Effective Electroelastic Properties Research Articles

Improving the energy density and flexibility of PMN-0.3PT based piezoelectric generator by composite designing

Ceramics based piezoelectric generators are known for their high energy density and poor flexibility. In this work, 0.7Pb(Mg1/3Nb2/3O3)-0.3PbTiO3 (PMN-0.3PT) and polydimethylsiloxane (PDMS) based 2–2 composite with optimum PMN-0.3PT content (vr) was designed that demonstrated enhanced output energy density and superior mechanical flexibility under dynamic mechanical excitation. vr-PMN-0.3PT/PDMS 2–2 composite with different PMN-PT reinforcement content (vr) and two different reinforcement configurations were fabricated and characterized for effective electro-elastic properties and energy harvesting response. Parallelly, using the finite element method and analytical models, effective electromechanical properties were calculated. Composites with parallel connectivity of the reinforcement phase demonstrated enhanced piezoelectric charge coefficient (d33c) even with low PMN-0.3PT content whereas the relative permittivity (κ33c) and elastic modulus (E33c) exhibited a linearly increasing trend with reinforcement volume fraction. At a compressive load of 50 N and 5 Hz frequency, a piezoelectric generator (PG) based on a vr = 0.2, vr- PMN-0.3PT/PDMS 2–2 composite with parallel connectivity produced a maximum short-circuit current density of 69 nA/cm2 and an open-circuit electric field of 189 V/cm, translating to a maximum output power density of ∼13 μW/cm3 higher than that of pristine PMN-0.3 PT based piezoelectric generator. Estimated mechanical flexibility was found to be ∼53 % higher than that of pristine PMN-0.3PT.

Random distribution of interphase characteristics on the overall electro-mechanical properties of CNT piezo nanocomposite: Micromechanical modeling and Monte Carlo simulation

A phenomenological study is carried out to speculate the statistical impacts of the CNT/polymer interphase on the overall electro-elastic behavior of piezo-polymer nanocomposites by presenting a full-field micromechanical model. The nanocomposite system consists of carbon nanotube (CNT) and PVDF. Various statistical distributions, including Weibull, log-normal, normal, beta, and uniform distributions on the thickness and strength of the interphase are carefully assessed. The results are compared with experimental data, and satisfactory agreements are reported. It is found that, compared to the random distribution of the interphase strength, the statistical distribution of the interphase thickness has more effect on the overall electro-elastic properties. For example, for the effective longitudinal modulus, the overall coefficients of variation are 14 %, 13 %, 13.56, and 10 %, respectively, for the normal, Weibull, beta, and uniform distributions of the thickness compared with the measured experimental values. Also, the effects of the CNT content, aspect ratio, and orientation on the effective electro-elastic properties by considering the various random distributions are fully examined. Moreover, using the Monte Carlo simulation, the probability of not meeting design specification (failure probability) is evaluated at the random distributions of the interphase strength and thickness to identify the optimum CNT content for which the values of the overall properties are maximum. It is obtained that the failure probabilities are different for 5–8 % CNT volume fraction in the distributions of the thickness, and for only 5 VF% CNT in the strength distributions. For other values of the CNT content, the failure probabilities are independent of the distribution of the interphase strength and thickness.

ЭЛЕКТРОУПРУГИЕ СВОЙСТВА НАЧАЛЬНО-НАПРЯЖЕННОЙ ПЬЕЗОКЕРАМИКИ PZT-4 С ОДНОНАПРАВЛЕННЫМИ ТУННЕЛЬНЫМИ ПОРАМИ

Prediction results and numerical analysis of effect on effective transversal-isotropic electroelastic properties of porous piezoceramics of PZT-4 with unidirectional cylindrical (tunnel) pores of values of its initial axisymmetric stress state are presented. Effective constants have been identified: Young's and shear modules, Poisson's ratio in the transversal plane of isotropy and the "longitudinally/transverse" piezomodule of porous ceramics, which are most significantly influenced by the nature and values of its initial deformation in comparison with other practically "invariant" constants. It has been found that the "transversal" hydrostatic initial deformation of the porous ceramic has a greater effect on the effective constants of the porous ceramic than the same values of the "longitudinal" axial initial deformation.

Study on effective electroelastic properties of one-dimensional hexagonal piezoelectric quasicrystal containing randomly oriented inclusions

In this paper, the effective electroelastic properties of one-dimensional (1D) hexagonal piezoelectric quasicrystal containing randomly oriented inclusions are considered. The explicit expressions are obtained for the Eshelby tensors for 1D hexagonal piezoelectric quasicrystals containing rod-shaped and penny-shaped inclusions. The closed forms of the electroelastic constants are acquired for four special cases of random orientations of inclusions. Numerical results are given for the 1D hexagonal piezoelectric quasicrystal containing randomly oriented ellipsoidal inclusions. The results indicate that the effective electroelastic properties of 1D hexagonal piezoelectric quasicrystal composites are strongly affected by both the aspect ratio and the orientation of inclusions.

Theoretical study on dynamic effective electroelastic properties of random piezoelectric composites with aligned inhomogeneities

Theoretical study on dynamic effective electroelastic properties of random piezoelectric composites with aligned inhomogeneities

Micromechanical modeling for the prediction of time-dependent effective properties and macroscopic coupled field response of polymer reinforced piezoelectric composites

In the time domain, a new straightforward micromechanical modeling is developed to predict the time-dependent behavior and the macroscopic coupled response of polymer piezoelectric composite materials. The modeling is based on the dynamic electroelastic Green’s tensor allowing the derivation of convolution localization equations in Stieltjes space. The Mori-Tanaka micromechanical model is adopted to derivate the dynamic electroelastic localization tensor. The presented modeling leads to an expression of the time-dependent effective electroelastic properties directly in the time domain, without an iteration procedure, through convolution products in Stieltjes space. It allows the prediction of the time-dependent behavior and the coupled macroscopic response while taking into account the constituent properties, volume fractions, and shape of inclusions. In implementing the expression of the effective behavior, one has to go through the computation of direct and inverse tensorial convolution products. A trapezoidal numerical scheme is adopted for this sake. Many numerical results are presented, and for the sake of validation, a comparison is made with the ones obtained based on the Laplace transform approach as well as with experimental and numerical results.

A Mori–Tanaka Based Micromechanical Model for Predicting the Effective Electroelastic Properties of Orthotropic Piezoelectric Composites with Spherical Inclusions

Piezoelectric nanocomposites consisting of an orthotropic piezo-active polymer matrix and with piezo-ceramic nanoparticles as reinforcement are potential candidates as materials for structural components of the next-generation energy-harvesting micro-devices that are compatible with flexible electronics. Prediction of effective electroelastic properties of such piezoelectric composites is an essential step towards design and development of such energy-harvesting micro/nano-structures. This paper proposes a micromechanical model for determination of effective elastic, piezoelectric and dielectric properties of unidirectional piezoelectric polymer composites having spherical type inclusions embedded in an orthotropic matrix. The model is based on Mori–Tanaka’s mean field homogenization scheme and involves the determination of piezoelectric Eshelby tensors. As an example, the effective electromechanical properties of PVDF (polyvinylidene fluoride)/PZT 7A (lead zirconate titanate) composite were determined using the micromechanical model and the results were validated with a finite element model and with experimental data available in literature. The results demonstrate that the micromechanics model developed here successfully predicts the effective electroelastic properties of piezoelectric orthotropic composite at low volume fractions of the reinforcement.

Maxwell homogenization scheme for piezoelectric composites with arbitrarily-oriented spheroidal inhomogeneities

In this work, the effective electro-elastic properties of piezoelectric composites are computed using the Maxwell homogenization method (MHM). The composites are made by several families of spheroidal inhomogeneities embedded in a homogeneous infinite medium (matrix). Each family of spheroidal inhomogeneities is made of the same material, and all the inhomogeneities have identical size and shape and are randomly oriented. The inhomogeneities and matrix materials exhibit piezoelectric transversely isotropic symmetry. It is shown that the shape of the “effective inclusion” substantially affects the effective piezoelectric properties. A new and simple form to calculate the aspect ratio of effective inclusion is presented. The effect on the overall piezoelectric properties due to the orientation of the inhomogeneities and different families of piezoelectric inhomogeneities is discussed. The MHM approach is applied in two examples, material with inhomogeneities having scatter orientation and composites with two different families of spheroidal inhomogeneities.

Overall properties of piezoelectric composites with spring-type imperfect interfaces using the mechanics of structure genome

In this study, the mechanics of structure genome has been extended to piezoelasticity problem of composite materials with spring-type imperfect interfaces model. This full field micromechanics approach is applied to predict the effective electro-elastic properties of piezoelectric composite materials containing imperfect contact between the matrix and the reinforcements. Examples of long fibers and spherical particles reinforced piezoelectric composite materials are used to demonstrate the robustness and accuracy of the proposed micromechanics theory. The size-dependency of the overall electro-elastic properties shows the importance of imperfect interfaces in modeling the electro-elastic behavior of composite materials.

Implementation of multiphase piezoelectric composites energy harvester on aircraft wingbox structure with fuel saving evaluation

The multiphase composite with active structural fiber (ASF) has proven able to provide better optimization between actuating and load bearing capability compared to a pure piezoelectric material. In this paper, the multiphase composite application is further extended for energy harvesting purpose. The Double-Inclusion model combined with Mori-Tanaka method is implemented in a computational code to estimate the effective electro-elastic properties of the multiphase composite. The effective composite properties obtained via the present code are in good agreement with the analytical, experimental and finite element results. The multiphase composite with different composition is applied to a typical jet aircraft wingbox with 14.5 m halfspan. The energy harvesting evaluation by means of hybrid FEM/analytical piezoelectric energy harvester model is presented. A new procedure to investigate the trade-off between the aircraft weight, the fuel saving and the energy harvested is developed. The results pointed out that the equivalent fuel saved from the power generated by the wingbox is more than enough for 1 h Auxiliary Power Unit (APU) operation.

Application of Mori–Tanaka method in 3–1 porous piezoelectric medium of crystal class 6

We consider a piezoelectric medium of hexagonal crystal system of class 6 containing a uniform distribution of circular cylindrical inclusions aligned with the axis of material symmetry. We determine the piezoelectric Eshelby tensor explicitly. In the case of cylindrical holes, we use the Eshelby tensor together with the multiscale Mori–Tanaka Method to obtain analytical formulae for the effective electroelastic properties of the homogenized medium. These formulae depend upon both the electroelastic properties of the matrix material and the volume fraction of the cylindrical holes. Using electroelastic properties reported in the literature, we obtain graphs of the effective properties of the porous medium versus the volume fraction of the pores and show that these effective electroelastic properties decrease for increasing porous volume fraction, as expected. In particular, for the case of the crystal subclass 6 mm, the results obtained via Mori–Tanaka Method agree well with results obtained via Method of Asymptotic Homogenization and Finite Element Method. This work is important in the evaluation of the effective electroelastic properties of heterogeneous solids with hierarchical structures, such as bones.

Numerical prediction of effective electro-elastic properties of three-dimensional braided piezoelectric ceramic composites

In this paper, a novel three-dimensional (3D) braided piezoelectric ceramic composites (BPCC) is developed to improve the mechanical properties of piezoelectric ceramics. Based on the reasonable three-cell model and finite element method, the numerical model of the 3D BPCC in displacement-electric coupling field is established. The effect of fiber volume fraction on the effective electro-elastic coefficients is investigated. The differences in the effective electro-elastic coefficients between the 3D BPCC and continuous straight fiber reinforced piezoelectric ceramic composites (SFPC) are demonstrated. Numerical results show that the 3D BPCC has excellent overall mechanical properties and electrical properties.

A crack with surface effects in a piezoelectric material

We study the contribution of surface piezoelectricity to the anti-plane deformations of a hexagonal piezoelectric material weakened by a crack. The surface piezoelectricity is incorporated by using an extended version of the continuum-based surface/interface model of Gurtin and Murdoch. The original boundary value problem is finally reduced to a system of two coupled first-order Cauchy singular integro-differential equations by considering a distribution of line dislocations and electric-potential-dislocations on the crack. Through a diagonalization strategy, the coupled system can be transformed into two independent singular integro-differential equations, each of which contains only one single unknown function and can be numerically solved by the collocation method. Our solution demonstrates that the stresses, strains, electric displacements and electric displacements exhibit the logarithmic singularity at the crack tips. The obtained solution is further used to predict the size-dependent effective electroelastic properties of a piezoelectric solid containing multiple nanocracks with surface piezoelectricity within the framework of non-interaction approximation.

Smart damping of vibration of annular plates by the design of a cylindrically orthotropic piezoelectric fiber-reinforced composite actuator

In the present work, the active control of vibration of annular plates is presented by the design of a cylindrically orthotropic short/continuous piezoelectric fiber-reinforced composite (SPFRC/CPFRC) actuator. The unidirectional piezoelectric fibers of the smart composite are oriented along the radial direction within a reference cylindrical coordinate frame and poled in the same direction. First, a finite element analysis of the effective electro-elastic properties of the smart composite is presented, and the optimal geometry of its unit cell is determined with an objective of improved magnitude of an effective piezoelectric coefficient (e11, 1 for radial direction) for both short (SPFRC) and continuous (CPFRC) forms of piezoelectric fibers. Next, an arrangement of surface electrodes is presented for its effectual utilization as an actuator based on the coefficient e11. Subsequently, the smart actuator is attached to the surface of a host annular plate in the form of actuator patches for substantiating its control performance by the numerical evaluation of controlled frequency responses of the overall smart annular plate. The actuator patches act as smart dampers by means of supplying voltage according to the velocity feedback control strategy. The numerical results reveal more control power of the SPFRC actuator than that of a CPFRC actuator even though the magnitude of the major effective coefficient (e11) for SPFRC is lesser than that for CPFRC. The overall analysis shows a meaningful control power of present cylindrically orthotropic SPFRC/CPFRC actuators in control of vibration of annular plates and suggests short piezoelectric fibers instead of continuous fibers within it (smart actuator) for achieving its larger control power, flexibility and conformability.

Design and finite element analysis of a short piezoelectric fiber-reinforced composite actuator

Piezoelectric distributed actuators are exhaustively utilized in control of the structural deformation/vibration. These actuators are also used in the form of smart composite of which active fiber composite (AFC) and macro-fiber composite (MFC) are the most popular smart composites. In the present work, few shortcomings of MFC/AFC actuator in its structural applications are identified and those are alleviated through the proposition of a short piezoelectric fiber-reinforced composite (SPFRC) actuator. The SPFRC is composed of equally spaced coaxial short piezoelectric fibers embedded within the polymer matrix. Every fiber is poled along its length that yields maximum piezoelectric stress/strain within the composite along the same direction in effect of co-directional applied electric field. This piezoelectric effect quantified by the coefficient (e11) is the main parameter in its use as an actuator with a special arrangement of electrodes in microscale. The SPFRC is designed with an objective of improved magnitude of major effective coefficient (e11), and it is performed through a continuum micro-mechanics finite element analysis of its effective electro-elastic properties. The actuation-capability of SPFRC actuator according to its present design is verified by analyzing the geometrically nonlinear electro-elastic deformations of a simply supported smart beam. The micro-mechanics analysis reveals a significant magnitude of e11 of SPFRC although it is lesser than the case of continuous fibers within the similar composite. However, the analysis of smart beam reveals better actuation-capability of the smart composite actuator when short fibers are used instead of continuous fibers retaining the same applied voltage and electrodes.

Dynamic effective property of piezoelectric composites with coated piezoelectric nano-fibers

Abstract This paper addresses the size-dependent dynamic effective electro-elastic properties of piezoelectric composites embedded with coated piezoelectric nano-fibers. By using the Effective Field Method of electric–elastic coupling wave, the randomly distributed coated nano-fibers in the piezoelectric media are reduced into a typical piezoelectric coated nano-fiber. To analyze the size-dependent effect, the coupling surface/interface theory is introduced to analyze the interface effect around the coating layers. Wave function expansion method is used to express the coupling wave field in the effective coupling field. The piezoelectrically stiffened elastic modulus and effective coupling wave number are obtained. Through analysis, it is found that the coupling surface/interface effect on the piezoelectrically stiffened elastic modulus show significant variation with the material properties of coating layer and the incident wave frequency. The effect of piezoelectric property of surfaces/interfaces on the effective shear modulus is also examined. Comparison with the existing results is given to validate this dynamic electro-elastic model.

Twelve-dimensional Stroh-like formalism for Kirchhoff anisotropic piezoelectric thin plates

A twelve-dimensional Stroh-like formalism is developed for the coupled stretching, bending and polarization of a Kirchhoff anisotropic piezoelectric thin plate which is inhomogeneous and laminated along the thickness direction. The structure and explicit expressions of the fundamental piezoelectric plate matrix and its inverse form are established. The formalism in a rotated coordinate system is presented. Then the fundamental piezoelectric plate matrix in dual coordinate systems can be addressed. Some identities associated with the new formalism are derived. It is rigorously proved that each 3×3 partitioned matrix of the introduced three 6×6 real matrices S, H and L and the 6×6 Hermitian matrix M is a second-order tensor. Sixty-four permuted forms of the twelve-dimensional formalism are presented. Finally, to demonstrate the applications of the new formalism, we investigate the effective electroelastic properties of a microcracked anisotropic piezoelectric thin plate within the framework of non-interaction approximation (NIA) and study the asymptotic problem associated with a semi-infinite interface crack between two dissimilar piezoelectric thin plates.

Evaluation of effective electroelastic properties of piezoelectric coated nano-inclusion composites with interface effect under antiplane shear

A theoretical study on piezoelectric coated nano-inclusion composites with interface effect under antiplane shear is reported. Based on the theory of Gurtin–Murdoch surface/interface theory and the generalized self-consistent method, a closed-form solution of the effective electroelastic moduli are obtained. The numerical results reveal the size dependence of the effective electroelastic moduli when the size of the coating and inclusion are on the order of nanometer. The effects of the coating thickness and inclusion radius on the effective electroelastic moduli of the composites are discussed.

Multi-Inclusion modeling of multiphase piezoelectric composites

Recent work on multifunctional materials has shown that a functionally graded interface between the fiber and matrix of a composite material can lead to improved strength and stiffness while simultaneously affording piezoelectric properties to the composite. However the modeling of this functional gradient is difficult through micromechanics models without discretizing the gradient into numerous layers of varying properties. In order to facilitate the design of these multiphase piezoelectric composites, accurate models are required. In this work, Multi-Inclusion models are extended to predict the effective electroelastic properties of multiphase piezoelectric composites. To evaluate the micromechanics modeling results, a three dimensional finite element model of a four-phase piezoelectric composite was created in the commercial finite element software ABAQUS with different volume fractions and aspect ratios. The simulations showed excellent agreement for multiphase piezoelectric composites, and thus the modeling approach has been applied to study the overall electroelastic properties of a composite with zinc oxide nanowires grown on carbon fibers embedded in the polymer. The results of this case study demonstrate the importance of the approach and show the system cannot be accurately modeled with a homogenized interphase.

An eigenfunction expansion-variational method for the anti-plane electroelastic behavior of three-phase fiber composites

The anti-plane electroelastic behavior of three-phase piezoelectric composites (fiber/interphase/matrix) with doubly periodic microstructures is dealt with. A new variational functional for a unit cell is constructed by incorporating the periodic boundary conditions into the energy functional. Then, by combining with the eigenfunction expansions of the complex potentials satisfying the fiber–interphase–matrix interfacial conditions, an eigenfunction expansion-variational method based on a unit cell is developed. The numerical results of the effective electroelastic moduli show a rapid convergence of the present method. A unified first-order approximation formula is also provided, where an equivalent parameter matrix reflecting the overall influence of the electroelastic properties of the fiber and interphase on the effective properties, is found. The equivalent parameter matrix can greatly simplify the complicated relation of the effective electroelastic properties to the internal structure of a three-phase fiber composite. Though the equivalent parameter matrix is extracted in the first-order approximation formula, its validity is also verified in the high-order numerical results.