Linear Piezoelectricity Research Articles

Flexoelectric anisotropy and shear contributions in lead-free piezocomposites

Flexoelectricity is the coupling between strain gradients and electric fields. This phenomenon can significantly enhance piezocomposite response in addition to linear piezoelectricity. This enhancement is especially important for lead-free piezocomposites, which generally underperform compared to lead-based counterparts. Flexoelectric enhancement is facilitated by structural anisotropy in piezocomposites. However, challenges in modeling flexoelectric effects arise from several unknowns. Firstly, the shear flexoelectric coefficient is not well-characterized experimentally. Secondly, significant discrepancies exist between theoretical predictions and experimental measurements of flexoelectric coefficients. Thirdly, the influence of matrix mechanical properties on flexoelectric behavior is poorly understood. To address these issues, we construct a parametric flexoelectric model of a lead-free piezocomposite with graded inclusion concentration. We then systematically analyze the impact of each parameter to identify which significantly influence flexoelectric behavior. This study is intended to provide direction to further experimental studies towards understanding and tailoring this subset of parameters.

A stabilized non-ordinary peridynamic model for linear piezoelectricity

Piezoelectric materials are used in a wide range of engineering applications as sensors, actuators, and transducers due to their intrinsic properties. However, analyzing these devices is not straightforward because of the material anisotropy and coupled electromechanical nature of the problems. In this study, a stabilized non-ordinary state-based peridynamic model for linear piezoelectricity is proposed. Fully coupled electromechanical simulation is conducted using an implicit method, and the tangent stiffness matrix is obtained via perturbation technique. Three two-dimensional electromechanical problems with combined static loading and various boundary conditions are used to validate the proposed technique. Then, the crack-opening displacements, and induced electric field on the crack-face are presented for a center-cracked PZT-5H plate. Hence, this study demonstrates that the proposed technique is capable of modeling linear piezoelectric materials and provides a promising method to study fracture and damage progression in piezoelectric materials.

Piezoelectricity of Bi2Se3 Nanosheet.

Bi2Se3, one of the most extensively studied topological insulators, has received significant attention, and abundant research has been dedicated to exploring its surface electronic properties. However, little attention has been given to its piezoelectric properties. Herein, we investigate the piezoelectric response in a five-layer Bi2Se3 nanosheet using scanning probe microscopy (SPM) techniques. The piezoelectricity of Bi2Se3 is characterized using both conventional piezoresponse force microscopy (PFM) and a sequential excitation scanning probe microscopy (SE-SPM) technique. To confirm the linear piezoelectricity of Bi2Se3 two-dimensional materials, measurements of point-wise linear and quadratic electromechanical responses are carried out. Furthermore, the presence of polarization and relaxation is confirmed through hysteresis loops. As expected, the Bi2Se3 nanosheet exhibits an electromechanical solid response. Due to the inevitable loss of translational symmetry at the crystal edge, the lattice of the odd-layer Bi2Se3 nanosheet is noncentrosymmetric, indicating its potential for linear piezoelectricity. This research holds promise for nanoelectromechanical systems (NEMS) applications and future nanogenerators.

On characterizing the viscoelastic electromechanical responses of functionally graded graphene-reinforced piezoelectric laminated composites: Temporal programming based on a semi-analytical higher-order framework

The electromechanical responses of single and multi-layered piezoelectric functionally graded graphene-reinforced composite (FG-GRC) plates are studied based on an accurate higher-order shear deformation theory (HSDT) involving quasi-3D sinusoidal plate theory and linear piezoelectricity. These FG-GRC plates are composed of randomly oriented graphene nanoplatelets (GPLs) reinforcing fillers and the piezoelectric PVDF matrix considering two different distribution patterns such as linear- and uniform- distribution (LD and UD) of GPLs across the thickness. The modified Halpin-Tsai (HT) and Rule of mixture (ROM) models are utilized to determine the effective material properties of FG-GRCs. The analytical model of FG-GRCs is extended further to analyze the time-dependent linear viscoelastic electromechanical behavior of the system based on Biot model of viscoelasticity in the framework of inverse Fourier algorithm. The viscoelastic electromechanical responses include the static deformation and electric responses of simply supported FG-GRC plates which are investigated by considering transverse mechanical and external electrical loading, as well as other critical parameters like aspect ratio and weight fraction of GPLs. The numerical results reveal that the electromechanical response of FG-GRC plates can be enriched due to the addition of a small weight fraction of GPLs. The coupled multiphysics-based computational framework proposed here for predicting the viscoelastic electromechanical behavior of laminated composites can be exploited for stimulating and developing a wide range of micro-electro-mechanical systems (MEMS) and devices incorporating time-dependent programming features.

A peridynamic model for electromechanical fracture and crack propagation in piezoelectric solids

This paper presents for the first time an approach to the problem of electromechanical fracture and crack propagation in piezoelectric solids with peridynamics. Fracture in piezoelectric ceramics is an important problem in engineering due to its complexity. The majority of the computational models available on the literature rely on sharp crack representations, which have difficulties dealing with complex crack patterns, or rely on diffusive crack models, such as the phase-field fracture model, that can predict complex patterns but does not represent cracks in a discrete way. On the other hand, peridynamics has been designed to solve this problems and is able to simulate discrete cracks as well as complex crack phenomena like fragmentation and branching. We present a novel approach to the implementation of different electric crack face boundary conditions in a peridynamic way, by a field selective bond breaking approach. Moreover, it is also presented the first electromechanical failure criterion for fracture in piezoelectric ceramics. We develop an energy based failure criterion due to its generality and wide range of applications. These approaches are presented in a way such that they are valid for any type of peridynamic formulation. The used numerical model is implemented using correspondence-based peridynamics with the linear piezoelectricity constitutive setting, using a meshfree discretization and solved quasi-statically with an implicit incremental-iterative scheme. Numerical examples are presented to demonstrate the capabilities of these new approaches and assess the performance of the model against experimental results. The model is capable of numerically predicting complicated fracture behaviour and crack propagation in an intrinsic/autonomous way, as demonstrated by the results.

Mathematical modeling of electro‐elastic dislocations in piezoelectric materials

AbstractIn this work, based on the theory of linear incompatible piezoelectricity with eigendistortion and eigenelectric field, the concept of electro‐elastic dislocations is presented. Both field variables, the displacement vector u and the electrostatic potential φ, possess a jump discontinuity at the dislocation surface. Electro‐elastic dislocations are described not only by the dislocation density tensor but also by a new introduced field, the so‐called electric dislocation density vector. In addition to electro‐elastic dislocations, inhomogeneities, body forces and body charges are also considered. Within this framework, material balance laws that correspond to the symmetries of translation, scaling and rotation are derived. All fundamental fields of configurational mechanics like the Eshelby stress tensor, the electro‐elastic Peach‐Koehler force, the Cherepanov force, the Eshelby force among others, which take place in the broken (translational, scaling and rotational) conservation laws anymore are given.

Analysis of surface effect and flexoelectric effect on the electromechanical responses of bilayered transversely isotropic rectangular micro-plate

A new model of a bilayered transversely isotropic piezoelectric rectangular micro-plate with a distributed load is developed on the basis of Kirchhoff's plate theory and the extended linear piezoelectricity theory to characterize the piezoelectric micromachined ultrasonic transducer. The model takes into account both the surface effect and the flexoelectricity effect. The governing equation at the simply supported boundary condition is derived according to the variation principle. Based on the new model, the size dependent electromechanical coupling behaviors of the bilayered piezoelectric rectangular micro-plate are investigated. Considering the flexoelectric effect and surface effect synchronously, the numerical result indicates that the size dependence of the normalized central deflection decreases as the residual surface stress increases. For negative residual stress, the surface effect is the main influencing factor. While for positive residual stress, the surface effect dominates only when the ratio of thickness to length is smaller than about 25; otherwise, the flexoelectric effect will be more crucial. Moreover, if the thickness of the piezoelectric layer is less than about 40 nm, the electrical potential and polarization show a stronger size dependence. These results will be helpful to design and manufacture a piezoelectric micromachined ultrasonic transducer.

Ultrathin flexible linear-piezoelectric ZnO thin film actuators: Tuning the piezoelectric responses by in-plane epitaxial strain

Linear piezoelectric materials and devices potentially serve as high-accuracy and fast-response sensors and actuators. However, linear piezoelectrics have been scarcely studied, while tuning the linear piezoelectric response of undoped ZnO remains a challenge. Here, linear piezoelectric zinc oxide (ZnO) thin film actuators are fabricated with a sandwich structure of AZO/ZnO/AZO epitaxially on CeO2/Hastelloy substrates, with AZO denoting the aluminum-doped ZnO electrodes and CeO2 denoting the cerium oxide buffer. Due to the lattice mismatch between ZnO and CeO2, compressive in-plane lattice strains are detected. Through varying the ZnO layer thickness, a strong correlation is found between the in-plane epitaxial strain and the piezoelectric constant which proves an effective method to improve the linear piezoelectric response of ZnO. Further, the better linear piezoelectric response of the thinner flexible ZnO layer resolves the controversy between the performance and the deformation-durability of flexible piezoelectric ZnO devices. The vertical piezoelectric constant of the ultrathin (∼32 nm) ZnO film is ∼ 8.14 pm/V, which is highly suitable for positioners working at the picometer scale. Future works harnessing the epitaxial strains to further improve the piezoelectric constant of ZnO materials potentially lead to the prosperity of linear piezoelectrics.

Compound influence of surface and flexoelectric effects on static bending response of hybrid composite nanorod

Nanoscale beams and rods are extensively used in several nano-electro-mechanical systems (NEMS) and their applications such as sensors and actuators. The surface and flexoelectricity phenomena have an extensive effect on nanosized structures and are related to their scale-dependent characteristics. This article presents the effect of different surface parameters and flexoelectricity on the electrostatic response of graphene-reinforced hybrid composite (GRHC) nanorods (NRs) using the theory of linear piezoelectricity, Euler-Bernoulli (EB), and Galerkin residual method. Based on these theories, the theoretical and finite element (FE) model is produced to investigate the static bending deflection of GRHC NRs when subjected to point and uniformly distributed load (UDL) considering different boundary conditions: cantilever (FC), fixed-fixed (FF), and simply supported (SS). This proposed FE model provides a useful tool for analyzing and investigating the outcomes of analytical models, which are found to be in good agreement. Our results presented in this article reveal that the effect of surface and flexoelectricity on the static bending response of GRHC NRs is noteworthy. These effects diminish with increased thickness/diameter of NR, and hence, these effects can be neglected for large-sized structures. The results presented here would help to identify the desired electrostatic response of GRHC NRs in terms of static bending response for a range of NEMS using different loading and boundary conditions as well as graphene volume fraction. This current study offers pathways for developing new proficient novel GRHC materials with enhanced control authority and present models can be exploited for numerous other materials as well as line-type structural systems such as beams, wires, rods, column/piers, and piles to study their global response.

Electromechanical behaviors in piezotronic quantum wells based on a quantum-corrected phenomenological theory

Piezotronic devices have attracted a great deal of attention due to their potential applications in self-powered tactile sensing, nano-device memory, human-electronic interface, etc. As the size of piezotronic devices shrinks, some interesting quantum effects begin to appear. In this paper, we establish a theory oriented to the engineering application of piezoelectric semiconductors, called quantum-corrected phenomenological (QCP) theory, by coupling the density-gradient theory and the linear piezoelectricity theory through Gauss's law. For numerical verification, we specifically studied the electromechanical behaviors in GaN/AlGaN heterostructure quantum wells (QWs) with both infinite and finite barrier height. The results of electron density, electric potential, and quantum potential are provided, and their dependence on the doping density, the applied stress, and the Al mole fraction is investigated. Some interesting quantum effects are revealed, and their influencing mechanisms are well investigated from a macroscopic perspective. Not only do the conclusions drawn in this paper enrich the fundamental understanding of the piezotronic effect in a QW structure, but also the proposed QCP theory can serve as a valuable tool for future device engineering.

Implicit non-ordinary state-based peridynamics model for linear piezoelectricity

In the present work, the development and analysis of linear piezoelectricity in the peridynamics framework is presented. The model is developed using non-ordinary state-based Peridynamics. The equations of motion are derived using Hamilton’s principle and the correspondence material model is developed by establishing the connection between the classical theory of linear piezoelectricity and the newly proposed peridynamic linear piezoelectricity framework. An implicit implementation is proposed for two-dimensional linear piezoelectricity. Moreover, for the stabilization of the proposed scheme, the bond-associated correspondence model is used. We demonstrate the capabilities of the proposed model by presenting some 2 D numerical examples.

Density-based topology optimisation considering nonlinear electromechanics

This work presents a first numerical study for the density-based topology optimisation in the challenging and scarcely explored context of nonlinear electromechanics, focusing on electro-active polymers, capable of undergoing large electrically induced deformations. This paper puts forward the following novelties. First, it presents an energy interpolation scheme for the electromechanical energy functional of solid and void regions. Regarding the latter, it recommends the use of an unconditionally stable definition deferring the development of artificial instabilities. Second, it carries out a numerical study assessing the convenience of different mechanical and electromechanical penalising exponents (denoted as pm and pe, respectively), featuring in the energy interpolation scheme. Third, it reports that, in contrast to the context of linear piezoelectricity, a choice of pe < pm must be avoided, as this fosters the sudden development of artificial instabilities, compromising the robustness.

Analytical Solution for Static and Dynamic Analysis of Graphene-Based Hybrid Flexoelectric Nanostructures

Owing to their applications in devices such as in electromechanical sensors, actuators and nanogenerators, the consideration of size-dependent properties in the electromechanical response of composites is of great importance. In this study, a closed-form solution based on the linear piezoelectricity, Kirchhoff’s plate theory and Navier’s solution was developed, to envisage the electromechanical behaviors of hybrid graphene-reinforced piezoelectric composite (GRPC) plates, considering the flexoelectric effect. The governing equations and respective boundary conditions were obtained, using Hamilton’s variational principle for achieving static deflection and resonant frequency. Moreover, the different parameters considering aspect ratio, thickness of plate, different loadings (inline, point, uniformly distributed load (UDL), uniformly varying load (UVL)), the combination of different volume fraction of graphene and piezoelectric lead zirconate titanate are considered to attain the desired bending deflection and frequency response of GRPC. Different mode shapes and flexoelectric coefficients are also considered and the results reveal that the proper addition of graphene percentage and flexoelectric effect on the static and dynamic responses of GRPC plate is substantial. The obtained results expose that the flexoelectric effect on the piezoelastic response of the bending of nanocomposite plates are worth paying attention to, in order to develop a nanoelectromechanical system (NEMS). Our fundamental study sheds the possibility of evolving lightweight and high-performance NEMS applications over the existing piezoelectric materials.

Nonlinear piezoelectric plate framework for aeroelastic energy harvesting and actuation applications

The use of piezoelectric materials in various applications, including the development of bio-inspired structures, vibration control, energy harvesting, among others, has been investigated by several researchers over the last few decades. In most cases, linear piezoelectricity is assumed in modeling and analysis of such systems. However, the recent literature shows that non-linear manifestations of piezoelectric materials are relevant and can modify the electromechanical behavior especially around the resonance. This work extends the investigation of non-linear piezoelectricity, by adding geometric nonlinearities and aerodynamic effects, to aeroelastic problems such as wind energy harvesting. A piezoaeroelastic model that combines a non-linear coupled finite element model and the doublet lattice model of unsteady aerodynamics is presented. The electromechanically coupled finite element model includes the non-linear behavior of piezoelectric material under weak electric fields. Model predictions are validated by experimental data for 1) a double bimorph actuation case and 2) a vibration based energy harvesting case. Later, the piezoaeroelastic behavior of a generator plate-like wing for wind energy harvesting is numerically investigated when linear as well as non-linear piezoelectricity is considered. The experimentally validated geometrically and materially non-linear framework presented here is applicable to both energy harvesting and actuation problems in the presence of air flow.

Airbag Helmet: Design and Analysis of Helmet Piezoelectric Accelerometer

The author invented an airbag helmet to provide effective protection for two-wheeled vehicle riders. This paper illustrates the desion and analysis of this Helmet Piezoelectric Accelerometer. Analysis is based on the finite element model of solid mechanics (e.g. linear elasticity and piezoelectricity) with a carefully selected software of COMSOL Multiphysics. Finite element analysis method helped the author to reduce the need for physical prototypes in design process. With a high degree of accuracy, the author modeled complex material physical deformations with detailed visualization and solved the problem. Equations were used for calculation during the process. This paper provides the design of comsol-based solid mechanics and piezoelectricity simulation and simulates the process of converting the mechanical vibration into voltage signals by using piezoceramics, so as to supply power to the airbag accelerometer and release the airbag in time. The reliability and safety of the design are verified by means of the mechanical and electrical simulation. In case of a traffic accident, the airbag will inflate instantly and form a balloon-shaped helmet wrapping the rider’s head to secure the head effectively.

On the Determination of Plane and Axial Symmetries in Linear Elasticity and Piezo-Electricity

We formulate necessary and sufficient conditions for a unit vector \(\pmb{\nu }\) to generate a plane or axial symmetry of a constitutive tensor. For the elasticity tensor, these conditions consist of two polynomial equations of degree lower than four in the components of \(\pmb{\nu }\). Compared to Cowin–Mehrabadi conditions, this is an improvement, since these equations involve only the normal vector \(\pmb{\nu }\) to the plane symmetry (and no vector perpendicular to \(\pmb{\nu }\)). Similar reduced algebraic conditions are obtained for linear piezo-electricity and for totally symmetric tensors up to order 6.

Nonlinear piezoelectricity and damping in partially-covered piezoelectric cantilever with self-sensing synchronized switch damping on inductor circuit

We examined a partially covered piezoelectric cantilever connected to a self-sensing synchronized switch damping on an inductor (SSDI) circuit. Nonlinear behavior, which cannot be explained by the single-degree-of-freedom model based on linear piezoelectricity, is observed in the frequency response as the excitation level increases. Here, we propose a new method that allows us to predict the attenuation performance in such a smart damping structure. We first derived the governing equation for a practical cantilever structure in which the piezoelectric elements are attached with glue and partially cover the cantilever. We include the nonlinear piezoelectricity and damping in the model. Then, we used a two-way coupled simulation technique to investigate the complex electromechanical dynamics for the piezoelectric cantilever connected to the self-sensing SSDI circuit. Our model replicates the nonlinear behavior observed experimentally. Intriguingly, the simulation revealed that, when connected to the SSDI circuit, the lower shift of the peak frequency observed in the open circuit vanished and the peak frequency shifted to higher frequency because of the increased piezoelectric coupling force. We emphasize the importance of nonlinear piezoelectricity and damping in the model and show that ignoring the peak frequency shift and the decrease in the displacement may lead to the wrong estimation in the attenuation performance, especially as the excitation level increases.

Atomic-Scale insight into the reversibility of polar order in ultrathin epitaxial Nb:SrTiO3/BaTiO3 heterostructure and its implication to resistive switching

Ferroelectric heterostructures with bi-stable state of polarization are appealing for data storage as well as tunable functionalities such as memristor behavior. While an increasing number of experimental and theoretical studies suggest that polarization persists in ultrathin epitaxial heterostructures approaching just a couple of unit cells, the switching of such polar order is much less well understood, and whether polarization can be reversed in ultrathin ferroelectric heterostructures remains to be answered. Here we fabricate high-quality 7-unit cell thick BaTiO3 (BTO) films on Nb-doped single crystalline SrTiO3 (NSTO) substrate, and demonstrate their apparent yet unambiguously false polarization reversal due to charge injection using comprehensive piezoresponse force microscopy (PFM) studies. The presence of weak polar order consistent with linear piezoelectricity is confirmed at the atomic scale by high resolution integrated differential phase contrast (IDPC) of scanning transmission electron microscopy (STEM) as well as macroscopic second harmonic generation (SHG), while the lack of polarization reversal under the voltage applied is supported by density functional theory calculation showing the persistence of dead layer on the surface. Nevertheless, poling-induced electric conduction differing by two orders of magnitude is observed, demonstrating resistive switching in ferroelectric heterostructure in the absence of polarization reversal, even with weak polar order. Our finding has technological implications on emerging memristor applications with potentially more accessible states than bi-stable polarization modulated mechanism, and raises technical challenges to unambiguously demonstrate polarization switching in ultrathin films at their critical size limit.

Flexoelectric and surface effects on the electromechanical behavior of graphene-based nanobeams

In this novel work, the electromechanical behavior of graphene-based nanocomposite (GNC) beams with flexoelectric and surface effects were investigated using size-dependent Euler-Bernoulli theory, linear piezoelectricity and Galerkin's weighted residual method along with modified strength of materials and finite element (FE) approaches. In addition, analytical and FE models were developed to study the static response of flexoelectric GNC nanobeams with various boundary conditions: cantilever, simply-supported and clamped-clamped. The developed models predict that the effective piezoelectric coefficients of GNC are responsible for the actuation capability of a graphene layer in the transverse direction due to the applied field in its axial direction and the predictions by both the models are found to be in good agreement. Results reveal that the flexoelectric and surface effects on the static response of GNC nanobeams are significant and should be taken into account. The electromechanical response of GNC nanobeams can be tailored to achieve the required coupled electromechanical characteristics of a vast range of NEMS using various boundary conditions and thickness of nanobeam as well as volume fraction of graphene. Our fundamental study sheds a light on the possibility of developing high-performance and lightweight graphene-based NEMS such as nanosensors, nanogenerators and nanoresonators using non-piezoelectric graphene.

Anti-plane fracture mechanics analysis of a piezoelectric material layer with strain and electric field gradient effects

The problem of an anti-plane crack in a polarized ceramic layer with both the strain and electric field gradient effects is studied. This model includes two characteristic length parameters l and m which describes the strain gradient and the electric field gradient effects, respectively. The analysis demonstrates that the near-tip asymptotic stress and electric displacement are governed by r−3/2 singularities. Due to stain gradient effect, stresses ahead of the crack tip are significantly higher than those in the classical linear piezoelectricity fracture mechanics. When the strain and electric field gradient parameters decrease to sufficiently small, the solutions reduce to the conventional linear elastic fracture mechanics results. The new contribution of this research is that it includes the effects of the strain gradient and electric field gradient simultaneously for a finite crack in a finite piezoelectric layer.