Effective Electromechanical Properties Research Articles

Effective flexoelectric properties of inclusion-based composites based on strain gradient theory and homogenization technique

This study focuses on enhancing flexoelectricity in composites and develops a new micromechanical analytical framework to determine the effective electromechanical properties of inclusion-based flexoelectric composites within the context of SGE. Initially, we specialize in studying isotropic materials and derive the governing Navier equations for the problem. Subsequently, we streamline these differential equations by introducing a Laplacian-type gradient state variable, departing from higher-order gradient-enrichment treatments. The study employs Green’s functions and stress polarization tensors for spherical inhomogeneities, deriving homogenized material properties through volumetric averages of microscopic properties weighted by displacement localization operators. The analytical scheme’s relevance is validated against results from reference models and experimental data. Effective composite properties are evaluated using numerical methods, with an emphasis on assessing the impact of reinforcement on these properties. Our findings lay the foundation for developing a micromechanical method to predict the electromechanical behavior of composites. Specifically, we demonstrate the efficacy of our proposed theory by deriving effective flexoelectric properties of particulate composites.

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.

The influence of thermo-electromechanical coupling on the performance of lead-free BNT-PDMS piezoelectric composites

In recent times, there have been notable advancements in haptic technology, particularly in screens found on mobile phones, laptops, light-emitting diode (LED) screens, and control panels. However, it is essential to note that the progress in high-temperature haptic applications is still in the developmental phase. Due to their complex phase and domain structures, lead-free piezoelectric materials such as Bi0.5Na0.5TiO3 (BNT)-based haptic technology behave differently at high temperatures than in ambient conditions. Therefore, it is essential to investigate the aspects of thermal management and thermal stability, as temperature plays a vital role in the phase and domain transition of BNT material. A two-dimensional thermo-electromechanical model has been proposed in this study to analyze the thermal stability of the BNT-PDMS composite by analyzing the impact of temperature on effective electromechanical properties and mechanical and electric field parameters. However, the thermo-electromechanical modelling of the BNT-PDMS composite examines the macroscopic effects of the applied thermal field on mechanical and electric field parameters, as phase change and microdomain dynamics are not considered in this model. This study analyzes the impact of thermo-electromechanical coupling on the performance of the BNT-PDMS composite compared to conventional electromechanical coupling. The results predicted a significant improvement in piezoelectric response compared to electromechanical coupling due to the increased thermoelectric effect in the absence of phase change and microdomain switching for temperature boundary conditions below depolarization temperature ( Td∼200∘ C for pure BNT material).

Novel lead-free 2–1–2 composite: predicted high piezoelectric sensitivity and significant hydrostatic response

A parallel-connected composite with 2–1–2 connectivity and two lead-free single-crystal (SC) components is proposed. Its high piezoelectric sensitivity is highlighted and its large hydrostatic parameters are described. The first type of composite layer represents a ferroelectric domain-engineered [001]-poled [Li, (K, Na)](Nb, Ta)O3 SC. In the second type of composite layer, piezoelectric Li2B4O7 SC rods in the form of an elliptic cylinder are regularly aligned in a large polymer matrix. The effective electromechanical properties of the composite were found in three stages, using the effective field and matrix methods that are applicable to piezoelectric media. A new orientation effect was studied, linked with rotations of SC rod bases in the polymer medium that forms the second type of layer. Since these rotations are in a Li2B4O7 SC with a unique elastic and piezoelectric anisotropy, the second type of layer exhibits a noticeable influence on the piezoelectric performance and hydrostatic response of the composite. A variation of the aspect ratio of the Li2B4O7 rod base becomes another important factor that can improve the hydrostatic parameters of the composite. Some effective parameters of related 2–1–2 composites were compared for different polymer components. Three diagrams were first constructed for the high-performance 2–1–2 [Li, (K, Na)](Nb, Ta)O3/Li2B4O7/polyethylene composite to show the ranges of rotation angles and volume fractions that correspond to the longitudinal piezoelectric voltage coefficient > 500 mV m N−1, hydrostatic piezoelectric coefficient > 200 mVm N−1 and hydrostatic figure of merit >10−11 Pa−1. These effective parameters are important in piezoelectric sensors and hydroacoustic and other applications of novel lead-free composites.

Effective electromechanical properties and energy harvesting response in PMN-0.3PT/PDMS flexible piezoelectric composites: a combined experimental and theoretical study

In this work, lead magnesium niobate-lead titanate (PMN-0.3PT) and polydimethylsiloxane (PDMS)-based flexible piezoelectric-polymer composites are designd and developd for efficient mechanical energy harvesting through a combined experimental-theoretical approach. A solid-state reaction method was employed to synthesize PMN-0.3PT piezo-ceramic, which was subsequently used for the fabrication of -PMN-0.3PT/PDMS piezoelectric-polymer 0–3 composite with different volume fractions, = 0.03, 0.25, and 0.50 of PMN-0.3PT reinforcement. Uniformly distributed PMN-0.3PT particles were found to retain their structural symmetry across the volume fractions and are well adhered to the PDMS matrix. The effective electromechanical properties of the composites were measured and compared with model predictions employing the finite element method and Eshelby–Mori–Tanaka-based micromechanical models. Considering that flexibility is a critical design parameter, we propose a new figure-of-merit term that would consider both electromechanical conversion as well as the mechanical flexibility of the material. We show that at = 0.5, PMN-0.3PT/PDMS 0–3 composite yields an optimum combination of energy harvesting performance and flexibility. Our study further demonstrates that the orientation of the PMN-0.3PT particles does not significantly influence the effective elastic and dielectric properties at low and moderate PMN-PT content, attributed to the lower aspect ratio of the reinforcement particles. The piezoelectric charge coefficient showed small yet finite change with increasing reinforcement content. A maximum current density, 35 nA cm−2, and electric field, 90 V cm−1, was obtained with a cyclic compressive stress of 0.22 MPa (force, 50 N) at 5 Hz, in a piezoelectric generator, based on = 0.5.

Nonlinear micromechanical modeling of fully coupled piezo-elastic composite under large deformation and high electric field

This paper presents mathematical modeling and predictions of effective nonlinear electro-mechanical behavior of piezoelectric materials under large deformation and high electric field. The heterogeneous inclusion problem is extended to investigate the fields dependent electro-elastic behaviors under high fields. The associated strain field dependent Green tensors are introduced. The field dependent interaction tensors, related to Eshelby’s tensors, are explicitly formulated and used to derive micromechanical models based on the Mori–Tanaka approach and the self-consistent model. Due to electric-strain field dependence nonlinear algebraic tensors equations are resulted. Iterative incremental schemes based on the Newton–Raphson algorithm are elaborated and explicit semi-analytical formulations of electric-strain field dependent effective electro-elastic moduli of piezoelectric multi-phase composites are obtained for various inclusion types. Strain and electric field’s effects on effective properties can be analyzed for various electro-elastic composites. Numerical results of field dependent effective electro-mechanical properties are given for several inclusion’s volume fraction and shapes as well as types of matrix and inclusions phases.

Computational Micromechanics Investigation of Percolation and Effective Electro-Mechanical Properties of Carbon Nanotube/Polymer Nanocomposites using Stochastically Generated Realizations: Effects of Orientation and Waviness.

The electrical and mechanical properties of carbon nanotube/polymer nanocomposites depend strongly upon several factors such as CNT volume fraction, CNT alignment, CNT dispersion and CNT waviness among others. This work focuses on obtaining estimates and distribution for the effective electrical conductivity, elastic constants and piezoresistive properties as a function of these factors using a stochastic approach with numerous CNT/polymer realizations coupled with parallel computation. Additionally, electrical percolation volume fraction and percolation transitional behavior is also studied. The effective estimates and percolation values were found to be in good agreement with experimental works in the literature. It was found that with increasing CNT volume fraction, the mechanical properties improved. However, due to the interaction of CNTs with one another through electrical tunneling, the conductivity and piezoresistivity properties evolved in a more complex manner. While the degree of alignment played a strong role in the effective properties making them anisotropic, the effect of waviness was found to be insubstantial.

Nonlocal model of electromechanical fields and effective properties of piezoelectric materials with rigid and electrically conductive inclusions

A rigid and electrically conductive line inclusion (or electrode) in piezoelectric materials is considered under the framework of nonlocal effects for the stress and electric displacement fields. Both the piezoelectric medium and the inclusion are of finite size. The poling direction of the piezoelectric medium and the plane of inclusion are parallel. Electromechanical fields and the equivalent values of the elastic modulus, piezoelectric constants and dielectric constants along the inclusion direction are evaluated. The effect of the nonlocal parameter of the piezoelectric material is particularly remarkable for the stress and electric displacement fields. The maximum stress and electric displacement close the inclusion tip reduce as the nonlocal effect of the medium become stronger. However, the effective electromechanical properties of the piezoelectric medium do not have an apparent dependence on the nonlocal effect.

Processing‐structure‐property relationship of multilayer graphene sheet thermosetting nanocomposites manufactured by calendering

AbstractThe dispersion state of multilayer graphene sheets in polymers has a strong impact on the properties of the nanocomposite, and is driven by the processing parameters of the dispersion method. Herein, multilayer graphene sheet/vinyl ester nanocomposites were manufactured using a three‐roll mill. The roller gaps and number of processing cycles were varied to study their effect on the dispersion state and their relationship with the effective electromechanical properties of the nanocomposites. It was found that reducing the roller gaps and increasing the number of processing cycles yields smaller (up to 7.4 μm in diameter) and more densely packed (up to ~1500 agglomerates/mm2) agglomerates. Nanocomposites manufactured with the three‐roll mill contain agglomerates up to 75% smaller and more densely packed than those manufactured with an ultrasonic tip. Electrical conductivity was higher for moderately‐sized, homogeneously distributed agglomerates (23 μm in diameter) with a high areal density (~920 agglomerates/mm2), while smaller agglomerates reduced electrical conductivity. Smaller agglomerates increased the mechanical properties but decreased the piezoresistive sensitivity. The agglomerate density proved to be a key factor governing the piezoresistive sensitivity, with a lower number of agglomerates per unit area promoting higher gauge factors.

A multi-scale model for the effective electro-mechanical properties of short fiber reinforced additively manufactured ceramic matrix composites containing carbon nanotubes

It is of paramount importance to accurately predict the mechanical properties of 3D-printed components for their usage and mechanical reliability. In this study, micromechanics models (mean-field and full-field) and the resistor network model are presented for predicting the effective elastic properties and electrical conductivity of 3D-printed material ceramic matrix composite. Due to the manufacturing process, two-scale (micro-scale and meso-scale) hierarchy is identified and the homogenization at each scale is performed with the appropriate model. The proposed approach is applied to short fiber reinforced additively manufactured alumina (Al2O3) ceramic matrix composite containing multi-walled carbon nanotubes (MWCNTs). The proposed models account for the reinforcements orientation distribution, reinforcements shape, porous reinforcements and multiple reinforcements. Parametric studies were carried out to show the sensitivity of the effective electro-mechanical properties of the 3D-printed composite filament to some geometric features which are related to processing. This work provides a methodology for predicting the effective electro-mechanical properties, derived from accurate micromechanics and resistor network models, for bridging lengths scales and use in macro-scale models to evaluate the electro-mechanical performance of composites part.

Statistical analysis of effective electro-mechanical properties and percolation behavior of aligned carbon nanotube/polymer nanocomposites via computational micromechanics

CNT (carbon nanotube) embedded polymer nanocomposites exhibit significant variation in their electro-mechanical properties depending upon factors such as CNT volume fraction, CNT dispersion, CNT alignment and properties of the polymer. Of interest is electrical percolation where the electrical conductivity of the CNT/polymer nanocomposite increases several orders of magnitude with increase in CNT volume fraction. Estimates and distributions for the electrical conductivity and piezoresistive coefficients of the CNT/polymer nanocomposite are obtained and analyzed with increasing CNT volume fraction and varying barrier potential, a parameter that controls the extent of electrical tunneling. The barrier potential is seen to play a key role in determining electrical percolation in terms of the CNT volume fractions that correspond to this percolation transition. The effect of CNT alignment is analyzed by comparing the electro-mechanical properties in the alignment direction versus the transverse direction, where it is found that the properties in the alignment direction are larger than that of the transverse direction. Estimates of piezoresistive coefficients are converted into gage factors and discussed in the context of experimental sources in literature. The methodology for this work involves generating several semi-random 5μm×5μm computational realizations for different CNT volume fractions with randomized CNT seeding. These realizations are then analyzed using finite elements to obtain volume averaged effective values, which are then subsequently used to generate estimates (mean from several realizations) for mechanical stiffness, electrical conductivity and piezoresistive coefficients. The distribution in these properties is also studied using measures of coefficient of variation, skewness and kurtosis. It is found that electrical percolation can be captured by the transition of these measures of variation from low to high and back down to low values with increase in CNT volume fraction.

The effective electromechanical properties of three-dimensional piezoelectric fiber networks

Cellular piezoelectric fiber networks are highly flexible and ultra-sensitive and are promising for functional devices. However, only a few studies on the correlation between their properties and complex microstructures are available. In this paper, stochastic piezoelectric network models with either uniformly or normally distributed fiber orientations are developed. The interactions between adjacent fibers are modeled by cross-linkers. The effective electromechanical properties of the networks are investigated by a commercially available finite element (FE) software in conjunction with a piezoelectric beam theory based user element. Theoretical analyses are also presented. A linear dependency of the effective elastic constants and piezoelectric stress constants on relative density is obtained, consistent with the stretching dominated deformation mechanism of the networks. The role of fiber orientation in the macroscopic electromechanical properties is elucidated, showing that piezoelectric networks with fiber orientation deviating from uniform distribution can have better elastic and piezoelectric stress coefficients. These findings can provide a design guide for the applications of fiber-based piezoelectric sensors and energy harvesters.

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.

Improved analytical homogenization of the piezoelectric macro-fiber composite: active layer embedded among passive layers

Predicting the effective electromechanical properties for piezoelectric fiber composite patches is crucial for analysis of smart structures equipped with such patches. In particular, analytical homogenization models are attractive but are limited by the complexity of the microstructure and the multiphysics involved. The macro-fiber composite (MFC) has emerged as the most popular piezoelectric fiber composite. But typical reports of its effective properties provide layerwise homogenization with low-order mechanical plate theories. This approach discards most of the out-of-plane properties and may introduce significant error from the assumptions about the plate kinematics. Moreover, the effective permittivities of the transducer are not available analytically. In an attempt to overcome these limitations, a new analytical scheme for homogenizing all layers in the MFC patch is proposed. Based on the newly discovered mechanics of structure genome, we avoid all kinematical assumptions and obtain an exact analytical solution for a periodic, multi-layered, linear-piezoelectric material. In doing so, we prove that in any such multi-layered composite, the in-plane strains and the transverse stresses are equal in each layer and the in-plane electric fields and transverse electric displacement are constant between the electrodes. Using this knowledge, a hybrid rule of mixtures is developed to homogenize all the MFC layers to obtain the complete set of properties of the full MFC. In doing the new analytical framework can homogenize any layered piezoelectric medium. Finally, since we were able to avoid the plate-kinematics assumptions, we present studies on their effect on the properties they obtain. We find that the in-plane elastic properties are not affected but the transverse shear moduli are overpredicted from 100% to 300%. What is more, studies are presented on how using the ubiquitous plane-stress-like assumptions to homogenize the fiber layers causes an 8% underprediction of the lateral elastic modulus of the MFC.

A balanced laminate of piezoelectric fiber composite for improved shear piezoelectric actuation of beams

A new balanced laminate of piezoelectric fiber composite (PFC) is presented for the improved shear mode piezoelectric actuation of beams. A micromechanics formulation is first presented for determination of its effective electromechanical properties, and then its shear actuation capability is investigated by means of utilizing it for actuation of bending deformation of a smart sandwich beam. The results reveal an indicatively higher shear actuation capability of the present balanced laminate of PFC over that of the monolithic shear piezoelectric actuators, and thus this laminate of PFC may be a potential material for shear piezoelectric actuators in control of flexible structures.

In-situ observation of evolving microstructural damage and associated effective electro-mechanical properties of PZT during bipolar electrical fatigue

We investigate the fatigue behavior of bulk polycrystalline lead zirconate titanate (PZT) during bipolar electric field cycling. We characterize the frequency- and cycle-dependent degradation in both the effective electro-mechanical properties (specifically, the electrical hysteresis and the macroscopic viscoelastic stiffness and damping measured by Broadband Electromechanical Spectroscopy, BES) and the microstructural damage evolution (quantified via scanning electron microscopy). The BES setup enables the mechanical characterization while performing electrical cycling so as to measure the evolving viscoelasticity without remounting the sample; particularly measuring the viscoelastic damping allows us to gain insight into the ferroelectric domain wall activity across the full electric hysteresis and over the full range of cycles. A clear dependence on the electric cycling frequency is observed in the rates of degradation of all measured properties including an up to 10% increase in dynamic compliance and a 70% decrease in electric displacement magnitude. We quantify the evolving micro-crack density across wide ranges of numbers of cycles and compare with changes in the effective compliance. Interestingly, the observed strong degradation in the ferroelectric hysteresis is contrasted by relatively mild changes in the effective viscoelastic moduli, while samples clearly indicate increasing levels of micro-damage.

Anisotropy Factors and Electromechanical Coupling in Lead-Free 1-3-Type Composites.

The effective electromechanical properties and anisotropy factors of novel lead-free 1-3-type composites are studied to demonstrate their large piezoelectric anisotropy and considerable level of electromechanical coupling. The composites studied contain two single-crystal (SC) components and a polymer component. The first piezoactive component is a domain-engineered [001]-poled SC based on ferroelectric alkali niobates-tantalates, and this component is in the form of a system of long rods that are parallel to the poling axis . The second SC component is a system of spheroidal piezoelectric Li2B4O7 inclusions aligned in a continuous and relatively large polymer matrix. The SC rods are surrounded by an SC/polymer matrix, and the connectivity of the composite is 1-0-3. It is shown that the conditions , which indicates a large degree of anisotropy of the piezoelectric coefficients, and and , which indicate a large anisotropy of the electromechanical coupling factors (ECFs), can be achieved simultaneously in specific ranges of the component volume fractions and inclusion aspect ratios. Moreover, in the same volume-fraction and aspect-ratio ranges, large ECFs ( -0.9) are also achieved. In this context, the important role of the elastic properties of the continuous anisotropic matrix is discussed. The properties and anisotropy factors of the lead-free 1-3-type composites are compared to the similar parameters of conventional lead-containing piezoelectric materials, and the advantages of the composite system studied are described.

Elastic properties and frequency characteristics of a piezo-active 3–0-type corundum-containing composite

A 3–0-type composite, that contains the PZT-type ferroelectric and corundum ceramics, is characterised as a piezoelectric material with relatively stable resonance frequencies for the planar and thickness modes of oscillation. The 3–0-type composite is manufactured by solid state sintering, the resulting composite microgeometry is studied by electronic microscopy, and parameters of the composite are measured by using the resonance-antiresonance method. It is observed that almost equal volume fractions of corundum mc and air pores mp are detected in the composite samples at 0.05 < mc < 0.18. The presence of both the corundum inclusions and air pores at an almost equal volume fraction influences the elastic properties and resonance frequencies. Experimental results on the elastic properties and frequency characteristics of the composite are interpreted in terms of a model that takes into account the electromechanical interaction between the 3–0 ferroelectric ceramic/corundum and 3–0 ferroelectric ceramic/pore regions. Effective electromechanical properties and related parameters of the composite are evaluated in terms of the effective field method and dilute approximation. The studied 3–0-type composite has potential to be applied as an active element of piezoelectric transducers, sensors, and other piezotechnical devices.

Dynamic modeling of smart shear-deformable heterogeneous piezoelectric nanobeams resting on Winkler–Pasternak foundation

Free vibration analysis is presented for a simply supported, functionally graded piezoelectric (FGP) nanobeam embedded on elastic foundation in the framework of third-order parabolic shear deformation beam theory. Effective electro-mechanical properties of FGP nanobeam are supposed to be variable throughout the thickness based on power-law model. To incorporate the small size effects into the local model, Eringen’s nonlocal elasticity theory is adopted. Analytical solution is implemented to solve the size-dependent buckling analysis of FGP nanobeams based upon a higher-order shear deformation beam theory where coupled equations obtained using Hamilton’s principle exist for such beams. Some numerical results for natural frequencies of the FGP nanobeams are prepared, which include the influences of elastic coefficients of foundation, electric voltage, material and geometrical parameters and mode number. This study is motivated by the absence of articles in the technical literature and provides beneficial results for accurate FGP structures design.

On the relationships between cellular structure, deformation modes and electromechanical properties of piezoelectric cellular solids

Piezoelectrically active cellular solids are reminiscent of passive structural cellular solids, and therefore, depending on their inner cellular architecture, their cellular ligaments can deform locally by either bending or axial stretching. Three main cellular solid structures (i.e. hexagonal, tetragonal and triangular) that exemplify bending and stretching dominated piezoelectrically active cellular solids are considered. Three-dimensional finite element models were developed to understand the relationships between cellular structure, deformation modes and their effective electromechanical properties. The principal elastic, dielectric and piezoelectric properties of piezoelectric 3-1 cellular solids are insensitive to inner structure or topology in the longitudinally poled systems and highly sensitive to structure in the transversely poled systems. The in-plane electromechanical properties are highly sensitive to cellular architecture and connectivity as well. The effective out-of-plane elastic properties for all the three cellular structures depend linearly on relative density (i.e. stretching dominated), while the dependence of the in-plane effective elastic properties is linear for triangular and tetragonal cellular structures (i.e. stretching dominated) and generally non-linear for hexagonal honeycombs (i.e. bending dominated). Amongst the longitudinally poled systems, the triangular structures exhibit the highest in-plane stiffness properties. Amongst the transversely poled systems, the tetragonal structure exhibits the best overall combination of piezoelectric figures of merit.