gping Shen

Fracture of piezoelectric materials: energy density criterion

Abstract In this paper, the concept of energy density factor S for piezoelectric materials is presented. In addition to the mechanical energy the electrical energy is included as well. The direction of crack initiation is assumed to occur when Smin reaches a critical value Scr that can be used as an intrinsic materials parameter and is independent of the crack geometry and loading. The result agrees with empirical evidence qualitatively and explains rationally the effect of applied electric field on fracture strength: positive electric fields decrease the apparent fracture toughness of piezoelectric materials while negative electric fields increase it.

Interface crack in Bi-piezothermoelastic media and the interaction with a point heat source

Abstract Using the extended version of Eshelby-Strohs formulation and the method of analytical continuation, the problems of interface cracks are reduced to a Hilbert problem of vector form. A general explicit closed form solution for piezothermoelastic interface crack problem is then obtained, the whole field solutions of temperature, heat flux, displacements, electric field, stress and electric induction are given, the explicit expressions for the crack opening displacements and electric potential are also provided. A solution is obtained for the interaction problem between the interface cracks and a point heat source.

The basis of meshless domain discretization: the meshless local Petrov–Galerkin (MLPG) method

Abstract The MLPG method is the general basis for several variations of meshless methods presented in recent literature. The interrelation of the various meshless approaches is presented in this paper. Several variations of the meshless interpolation schemes are reviewed also. Recent developments and applications of the MLPG methods are surveyed.

Effects of surface and flexoelectricity on a piezoelectric nanobeam

The effects of surface and flexoelectricity have been found in the presence of strong size dependence and should be technically taken into account for nano-scaled dielectric structures. This paper proposes a Bernoulli–Euler beam model to investigate the electromechanical coupling response of piezoelectric nanostructures, in which the effects of surface elasticity, dielectricity and piezoelectricity as well as bulk flexoelectricity are all taken into consideration. The governing equations with non-classical boundary conditions are naturally derived from a variational principle. Then the present beam model is directly applied to solve the static bending problems of cantilever beams. Without considering the residual surface stresses, the bending rigidity can be defined the same as that in classical piezoelectricity theory. The bending rigidity is found to increase for silicon nanowires and decrease for silver nanowires. Also the flexoelectric effect in piezoelectric nanowires has a momentous influence on the bending rigidity. The residual surface stresses which are usually neglected are found to be more important than the surface elasticity for the bending of nanowires. However, this has no influence on the effective electromechanical coupling coefficient. The deflections reveal the significance of the residual surface stresses and the bulk flexoelectric effects. The effective electromechanical coupling coefficient for piezoelectric nanowires is dramatically enhanced, which demonstrates the significant effects of the bulk flexoelectricity and surface piezoelectricity. The effects of surface and flexoelectricity decrease with the increase of the beam thickness, and therefore these effects can be ignored for large-scale structures. This work is very helpful in designing cantilever-beam-based nano-electro-devices.

SIZE-DEPENDENT PIEZOELECTRICITY AND ELASTICITY DUE TO THE ELECTRIC FIELD-STRAIN GRADIENT COUPLING AND STRAIN GRADIENT ELASTICITY

A size-dependent nonclassical Bernoulli–Euler beam model based on the strain gradient elasticity is proposed for piezoelectric nanowires. The governing equations and the corresponding boundary conditions are naturally derived from the variational principle. Different from the classical piezoelectric beam theory, the electric field–strain gradient coupling and the strain gradient elasticity are both taken into account. Static bending problem of a cantilever piezoelectric nanobeam is solved to illustrate the effect of strain gradient. The present model contains material length scale parameters and can capture the size dependent piezoelectricity and elasticity for nanoscale piezoelectric structures. The numerical results reveal that the deflections predicted by the present model are smaller than that by the classical beam theory and the effective electromechanical coupling coefficient is dramatic enhanced by the electric field–strain gradient coupling effect. However, the differences in both the deflections and effective EMC coefficient between the two models are very significant when the beam thickness is very small; they are diminishing with the increase of the beam thickness. This model is helpful for understanding the electromechanically coupling mechanism and in designing piezoelectric nanowires based devices.

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 active control model of laminated piezothermoelastic plate

Abstract After the Hamilton principle for thermo-mechanical–electric coupling problem is derived, the third-order shear deformation theory is extended to encompass piezothermoelastic laminated plates. Based on the velocity feedback control, a model for the active vibration control of laminated plates with piezothermoelastic sensor/actuator is established. An analytical solution is obtained for the case of general forces acting on a simply supported piezothermoelastic laminated plate. Numerical results are presented. The factors that influence the controlled responses of the plate are examined.

Nonlinear electromechanical interfacial fracture for piezoelectric materials

Abstract This work is concerned with the analytical characterization of the electromechanical nonlinear effects on the fields surrounding the tip of an interface crack between ferroelectric-plastic bimaterials. A strip electric saturation and mechanical yielding model is developed for a mode III interfacial crack with electrical polarization reaching a saturation limit and shear stress reaching a yield stress along a line segment in front of the crack. The electrical saturation zone and mechanical yielding zone may have different length scales depending on loading conditions. This model may be considered as a generalization of the classical Dugdale model for plastic yielding near cracks in homogenous materials. The results reveal insight into the structure of stress and electric displacement fields for different load conditions. The energy release rate and COD δ III are also obtained, which indicates the possibility of fracture criterion based on the COD δ III .

Buckling and vibration of flexoelectric nanofilms subjected to mechanical loads

Piezoelectric nanofilms (PNFs) are widely used in microelectromechanical systems, buckling commonly occurs when subjected to compressive mechanical loads in their applications. In this paper we comprehensively study the flexoelectric effect on the buckling and vibrational behaviors of PNFs. The results from the analytical solutions indicate the significance of the flexoelectricity. The critical buckling loads and natural frequency are enhanced by the flexoelectricity. Analytical results indicate that the critical buckling load is not only influenced by the thickness of the PNFs, but also by the in-plane aspect ratio. When the thickness of the PNFs is several micrometers, the critical buckling load predicted by the present model is much higher than the prediction by the classical piezoelectric plate model. And the natural frequency calculated by the current model is much higher than that obtained by the classical piezoelectricity plate theory when the thickness is several tens of nanometers.

General approach on chemistry and stress coupling effects during oxidation

In this paper, the mechanism of growth strain is discussed based on the irreversible evolving equations by considering the coupling effects of stress and chemical reaction during isothermal oxidation, and a simple model relating the growth strain and the oxide thickness is developed. If the effect of the stress on the chemical reaction is not taken into account, the model reduces to the Clarke assumption. The expression of Dox is exhibited, and its value can be determined by experiments. The stress evolving equations are derived, where the viscoplastic strain of the oxide and metal and the growth strain of the oxide are considered. Numerical results are given and compared with results from experiments and the existing model. There is good agreement between the proposed model and the experimental data.