetric mean curvature and couple stress tensors . This, in turn, permits the development of a fully-consistent finite element method for the solution of size-dependent piezoelectric boundary value problems. In this paper, an overview of size-dependent piezoelectricity is first provided, followed by the development of the variational formulation and finite element representation specialized for the planar response of centrosymmetric cubic and isotropic materials. The new formulation is then applied to several illustrative examples to bring out important characteristics predicted by this consistent size-dependent piezoelectric theory. • We develop a finite element method for consistent size-dependent piezoelectricity. • Our formulation is based on skew-symmetric mean curvature and couple stress tensors. • Unlike existing formulations, our theory is consistent with Maxwell's equations. • We employ Lagrange multipliers to impose displacement-rotation compatibility. • We solve several illustrative problems to reveal key characteristics of the theory.

Piezoeffect in polar materials using moment theory

A method for describing the piezoelectric effect in a polar material is proposed based on the use of a composite particle model with seven degrees of freedom and a nonzero dipole moment. Based on micropolar theory, a system of equations is obtained which differs from the classical theory of piezoelectricity in the presence of additional terms. It is shown that under certain assumptions, the proposed system of equations becomes the classical system but the piezoelectric moduli depend strongly on the spontaneous polarization vector. It is shown that for anisotropic media with different symmetries, the structure of the third-rank piezoelectric tensors obtained using the proposed micropolar theory coincides with the structure of the tensors obtained using classical theory. For the media considered, dispersion relations are given and it is shown that in the proposed theory, unlike classical theory, the piezoelectric moduli are proportional to the spontaneous polarization.

Oscillations of a layer of a crystal with cubic symmetry under the action of harmonic electric field

The linearized relations of the local gradient theory of nonferromagnetic dielectrics are used for the description of the mechanical vibrations of an infinite layer in a crystal with cubic symmetry that are induced by a time-dependent electric field. It is shown that, contrary to the classical linear theory of piezoelectricity, the local gradient theory describes the piezoelectric effect in highly symmetric crystals. When local mass displacements are taken into account, short waves become dispersive, which does not follow from the linear classical theory of piezoelectricity. The obtained results are compared with previously published results, which are based on Mindlin’s gradient theory of dielectrics. Some model parameters are evaluated.

Effect of flexoelectricity on electrostatic potential in a bent piezoelectric nanowire

Flexoelectricity presents a strong size effect, and should not be ignored for nanodevices. By taking the flexoelectricity into account, an analytical solution is deduced for the piezoelectric potential generated in a bent ZnO nanowire (NW) cantilever. It is shown that the electric potential in the NW is not independent of z-coordinate, which is different from the results based on the classical piezoelectric theory. The results also show that the effect of flexoelectricity on the voltage is significant in a bent ZnO NW even though the flexoelectric coefficients are set to be the minimum. Moreover, we find that the flexoelectricity plays an important role in filling the gap between the results from the classical piezoelectric theory and experimental results. It is indicated that one can use the flexoelectricity to modify the transfer efficiency from mechanical energy to electrical energy through strain engineering.

An investigation of the tertiary coupling effect under the longitudinal mode of a piezoelectric crystal

In this article, multiple piezoelectric effects are investigated on the basis of the classical piezoelectric theory. The objective reality of multiple piezoelectric effects is elucidated from theoretical analysis first. Based on four kinds of piezoelectric equations, the relationship between the generation of multiple piezoelectric effects and boundary conditions is analysed, the process of their generation is elaborated, and the formulae of the tertiary piezoelectric effect are deduced. Then, the experimental results of the tertiary coupling effect are obtained under the longitudinal mode of a PZT-5 stack by the methods that are equivalent to changing boundary conditions. Experimental data show that the output of the tertiary direct and converse piezoelectric effect is also linear with the applied force and voltage, respectively. However, the output directions are opposite to that of the primary piezoelectric effect. The theoretical analysis is justified by experimental results and the experimental methods presented are proved to be scientific and feasible. Moreover, the influence of the tertiary piezoelectric effect on the piezoelectric coefficient and the performance of sensors and actuators is further analysed. The study of multiple piezoelectric effects provides a new method for the improvement of the performance of piezoelectric sensors and actuators.

A Review of a Few Topics in Piezoelectricity

This is a review article on a few special topics in piezoelectricity: gradient and nonlocal theories, fully dynamic theory with Maxwell equations, piezoelectric semiconductors, and motions of rotating piezoelectric bodies. They all require some extension of the classical theory of piezoelectricity. They are relatively new, more advanced, and growing subjects with applications or potential applications in various electromechanical devices. The article contains 209 references. (In memory of Raymond D. Mindlin (1906–1987)).

A linearized theory of elastic dielectrics which couples electrically to flexural vibrations

Assuming that the free energy depends on the deformation gradient and the spatial electric field, we derive the expressions for the Cauchy stress tensor and the spatial electric displacement from an observer invariant quadratic form of the free energy via the strict definitions of these quantities. Specific forms of the Piola-Kirchhoff stress tensor and the material electric displacement are then deduced and linearized in a particular sense. As an application of the resulting theory, we formulate the problem of an electrically driven disc within the context of the classical bending theory of thin plates. The material of the disc is assumed to have at most the symmetry of a hexagonal system of classC6v.The resulting coupled differential equations for the axial mechanical displacement of the middle surface and the material electric potential indicate that the problem is not empty. This result is of particular interest in view of the fact that it is generally held that the classical theory of piezoelectricity does not permit such couplings to occur.

Electrical effects in bone

This paper presents a review of the work carried out on the electromechanical properties of bone over the the past three decades. Research in this field has established the piezoelectric nature of bone and identified collagen as the generating source in dry bone. Some of the characteristics of the strain generated potential (SGP) signal from dry and hydrated bone were found to be unaccountable in terms of a classical piezoelectric theory. Modifications of the theory were suggested and in the case of fully hydrated bone, a new mechanism (streaming potential) has emerged. The paper also reports on recent developments in the field and presents results from microstructural (osteonic) studies and from fluid-filled bone. The review indicates the need for actual in vivo work because most of the reported data were obtained, in the last decade, from in vitro work and were considered valid in vivo. Modelling of the mechanism which produces the SGP has been considered to explain the characteristics of these potentials. A representative model recently developed by the present authors and co-workers is reported. This model relates the generated potential to reorientation of spontaneous dipoles and differentiates between the generated and recorded signal, thus identifying effects from the measuring circuitry. The clinical aspects of electricity of bone in assisting fracture healing and the different techniques employed are mentioned briefly. Emphasis on new techniques of piezoelectric implants and their future development is also reported.

The distribution of induced electrical activity in bent long bone.

Abstract An analytical model based on classical piezoelectric theory was used to related electrical effects to the stress-state in a bone cross-section for simple bending of a cylindrical bone shaft. The results demonstrate that the overall polarities of the polarization volume charge and the induced electrical potential compare favorably with available experimental findings. Both the polarization charge and the induced electrical potential are shown to be highly sensitive to the angle between the material and bone axes between 0 and 10 degrees. A reduction of the bone cross-sectional area results in a higher magnitude in the polarization charges and the induced electrical potential at all points in a cross-section. No appreciable difference in the predicted electrical effects is observed for the use of two relevant piezoelectric d -matrixes.

Polarization gradient in elastic dielectrics

By inclusion of the polarization gradient in the stored energy function of elastic dielectrics, the classical theory of piezoelectricity is extended to accommodate an electro-mechanical interaction in centrosymmetric (including isotropic) materials and a surface energy of deformation and polarization.