SOME PROBLEMS IN ELECTROSTRICTIVE AND MAGNETOSTRICTIVE MATERIALS

Some of the previous theories in the electrostrictive and magnetostrictive materials and their differences are discussed in this paper. A variational principle in the general thermodynamic sense is given and the governing equations can be derived from this principle. Illustrational examples are given.

Coupled FEM Analyses on Electro-mechanical Problem of Electrostrictive Plate with Elliptical Hole

A detailed theoretical construction of general coupled 3DFEM analyses of anisotropic dielectrics is first presented by considering the electric body force and body couple moment.A 3Delectrostrictive element is subsequently defined in ABAQUS user subroutine UEL and the post-processing of finite element method(FEM)results is realized by UVARM and dummy element method.Then the developed technique is used to solve the electro-elastic field of an isotropic electrostrictive plate with an elliptical hole subjected to electrical load.By comparing the coupled and uncoupled numerical results,the traditional uncoupled analytical method can cause a large error when the applied electric field or the electrostrictive performance of the dielectric is high,and thus the present coupled analysis is especially necessary.

Control model for experiments on piezoelectric and electrostrictive elements

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WAVE PROPAGATION IN ELECTROSTRICTIVE MATERIALS UNDER BIASED FIELDS

Constitutive relations for nonlinear, isotropic, electroelastic solids quadratic in the ?nite strain tensor and the referential electric ?eld are derived from the full nonlinearity theory of electroelasticity by tensor invariants, which can describe the behavior of electrostrictive ma- terials. The equations are linearized for small, dynamic ?elds superposed on ?nite, static biased ?elds. These linear equations are used to study plane waves propagating in an electroelastic body under various mechanical and/or electric biased ?elds. It is shown that the speed of the acoustic waves exhibits a strong dependence upon those material parameters in the nonlinear constitu- tive relations. Experimental determination of these material parameters using this dependence is discussed.

ANALYSIS OF AN ELECTROSTRICTIVE STACK ACTUATOR FOR ACTIVE TRAILING EDGE FLAPS

Stack\} actuator is a solid\|state driving component of Active Tailing Edge Flap in smart rotor systems. It is a multi\|layer serial structure of basic units composed of electrostrictive and adhesive layers. In this paper, a dynamic model of the actuator is derived based on the constitutive equation of electrostrictive material and the equation of motion. Theoretical analysis is made on the factors involved in the design of the actuator, which reveals that the electrostrictive layer and the adhesive layer should be optimized to compromise between displacement and frequency requirements. In the final part of the paper, the experiment of an ATEF system is introduced. The results show that the model is reasonable. It also suggests that the bending stiffness of elastic mechanism is an important factor in design, which should be carefully studied to provide satisfactory dynamic response of the ATEF system.

The Experimental Study of Micro-Tool Servo with Electrostrictive Actuator

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Ferroelectric-to-relaxor transition and ultrahigh electrostrictive effect in Sm^(3+)-doped Pb(Mg_(1/3)Nb_(2/3))O_(3)-PbTiO_(3)ferroelectrics ceramics

Rare-earth Sm^(3+)-doped Pb(Mg_(1/3)Nb_(2/3))O_(3)-0.25PbTiO_(3)(PMN-0.25PT)ferroelectric ceramics with doping amounts between 0%-3%were developed via a conventional solid-state method.The doping effect of Sm^(3+)ions on the PMN-0.25PT matrix was systematically investigated on the basis of the phase structure,temperature-dependent dielectric,ferroelectric,and electrotechnical properties.Due to the disruption of long-range ferroelectric order,the addition of Sm^(3+)ions effectively lowers the Tm(temperature corresponding to maximum permittivity)of the samples,leading to enhanced relaxor ferroelectric(RFE)characteristic and superior electric field-induced strain(electrostrain)properties at room temperature.Intriguingly,a considerable large-signal equivalent piezoelectric coefficient d∗_(33)of 2376 pm/V and a very small hysteresis were attained in the PMN-0.25PT component doped with 2.5 mol.%Sm^(3+).The findings of piezoelectric force microscopy indicate that the addition of Sm^(3+)increases the local structural heterogeneity of the PMN-0.25PT matrix and that the enhanced electromechanical performance is due to the dynamic behavior of polar nanoregions.Importantly,strong temperature-dependent electrostrain and electrostrictive coefficient Q33 are observed in the critical region around Tm in all Sm^(3+)-modified PMN-0.25PT ceramic samples studied.This work elucidates the phase transition behavior of Sm^(3+)-doped PMN-0.25PT and reveals a critical region where electrostrictive properties can be greatly improved due to a strong temperature-dependent characteristic.

Electrocaloric and electrostrictive effect of polar P(VDF-TrFE-CFE) terpolymers

The electrocaloric effect(ECE)is the adiabatic temperature change or isothermal entropy change caused by the polarization change of a dielectric material when subjected to a change of external electric field.The electrostrictive effect is a form of elastic deformation of a dielectric induced by an electric field,associated with those components of strain which are independent of reversal field direction.It was found that both the ECE,e.g.,adiabatic temperature change,and the electrostrictive strain in poly(vinylidene fluoride
trifluoroethylene
chlorofluoroethylene)(P(VDF-TrFE-CFE))terpolymers are proportional to the square of the electric field.The adiabatic temperature change
ΔT of ECE versus electric field can be illustrated using a modified Belov
Goryaga equation.
ΔT is proportional to E^(2) when E is small.For electrostrictive effect,the rigid-ion model assumes that the anharmonic movement of the ions leads to the quadratic strain
electric field relation.The quotient of electrostrictive coefficient Q over the phenomenological coefficient
is empirically a constant,indicating that the larger the electrostrictive coefficient,the larger the ECE,which opens a new way to find out new electrocaloric materials.

Enhanced strain and electrostrictive properties in lead-free BNT-based ceramics via rare earth doping

Bi_(0.5)Na_(0.5)TiO_(3)(BNT)-based ceramics are one of the most promising lead-free ferroelectrics due to their high strain property.Compared to other chemical modifications,rare earth ions doping provides sig-nificant possibility to optimize the strain property of BNT-based ceramics.In this work,the effects of rare earth ions on phase structure,microstructure,and strain&electrostrictive properties of lead-free BNT-based ceramics were systematically investigated.Rare earth ions(i.e.,La^(3+),Sm^(3+),Yb^(3+),Dy^(3+),and Nd ^(3+))were selected as the doping ions.Introducing moderate La^(3+)ions can drive the ferroelectric state of BNT-based ceramics to nonergodic relaxor state or ergodic relaxor state.The enhanced strain response of~0.40-0.42% and high converse piezoelectric coefficient of~600-630 pm/V can be achieved under 60-70 kV/cm for La^(3+)-doped ceramic with nonergodic relaxor state.Besides,the giant electrostrictive coefficient Q 33 of~0.047 m 4/C 2 can be obtained for La ^(3+)-doped ceramic with ergodic relaxor state.Other rare earth ions also present the promotion effect on strain enhancement for BNT-based ceramics.This study affords a significant guidance to optimize strain and electrostrictive properties of BNT-based ce-ramics via rare earth ions doping.

Stress analysis of electrostrictive material with an elliptic defect

It is shown that the constitutive equation and electric body force used to discuss the stress analysis of electrostrictive material in some previous literature are not appropriate. This paper presents the corrected stress solution for the infinite plane with an insulated elliptic hole under an applied electrical field. The numerical result obtained for the PMN material constants show that the stress near the end of the narrow elliptic hole is the tensile stress.

NONLINEAR ELECTROSTRICTIVE PROPERTIES OF PbZrO_(3):Sn SINGLE CRYSTALS WITH ANTIFERROELECTRIC PHASE TRANSITIONS

The electrostrictive properties above Te max represented by the field-related and polarization-related M and Q coefficients have been measured for PbZr_(1-x)Sn_(x)O_(3)single crystals with ani-ferroelectric phase transitions.The investigations presented in this paper have proved that the M_(11)(T)and Q_(11)(T)runs bring direct information of the pre-transitional effects connected with the co-existence of local polar objects with nonpolar matrix.Due to this co-existence,nonlinear Q_(11)(T)dependence in the neighborhood of T_(C)has been detected.Observed even in a wide tem-perature above T_(C),this co-existence is a natural feature of the material with ABO_(3)perovskite structure that undergoes structural transition to po lar phase.

Coupling effects between elastic and electromagnetic fields from the perspective of conservation of energy

Coupling effects among different physical fields reflect the conversion of energies from one field into another substantially.For simple physical processes,their governing or constitutive equations all satisfy the law of conservation of energy(LCE).Then,an analysis is extended to the coupling effects.First,for the linear direct and converse piezoelectric and piezomagnetic effects,their constitutive equations guarantee that the total energy is conserved during the process of energy conversion between the elastic and electromagnetic fields.However,the energies are converted via the work terms,(βijkEi),kvj and(γijkHi),kvj,rather than via the energy terms,βijkEiejk andγijkHiejk.Second,for the generalized Villari effects,the electromagnetic energy can be treated as an extra contribution to the generalized elastic energy.Third,for electrostriction and magnetostriction,both effects are induced by the Maxwell stress.Moreover,their energies are purely electromagnetic and thus both have no converse effects.During these processes,the energies can be converted in three different ways,i.e.,via the non-potential forces,via the cross-dependence of the energy terms,and directly via the electromagnetic interactions of ions and electrons.In the end,the general coupling processes which involve elastic,electromagnetic fields and diffusion are also analyzed.The advantages of using this energy formulation are that it facilitates discussion of the conversion of energies and provides better physical insights into the mechanisms of these coupling effects.

Nonlinear dynamic analysis of dielectric elastomer membrane with electrostriction

The dielectric elastomer(DE)is an important intelligent soft material widely used in soft actuators,and the dynamic response of the DE is highly nonlinear due to the material properties.In the DE,electrostriction denotes the deformation-dependent permittivity.In the present study,we formulate the nonlinear dynamic governing equations of the DE membrane considering the electrostriction effect.The free vibration and parametric excitation of the DE membrane with different geometric sizes are calculated.The free vibration bifurcations induced by the initial location and the voltage are both discussed according to an energy-based approach.The amplitude-frequency characteristics and bifurcation diagrams of parametric excitation are also given.The results show that electrostriction decreases the free vibration amplitude and increases the frequency,but it has less influence on the parametric excitation oscillation frequency and decreases the parametric excitation amplitude except when the membrane resonates.The initial location and the applied voltage can induce the snap-through instability of the free vibration.A large geometric size will lead to a much lower resonance frequency.The resonance amplitudes increase while the resonance frequencies decrease with the increase in the applied voltage.The critical voltage of snap-through instability for the parametric excitation is larger than that for the free vibration one.

The Study of Optoacoustic First and Second Sound Waves in Superfluid Helium under the Effect of Gaussian Laser Light Considering Electrostriction Mechanism

The present paper is aimed to study the effect of Gaussian laser light on first and second sound waves in superfluid helium theoretically using optoacoustic method. The mechanism applied in this study is electrostriction mechanism. This study considers crystal parts of superfluid helium with a zero absorption coefficient applying electrostriction mechanism. Affecting Gaussian laser light on these crystal parts, a spectrum of cylindrical first and second sound waves and cylindrical slow and rapid waves is obtained. Meanwhile, frequency of waves amplitudes proportionate to time period of laser light is calculated.

Surface Tension and Electrostriction in a Suspended Bridge of Dielectric Liquid

The mechanism of the formation of a surprisingly long suspended liquid bridge subjected to a dc electric field has been intensively studied in the past few decades. However, the role of electrostriction and quantitative evaluation of surface tension in the bridge have not been evaluated. We present combined theoretical and experimental studies on this issue. Electrostriction is pointed out to be the driving force that pushes liquid upward against gravity and into the gap between two containers and forms the suspended bridge, which is within the framework of the Maxwell pressure tensor. Through a comparison between experiment and theory, the surface tension is found to play an important role in holding the long suspended bridge. Ignorance of the surface tension leads to much smaller bridge length than the experimental values. The dynamic stability of the bridge with respect to its diameter, length and conductance is also discussed.

Design of superior electrostriction in BaTiO_(3) -based lead-free relaxors via the formation of polarization nanoclusters

Electrostrictive materials have wide applications in modern high-precision electronic devices.Driven by growing environmental concerns,there is demand for lead-free materials with superior electrostriction behaviors.In this study,we demonstrate a record-high electrostrictive coefficient of~0.0712 m^(4) C^(-2) in perovskite ferroelectric ceramics,along with hysteresis-free strain as well as excellent frequency and thermal stabilities,in lead-free BaTiO_(3)-based ceramics through a polarization nanocluster design.By appro-priately introducing Li+and Bi^(3+)into the BaTiO 3 lattice matrix,the long-range ferroelectric ordering can be broken,and polarization nanoclusters can be formed,resulting in a relaxor state with concurrently suppressed polariza-tion and maintained electro-strain.A three-dimensional atomic model constructed using advanced neutron total-scattering data combined with the reverse Monte Carlo method indicates the existence of Bi and Li segregations at the subnanometer scale,which confirms the prediction made by density functional theory calculations.Such a short-range chemical order destroys the long-range ferroelectric order of the off-centered Ti polar displacements and leads to the embedding of Li+/Bi ^(3+)-rich polar nanoregions in the Ba^(2+)-rich polarization disorder matrix.Further,a completely reversible electric-field-induced lattice strain is observed,giving rise to pure electrostriction without hysteresis behavior.This work provides a novel strategy for developing lead-free relaxor ferroelectrics with high electrostriction performance.

Modeling large reversible electric-field-induced strain in ferroelectric materials using 90° orientation switching

Reversible large electric-field-induced strain caused by reversible orientation switchings in BaTiO3 is modeled using the Landau's theory of phase transition. A triple well free energy function is constructed. Each of its minima is associated with one of the polarization orientations involved. Nonlinear constitu- tive laws accounting for reversible orientation switchings and electrostriction effects are obtained by using thermodynamic equilibrium conditions. Hysteretic dynamics of one-dimensional structures is described by coupled nonlinear differential equations. Double hysteretic loops in the electric and me- chanic fields are both successfully modeled. Giant reversible electrostriction is modeled as a conse-quence of reversible orientation switchings via electro-mechanical couplings. Comparisons with ex-perimental results reported in literatures are presented.

Polyurethane-based Actuators with Various Polyols

This study dealt with the electrostrictive responses of polyurethane （PU） actuators with different microphase separation structure, which was a promising candidate for a material used in polymer actuators. In order to construct PUs with different higher-order structure, PUs with various types of polyol were synthesized： poly（neopentyl glycol adipate） （PNAD）, poly（tetramethylene glycol） （PTMG）, and poly（dimethyl siloxnae） （PDMS）. Synthesized PU was characterized by Fourier transform-infrared （FT-IR） spectroscopy and gel per- meation chromatography （GPC）. Thermal analysis and mechanical properties of PU films were carried out with differential scanning calorimetry （DSC） and UTM （universal testing machine）, respectively. And PU actuator was formed in a type of monomorph, which was made by carbon black electrodes on the both surfaces of PU film by spin coating method. Actuation behavior was mainly influenced on microphase separation struc- ture and mechanical property of PU. In result, PU actuator with PNAD, polyester urethane, had the largest field-induced displacement.

On the high temperature phase transition in Ba(Zr_(0.20)Ti_(0.80))O_(3) ceramic

Temperature dependent X-ray diffraction(XRD)and dielectric properties of perovskite Ba(Zr_(0.2)Ti_(0.8))O_(3) ceramic prepared using a standard solid-state reaction process is presented.Along with phase transitions at low temperature,a new phase transition at high temperature(873℃ at 20 Hz),diffusive in character has been found where the lattice structure changes from monoclinic(space group:P2=m) to hexagonal(space group:P6=mmm).This result places present ceramic in the list of potential candidate for intended high temperature applications.The AC conductivity data followed hopping type charge conduction and supports jump relaxation model.The experimental value of d_(33)=98 pC/N was found.The dependence of polarization and strain on electric field at room temperature suggested that lead-free Ba(Zr_(0.2)Ti_(0.8))O_(3) is a promising material for electrostrictive applications.

Ultra-slim electrostrains with superior temperature-stability in leadfree sodium niobate-based ferroelectric perovskite

Large electrostrains with high temperature stability and low hysteresis are essential for applications in high-precision actuator devices.However,achieving simultaneously all three of the aforementioned features in ferroelectric ceramics remains a considerable challenge.In this work,we firstly report a high unipolar electrostrain(0.12%at 60 kV/cm)in(1ex)NaNbO_(3)-x[(Ba0.85Ca0.15)(Zr_(0.1)Ti_(0.9))O_(3)](NN-xBCZT)ferroelectric polycrystalline ceramics with excellent thermal stability(variation less than 10%in the temperature range of 30-160℃)and ultra-low hysteresis(<6%).Secondly,the high-field electrostrain response is dominated by the intrinsic electrostrictive effect,which may account for more than 80%of the electrostrain.Furthermore,due to the thermal stability of the polarization in the pure tetragonal phase,the large electrostrain demonstrates extraordinarily high stability from room temperature to 140℃.Finally,in-situ piezoelectric force microscopy reveals ultra-highly stable domain structures,which also guarantee the thermal stability of the electrostrain in(NN-xBCZT ferroelectrics ceramics.This study not only clarifies the origin of thermally stable electrostrain in NN-xBCZT ferroelectric perovskite in terms of electrostrictive effect,but also provides ideas for developing applicable ferroelectric ceramic materials used in actuator devices with excellent thermal stability.