Piezoelectric Inclusions Research Articles

T-matrix of piezoelectric shunt inclusions on a thin plate

Developing piezoelectric-based plate-like metamaterials necessitates an effective modeling method to elucidate the omnidirectional wave properties of piezoelectric coupled inclusions on a thin plate. The commonly used methods, such as the transfer-matrix method and finite element method, are inadequate for analyzing the transmission and reflection of omnidirectional waves in a two-dimensional elastic medium. Unlike the existing methods, the multiple scattering method employs Bessel functions as the displacement-basis methods which can accurately describe the propagation and scattering characteristics of omnidirectional waves. This paper develops a novel T-matrix formulation to support the multiple scattering method, representing the input-output relationship between incident and reflected waves from a piezoelectric shunt inclusion on a host thin plate. The piezoelectric shunt inclusion comprises a varying-thickness substrate bonded with piezoelectric shunting patches. The T-matrix of the piezoelectric shunt inclusion is formulated by integrating the wave-based method with Rayleigh-Ritz method. The derived T-matrix is then used to semi-analytically analyze the far-field scattering and reflection properties of a single inclusion. Numerical results capture the scattering properties resulting from trapped mode resonances of the piezoelectric shunt inclusion. Additionally, the capability of the piezoelectric shunt damping to design and tune multiple critical coupling conditions for axisymmetric modes of thin plates is parametrically investigated by varying the values of inductors and resistors.

The effect of property contrast in two-component piezoelectric composites

A Mori - Tanaka model of piezoelectric composites is used to study the effect of property contrast between the components of a two-component composite. The composite comprises a piezoelectric matrix and piezoelectric inclusions whose property values are scaled from those of the matrix. The scaling method allows a wide range of material combinations to be approximated without using explicit properties of specific materials. Additionally, the aspect ratio and volume fraction of inclusions is varied to seek optimum values of the piezoelectric coefficients in the composite. It was found that scaling the properties in the electroelastic moduli reveals significant results for the piezoelectric performance coefficients dhgh, κ33, g33 and kt. By varying the material scaling factors alongside the inclusion aspect ratio it is demonstrated that giant enhancements of the transducer figure of merit dhgh could potentially be achieved through composite design. This approach identifies some novel opportunities for optimised piezoelectric composites.

Free vibration analysis of twin piezoelectric inclusions embedded in elastic medium

The present study is the first attempt to investigate the free vibration behavior of the rectangular plate including two equal (twin) internal parallel piezoelectric inclusions (lying width-wise in the plate) utilizing the 3D exact equations of electroelasticity theory. For the solution, the finite element method is applied. By Hamilton’s principle, the equation of motion and boundary conditions are obtained to derive the finite element equations using the electrical energy of the piezoelectric material and the mechanical energy of the structure. Lateral edge surfaces of the plate have zero electrical potential and are simply supported. Ideal contact conditions are satisfied by the interface surfaces between the elastic medium and piezoelectric (abbreviated as PZT) inclusions. After investigating the convergence and validation of the approach, the influence of various parameters on the natural frequencies of the plate behavior, such as the mutual effect of PZT inclusions, coupling effect between the electrical and mechanical fields, the effect of the size, location, material, and polled directions of the PZT inclusions, and the material of the elastic medium, is investigated.

Electric control of a phononic crystal constituted of Piezoelectric layers using Schottky diode

A one-dimensional piezoelectric phononic crystal (PPC) consisting of a periodic pattern made of two perfectly bonded materials: one active (piezoelectric), the other passive (elastic) and exhibiting a strong acoustic impedance contrast is studied. We are interested in the tunability of piezoelectric inclusions in order to control the propagation of ultrasonic waves in the MHz range from a nonlinear electrical component connected to the terminals of the piezoelectric elements. After modeling the dynamic resistance of the Schottky diode, based on the piezoelectricity equations, a one-dimensional analytical model is proposed to take into account the resistive impedance effect of this diode connected to the electrodes of the active plate. Thus, we have shown that the application of various electrical boundary conditions (EBCs) on the electrodes (open-circuit, short-circuit, connecting an electrical load) allows to change the effective properties of the piezoelectric plate in particular and those of the PPC in general. The dispersion of the waves is then electrically tuned and, depending on the applied EBCs, we have demonstrated numerically the possibility of opening Bragg or hybridization gaps in the PPC band structure.

Configurational forces in ferroelectric structures analyzed by a macromechanical switching model

Polycrystalline ferroelectric ceramics are widely used in sensors, actuators, microelectromechanical systems, etc. If a ferroelectric structure possesses some defects like voids or inhomogeneities, its reliability is reduced, and undesired non-homogeneous local concentrations of the electromechanical fields occur. Under the applied external loading, a domain switching region evolves in the vicinity of defects, which is manifested as a reorientation of the remanent polarization vector. In the current work, the nonlinear electromechanical behavior of ferroelectric ceramics is computed by means of three-dimensional finite element analysis, using the phenomenological continuum mechanics model suggested by Landis (J. Mech. Phys. Solids 50(1):127–152, 2002. https://doi.org/10.1016/s0022-5096(01)00021-7) and numerically implemented by Stark (Int. J. Solids Struct. 80:359–367, 2015. https://doi.org/10.1016/j.ijsolstr.2015.09.004). This constitutive law is combined with user-developed elements in Abaqus commercial code for nonlinear coupled electromechanical analyses. By use of the numerical simulations, the evolution of all field variables, in particular of the polarization, is tracked. In a post-processing step, the configurational forces are computed, which express the thermodynamic driving forces acting on the defect. As a typical defect, we consider a circular void in the ferroelectric structure exposed to an alternating electric field. Additionally to the void, other inhomogeneities, namely, a strip of dissimilar material as well as dielectric and piezoelectric inclusions, are investigated. For all cases, the redistribution and evolution of the configurational forces are studied. Besides the essential findings and methodology achieved in this work, the developed software can serve as a basis for further investigations on the failure of composite smart structures and explicit crack modeling using fracture mechanical concepts.

Simulation of antiplane piezoelectricity problems with multiple inclusions using the generalized finite difference method

In this paper, antiplane piezoelectricity problems with multiple inclusions are studied by the generalized finite difference method (GFDM). Developed from the Taylor series and the Moving Least Squares, the GFDM expresses the derivatives of variables as the combination of values of surrounding nodes where the sparse matrix will be obtained considering the boundary conditions and interface conditions. Stress concentration and electric field concentration are analyzed in three numerical examples, which contain circular and elliptical piezoelectric inclusions in various sizes, locations, and material parameters. The applicability and validity of the proposed method are verified through the comparison with reference results.

Wave attenuation in 1-3 phononic structures with lead-free piezoelectric ceramic inclusions

The unit cell wave attenuation of elastic Bloch waves in 1-3 piezoelectric phononic structures with BaTiO3 inclusions in a polymeric matrix is reported. This attenuation can be observed by the evanescent Bloch waves in the complex dispersion diagram of the periodic piezoelectric ceramic structure. Full and complete Bragg-type band gaps are observed. The piezoelectricity of the periodic lead-free ceramic inclusions improves the band gap width and wave attenuation in a specific frequency spectrum. These characteristics can be used for the wave attenuation design using smart periodic structures, for surface acoustic wave (SAW) filter and 1-3 piezocomposite transducer design using piezoelectric phononic structures with BaTiO3 inclusions.

Numerical investigation of sensing and energy harvesting performance of 0-3 and triply periodic minimal surface-based K0.475Na0.475Li0.05(Nb0.92Ta0.05Sb0.03)O3 and polyethylene piezocomposite: A comparative study

The present paper is devoted to conducting a comparative study on the sensing and energy harvesting performance of a 0-3 and triply periodic minimal surface (TPMS)-based piezocomposite with [Formula: see text] ( KNLNTS) material as piezoelectric inclusions and polyethylene as the matrix material. Different types of TPMS are reported in literature like Neovius, Fischer-Koch S, Schwarz CLP, Schoen Gyroid, Schoen IWP, Schwarz Primitive, etc. In the present study, Schwarz primitive TPMS is considered. Representative volume elements (RVEs) with four different volume fractions are generated and the finite element simulations are performed to compute the effective elastic and piezoelectric properties. The homogenization technique is used to calculate the effective properties. The calculated values of the effective properties are further used to calculate the sensing voltage between the electrodes and harvested power across the resistance. The effective elastic and piezoelectric properties increase with an increase in volume fraction of the piezoelectric inclusions resulting in a higher sensing voltage and power. Significant improvement in the effective elastic and piezoelectric properties of TPMS-based piezocomposite was observed. TPMS-based piezocomposite exhibited superior performance as compared to their 0-3 counterparts.

The electroelastic fields inside and outside a piezoelectric parabolic inclusion with uniform eigenstrains and eigenelectric fields

AbstractUsing the Stroh octet formalism, we obtain the electroelastic fields in an infinite homogeneous piezoelectric medium containing a parabolic Eshelby inclusion undergoing uniform eigenstrains and eigenelectric fields. We prove that the internal electroelastic field defining stresses, total strains, electric displacements, total electric fields and rigid‐body rotation inside the parabolic inclusion is uniform. The internal uniform electroelastic field is expressed explicitly in terms of the reduced generalized compliances and the imposed eigenstrains and eigenelectric fields. The decaying non‐uniform electroelastic field in the exterior of the parabolic inclusion is also obtained.

Comparison of effective parameters of lead-free 1–3-type composites based on ferroelectric single crystals

The article reports results of the comparative study on the performance of lead-free 1–3-type composites based on domain-engineered lead-free ferroelectric single crystals. Of interest are the 1–3–0 ferroelectric single crystal/porous polymer and 1–0–3 ferroelectric single crystal/piezoelectric single crystal/polymer composites with heterogeneous matrices. In the 1–3–0 composite this matrix is a polymer medium with the system of spheroidal air pores. In the 1–0–3 composite the polymer matrix contains a system of spheroidal piezoelectric single crystal inclusions, and the arrangement of these inclusions is similar to that of the pores in the matrix of the related 1–3–0 composite. Volume-fraction and aspect-ratio dependences of the piezoelectric properties, squared figure of merit and electromechanical coupling factors of the 1–3-type composites are analysed, and comparison of the effective parameters of the composites is made. The role of the composite microgeometry in forming the piezoelectric anisotropy and squared figures of merit is discussed. Due to large electromechanical coupling factors, squared figures of merit and anisotropy factors, the studied lead-free 1–3-type composites are of interest as advanced materials suitable for piezoelectric transducer, sensor and energy-harvesting applications.

Multiscale design of nanoengineered matrices for lead-free piezocomposites: Improved performance via controlling auxeticity and anisotropy

Multiscale material design has made it possible to control the properties of a material through introducing structures at multiple length scales. This structuring brings about unusual material behaviour that is not seen in a continuum material. Here we introduce a multiscale design for the matrix components of a lead-free piezocomposite. This combines a microscale stiff polymeric structure embedded within a softer matrix to form a composite matrix. By controlling the microscale features of the embedded structure, we tune the mechanical behaviour of the matrix by rendering it either nonauxetic (hexagonal structure) or auxetic (inverted hexagonal structure). Further, the mechanical and electrical properties of the matrix are controlled at the nanoscale by addition of carbon nanotubes within the embedded polymeric structure. By engineering the matrix at the nano and the microscale, we firstly demonstrate that the auxetic matrix can result in three orders of magnitude higher piezoelectric response by amplifying the strains within the piezoelectric inclusions. We further demonstrate that by using the matrix with the nonauxetic embedded structure, it is possible to design piezoelectric composites with pronounced anisotropy in their longitudinal and transverse responses. This is an important requirement for designing materials with directional sensing ability. Our findings show that the multiscale material design proposed here has important implications for both energy harvesting and directional sensing. Further, the approach taken here yields considerable performance improvements while using limited quantities of nanomaterial. The multiscale matrix design is scalable and amenable to fabrication through emerging methods such as additive manufacturing.

Band structure and transmission spectra in multiferroic based Sierpinski-carpet phononic crystal

In this study, the band structure and transmission spectra in multiferroic based Sierpinski-carpet phononic crystal are investigated based on finite element simulation. In order to obtain the band structure of the phononic crystal (PnC), the Floquet periodicity conditions were applied to the sides of unit cell. The square lattice PnC consists of various piezoelectric inclusion in a rubber matrix with circular and triangular cross section.

Design of polymeric auxetic matrices for improved mechanical coupling in lead-free piezocomposites

While lead-free piezocomposites offer an environmentally friendly solution to mechanical sensing and energy harvesting, they lag state-of-the-art lead-based materials in terms of performance. It is therefore important to develop new material designs to bridge this performance gap. Considering composites where rigid piezoelectric inclusions are embedded in soft matrices, a major cause of poor performance is weak coupling of applied strains to the inclusions. We show here that by designing matrices with negative Poisson’s ratios (auxetic matrices) it is possible to considerably improve this coupling. We first demonstrate this concept using a matrix which is inherently auxetic where we show an improvement of 40%–50% in the piezoelectric response. Based on the observations made, we develop a scalable design for auxetic matrices using conventional non-auxetic polymeric materials. This is done by embedding rigid auxetic structures in softer matrices. We show that with such designed auxetic matrices, which are amenable to fabrication through 3D printing, it is possible to achieve considerably larger piezoelectric response with a significant retention of the matrix softness. Particularly, we show that auxetic designs can show piezoelectric enhancements exceeding 300% compared to non-auxetic reference designs having similar a non-auxetic rigid backbone of similar volume as the auxetic backbone. Therefore, the use of matrices with negative Poisson’s ratios is a promising design avenue to decouple mechanical coupling of strain to inclusions and matrix hardness. This strategy can pave way to design of softer piezocomposites with superior responses employing only structured polymeric materials without the use of expensive nanomaterials.

Ferroelectric based fractal phononic crystals: wave propagation and band structure

In this study, the band structure and transmission in multiferroic based Sierpinski carpet phononic crystal are investigated based on finite element simulation. In order to obtain the band structure of the phononic crystal (PnC), the Floquet periodicity conditions were applied to the sides of the unit cell. The square lattice PnC consists of various piezoelectric inclusion in a rubber matrix with square and circular cross section.

Advanced modeling of lead-free piezocomposites: The role of nonlocal and nonlinear effects

Lead-free piezocomposites are an ecofriendly route for sensing and harvesting energy from mechanical stimuli and it is important to develop accurate models which can capture essential physical processes underlying their performance. Current piezocomposite design heavily relies on the linear piezoelectric model which neglects nonlocal and nonlinear electro-elastic processes. Here we develop a more accurate modelling paradigm to determine the contributions from nonlocal flexoelectric and nonlinear electrostrictive effects towards the performance of lead-free piezocomposites. We find that in the case of microscale randomly shaped piezoelectric inclusions which represent a practical scenario, the flexoelectric effect does not contribute appreciably towards the piezoelectric response. However, the nonlinear electrostrictive effects impart significant strain-dependent responses. Further, in nano-modified composites, we find that the nonlinear electro-mechanical coupling can have different effects on the transverse and the longitudinal electro-elastic responses. In particular, the longitudinal electric field response, with the nonlinear contribution, is less sensitive to the polycrystalline structure of the piezoelectric inclusions. These observations clearly indicate that at larger strains, nonlinear effects cannot be neglected. In general, our results entail that it is important to include nonlocal and nonlinear processes for reliable and accurate modelling of piezocomposites.

Design of nano-modified PVDF matrices for lead-free piezocomposites: Graphene vs carbon nanotube nano-additions

Graphene nano-additions to polymer matrices have demonstrated exceedingly better mechanical properties compared to carbon-nanotube modified matrices. Therefore, in the context of mechanically superior high-performance piezo-composites, graphene-modified composite architectures represent an important design direction. In this paper, we first develop an effective property model for graphene-modified piezoelectric matrices, taking into account the mechanical anisotropy of the matrix. We further evaluate the piezoelectric performance of the matrix architecture which incorporates lead-free BaTiO3 polycrystal inclusions. In order to obtain comparisons with well-established composites, we compare the electro-elastic response of two composite architectures in which the matrix is modified by multiwalled CNTs and graphene respectively. It is seen that, near percolation of the nano-additions, graphene-based systems exhibit an order of improvement in the piezoelectric response compared to the composite without nano modification. This improvement is comparable to CNT-based systems, but the matrix hardening is lesser than half the hardening observed in CNT-modified composites. This feature is due to a considerably smaller percolation threshold of graphene compared to CNTs which brings about percolative conditions at very small filler concentrations. We further investigate the dependence of the electric flux and fields in the graphene-modified piezocomposite on the polycrystallinity of the piezoelectric inclusions to identify the polycrystalline configurations that can lead to improved performance in such nanomodified piezocomposites.

Design of lead-free PVDF/CNT/BaTiO3 piezocomposites for sensing and energy harvesting: the role of polycrystallinity, nanoadditives, and anisotropy

Lead-free piezoelectric composites with polymeric matrices offer a scalable and eco-friendly solution to sensing and energy harvesting applications. Piezoelectric polymers such as PVDF are particularly interesting because of the possibility to engineer the performance of these materials through addition of higher-performance piezoelectric inclusions and nanomaterials and to scalably manufacture such composites by emerging techniques such as 3D printing. This work makes two contributions, namely towards composite design and towards development of accurate effective property models. In the context of composite design, we evaluate the piezoelectric performance of PVDF modified by the addition of polycrystalline-BaTiO3 and multiwalled carbon nanotubes. Firstly, the addition of BaTiO3 dramatically improves the electric field within the composite offering significant advantages specially at low BaTiO3 concentrations. Secondly, the addition of carbon nanotubes to the matrix, particularly at higher BaTiO3 loadings, leads to an order of magnitude increase in the piezoelectric flux generation. Further enhancement in the flux generation is also possible by tuning the polycrystallinity of the BaTiO3 inclusions. However, these behaviours are inclusion-driven and the piezoelectric behaviour of the matrix does not contribute to this improvement. Importantly, a small addition of BaTiO3 and CNT into the PVDF matrix, away from percolation, can simultaneously improve flux and electric field generation. In this part of the work, we assume an isotropic PVDF matrix. Given that PVDF is elastically anisotropic, the second aspect of this work is the development of an effective property model for CNT-modified PVDF, taking into account the elastic anisotropy of poled PVDF, to predict the elastic coefficients of CNT-modified PVDF matrices, thus undertaking a key step towards modelling anisotropic piezoelectric composites. We show that the anisotropy-based model makes similar predictions in the effective composite behaviour, indicating that in the case of PVDF-based piezocomposites, the anisotropy of the matrix does not significantly affect the piezoresponse.

Numerical Modeling of PZT- Piezoelectric Composites with Passive and Active Polymer Matrix

Piezoelectric composite materials with a polymer matrix are important for underwater acoustic and biomedical imaging applications. The dependence of electromechanical properties of piezoelectric composite on constituent material characteristics and shape of piezoelectric inclusions is a central problem that provides the opportunity to tailor the performance of piezoelectric composites according to design needs. A numerical model has been developed to investigate the electromechanical properties of 1-3 piezoelectric composites with a passive and active polymer matrix. Maxwell Homogenization method is employed to homogenize the solution domain. It is demonstrated that the use of PVDF as an active polymer matrix has a significant influence on piezoelectric charge coefficient d31, hydrostatic coefficient dh, voltage coefficient gh, and hydrophone figure of merit ghdh when compared to the passive Araldite-D polymer matrix. Overall, a 5 to 30% volume fraction of PZT-7A fiber inclusions in an active polymer matrix is the optimum ratio that has a significant effect on piezoelectric properties. The accuracy and effectiveness of homogenized material constants were verified by comparing the derived composite properties with experimental work published elsewhere. These results provide much needed intuitiveness in the development of piezoelectric polymer composite with better performance for transducer applications.

Improving the performance of lead-free piezoelectric composites by using polycrystalline inclusions and tuning the dielectric matrix environment

Piezoelectric composites are a class of smart materials which can be manufactured in a scalable manner by additive processes, while catering to a wide range of applications. Recent efforts are directed towards composites of lead-free piezoelectric materials with a goal of achieving performances comparable to lead-based composites. While there has been extensive research in fabrication methodologies such as 3D printing, which can manufacture complex piezoelectric structures in a scalable manner, there are important remaining questions as to how the performance of lead-free piezoelectric composites can be further improved. Fundamental to this is the understanding of key factors underlying piezoelectric performance: the electro-elastic interactions between the piezoelectric material and the matrix, the effects of the polycrystalline microstructure of the piezoelectric inclusions, the effect of randomly shaped polycrystalline fillers, and the effect of the volume fraction of the piezoelectric material in the matrix. A strong motivation for using polycrystalline fillers is that they can exhibit enhanced piezoelectric and mechanical properties compared to single crystalline materials. Moreover, polycrystalline materials are amenable to scalable manufacturing. We computationally investigate these important aspects of piezoelectric composite design and performance by taking into account for the first time the polycrystalline nature of lead-free piezoelectric inclusions, in the context of a matrix-inclusion composite. We achieve this by dispersing randomly shaped polycrystalline inclusions at random positions in the matrix which allows us to better understand the behavior of practical composite architectures. In such cases, our analysis reveals that although polycrystalline piezoelectric materials, in isolation, can outperform their single crystal counterparts, in a composite architecture these enhancements are not straightforward. We identify the sources of loss which prevent polycrystalline inclusions from enhancing the performance of the composites. By tuning the dielectric environment in the matrix through the inclusion of metallic nanoparticles, we demonstrate how the performance of the composites can be further significantly improved. Specifically, when the metal nanoparticles are near the percolation threshold, we show that polycrystalline piezoelectric inclusions perform better than single crystals, with an improvement of around 14.6% in the effective piezoelectric response. We conclude that such novel architectures, devised by a combination of polycrystalline piezoelectric inclusions in a high permittivity environment, can improve the performance of the composites beyond the single crystal design and thus offer a promising direction for 3D printable lead-free piezoelectric composites.

A new approach for electro-elastic analysis of piezoelectric fiber composites with arbitrary shaped inclusions under anti-plane shear and in-plane electric loadings

Electro-elastic analysis of piezoelectric fiber composites with arbitrary shaped inclusions subjected to far field uniform anti-plane shear and in-plane electric loadings is performed in this study in order to increase the electromechanical performance and protect the vulnerable piezoelectric inclusion from electromechanical damage. A three-phase model with a representative volume element of piezoelectric fiber composites with arbitrary shaped inclusions is proposed based on the generalized self-consistent theory. Meanwhile, a new conformal mapping method based on Cauchy integral and series expansion is also proposed to map an arbitrary two-connected domain into an annular domain. Both of the electro-elastic responses and the effective moduli of the piezoelectric fiber composites with arbitrary shaped inclusions for the anti-plane problem are obtained using the complex potentials in series form and the homogenization strategy. Comparisons with literature show a good agreement. Additionally, the effects of the fiber shape and the fiber volume fraction on the normal shear stress and the tangential electric field distributions outside the piezoelectric fiber, and the effective moduli are investigated using the proposed model and method. It is shown that the normal shear stresses and the tangential electric fields outside piezoelectric fiber have intense fluctuations at the corner of the inclusion. Both of the electro-elastic responses and the effective moduli of piezoelectric fiber composites become larger as the shape of piezoelectric inclusion sharpens and the fiber volume fraction increases. Furthermore, the proposed model and method can be used for determining the appropriate shape and volume fraction of the piezoelectric inclusion to significantly reduce stress and electric field concentrations around the inclusion and optimize the electromechanical performance of piezoelectric fiber composites.