Electroelastic field concentrations and polarization switching induced by circular electrode at the interface of piezoelectric disk composites

The electromechanical field concentrations due to circular electrode at the interface of piezoelectric disk composites have been discussed. This paper consists of two parts. In the first part, the problem of an internal electrode embedded at the interface of two dissimilar semi-infinite piezoelectric solids was formulated by means of Hankel transforms, and the solution was solved exactly. In the second part, finite element analysis was carried out to study electromechanical response in piezoelectric disk composites containing a circular electrode at the interface by introducing a model for polarization switching in local areas of field concentrations. A nonlinear behavior induced by localized polarization switching was observed between the strain and the voltage applied to the electrode.     

层状压电陶瓷致动器中力电耦合场奇异性的数值分析

首先推导了不同压电材料界面裂纹尖端处的扇形区域内包含基本方程、裂纹面D-P边界条件和交界面处边界条件的弱形式。通过假设力电耦合位移场(位移和电势)与到裂纹尖端距离的(λ 1)次方成正比,可以得到一个分析压电材料裂纹尖端处力电耦合场奇异性的特殊的一维有限元列式。该一维有限元列式只需对扇形区域在角度方向上离散,最后的总体方程为一个关于λ的二次特征根方程。探讨了层状压电陶瓷致动器中可能出现奇异力电耦合场的部位的裂纹面边界条件及交界面处边界条件,进而将该一维有限元法进行推广,用于研究了这些部位的力电耦合场的奇异性。通过数值算例与相应的精确解的比较表明该方法是正确的,而且仅用很少单元就可以得到非常精确的结果。     

Nonlinear sensing of ionic polymer metal composites

In this paper, we develop a physics-based model for the charge dynamics of ionic polymer metal composites (IPMCs) in response to mechanical deformations. The proposed chemoelectromechanical model is based on the Poisson–Nernst–Planck system that describes the evolution of the voltage field and the counterion concentration as a dynamic strain is imposed to the IPMC. We use the method of matched asymptotic expansions to find a closed form solution for the Poisson–Nernst–Planck equations and derive an equivalent nonlinear circuit model that is amenable for parametric studies. We report results for a variety of loading scenarios to gather insight into the nonlinear characteristics of IPMC electrical response and their potential application in sensors and energy harvesting devices.     

Transient response of piezoelectric composites caused by the sudden formation of localized defects

A continuum model is presented which is capable of generating the transient electroelastic field in piezoelectric composites of periodic microstructure, caused by the sudden appearance of localized defects. These defects are simulated by associating to every one of the ten piezoelectric parameters of the constituents a distinct damage variable. This procedure enables the modeling of localized cracks, soft and stiff inclusions and cavities. As a result, the constitutive equations of the piezoelectric phases appear in a specific form that includes eigen-electromechanical field variables which represent these defects. The method of solution is based on the combination of two distinct approach. In the first one, the representative cell method is employed according to which the periodic composite, which is discretized into several cells, is reduced to a problem of a single cell in the discrete Fourier transform domain. The resulting coupled elastodynamic and electric equations, initial, boundary and interfacial conditions in the transform domain are solved by employing a wave propagation in piezoelectric composite analysis which forms the second approach. The method of solution is verified by comparison with an analytical solution for the transient response of a piezoelectric material with a semi-infinite mode III-crack. Several applications are presented for the sudden formation of cracks in homogeneous and layered piezoelectric materials which are subjected to various types of electromechanical loading, and for the sudden appearance of a cavity. The effect of electromechanical coupling on the dynamic response is discussed.     

Nonlinear creep-recovery response of a polymer matrix and its composites

The nonlinear-viscoelastic response of neat epoxy resin and unidirectional graphite/epoxy and glass/epoxy composites was characterized. Numerical techniques were developed for the efficient evaluation of the viscoelastic parameters in the Schapery integral representation that was used. A microcomputer-based test facility for automatic creep-recovery testing was developed. The time-dependent response of the composites correlated well with predictions obtained using a finite-element micromechanics program with the neat-epoxy-resin viscoelastic data as input.     

Static analysis of 2-2 cement-based piezoelectric composites

Exact static analysis of 2-2 cement-based piezoelectric composites is presented based on the theory of piezo-elasticity in this paper. Displacement method was used, and the solutions of four different kinds of piezoelectric composites under load were obtained. The effects of polarization direction of piezoelectric layers and material parameters on the solutions are discussed. The relationship between the blocking force and the applied voltage for the actuators was obtained. The solutions were compared with both numerical and experimental results, and good agreement was found.     

Effective constants and electromechanical coupling coefficients of unidirectionally reinforced piezoelectric ceramics

Institute of Mechanics, Ukrainian Academy of Sciences, Kiev. Translated from Prikladnaya Mekhanika, Vol. 28, No. 3, pp. 31–42, March, 1992.     

Nonlinear magneto-electric response of a giant magnetostrictive/piezoelectric composite cylinder

In this study,we investigate the nonlinear coupling magneto-electric(ME) effect of a giant magnetostrictive/piezoelectric composite cylinder.The nonlinear constitutive relations of the ME material are taken into account,and the influences of the nonlinear material properties on the ME effect are investigated for the static and dynamic cases,respectively.The influences of different constraint conditions on the ME effect are discussed.In the dynamic case considering nonlinear material properties,the double frequency ME response(The response frequency is twice the applied magnetic frequency) is obtained and discussed,which can be used to explain the experiment phenomenon in which the input signal with frequency f is converted to the output signal with 2 f in ME laminated structures.Some calculations on nonlinear ME effect are conducted.The obtained results indicate that the nonlinear material properties affect not only the magnitude of the ME effect in the static case but also the ME response frequency in the dynamic case.     

Nonlinear shear behavior and interlaminar shear strength of unidirectional polymer matrix composites: A numerical study

Detailed finite element implementation is presented for a recently developed technique (He et al., 2012) to characterize nonlinear shear stress–strain response and interlaminar shear strength based on short-beam shear test of unidirectional polymeric composites. The material characterization couples iterative three-dimensional finite element modeling for stress calculation with digital image correlation for strain evaluation. Extensive numerical experiments were conducted to examine the dependence of the measured shear behavior on specimen and test configurations. The numerical results demonstrate that consistent results can be achieved for specimens with various span-to-thickness ratios, supporting the accurate material properties for the carbon/epoxy composite under study.     

Solution of two-dimensional scattering problem in piezoelectric/piezomagnetic media using a polarization method

Using a polarization method, the scattering problem for a two-dimensional inclusion embedded in infinite piezoelectric/piezomagnetic matrices is investigated. To achieve the purpose, the polarization method for a two-dimensional piezoelectric/piezo-magnetic "comparison body" is formulated. For simple harmonic motion, kernel of the polarization method reduces to a 2-D time-harmonic Green's function, which is ob-tained using the Radon transform. The expression is further simplified under condi-tions of low frequency of the incident wave and small diameter of the inclusion. Some analytical expressions are obtained. The analytical solutions for generalized piezoelec-tric/piezomagnetic anisotropic composites are given followed by simplified results for piezoelectric composites. Based on the latter results, two numerical results are provided for an elliptical cylindrical inclusion in a PZT-5H-matrix, showing the effect of different factors including size, shape, material properties, and piezoelectricity on the scattering cross-section.     

Domain switching and non-linear coupling of ferroelectric composites

One of the most notable characteristics of ferroelectric materials is that they could undergo spontaneous polarization and spontaneous strain changes by applied fields. Reorientation of the spontaneous polarization and spontaneous polarization strain of ferroelectric inclusions in ferroelectric composites can change microstructures and affect effective electroelastic properties of ferroelectric composites. Based on orientation distribution function and its evolution as well as switching criterion, non-linear electromechanical coupling behaviour of ferroelectric composites is studied by application of micromechanics. A constitutive model of ferroelectric composites is developed. Comparison between analytical and experimental results shows that the model presented can describe many non-linear electromechanical coupling problems of ferroelectric composites such as polarization or depolarization, etc.     

Numerical solution of polarization saturation/dielectric breakdown model in 2D finite piezoelectric media

The polarization saturation (PS) model [Gao, H., Barnett, D.M., 1996. An invariance property of local energy release rates in a strip saturation model of piezoelectric fracture. Int. J. Fract. 79, R25–R29; Gao, H., Zhang, T.Y., Tong, P., 1997. Local and global energy release rates for an electrically yielded crack in a piezoelectric ceramic. J. Mech. Phys. Solids 45, 491–510], and the dielectric breakdown (DB) model [Zhang, T.Y., Zhao, M.H., Cao, C.F., 2005. The strip dielectric breakdown model. Int. J. Fract. 132, 311–327] explain very well some experimental observations of fracture of piezoelectric ceramics. In this paper, the nonlinear hybrid extended displacement discontinuity-fundamental solution method (NLHEDD-FSM) is presented for numerical analysis of both the PS and DB models of two-dimensional (2D) finite piezoelectric media under impermeable and semi-permeable electric boundary conditions. In this NLHEDD-FSM, the solution is expressed approximately by a linear combination of fundamental solutions of the governing equations, which includes the extended point force fundamental solutions with sources placed at chosen points outside the domain of the problem under consideration, and the extended Crouch fundamental solutions with extended displacement discontinuities placed on the crack and the electric yielding zone. The coefficients of the fundamental solutions are determined by letting the approximated solution satisfy certain conditions on the boundary of the domain, on the crack face and the electric yielding zone. The zero electric displacement intensity factor in the PS model or the zero electric field strength intensity factor in the DB model at the outer tips of the electric yielding zone is used as a supplementary condition to determine the size of the electric yielding zone. Iteration approaches are adopted in the NLHEDD-FSM. The electric yielding zone is determined, and the extended intensity factors and the local J-integral are calculated for center cracks in piezoelectric strips. The effects of finite domain size, saturation property and different electric boundary conditions, as well as different models on the electric yielding zone and the local J-integral, are studied.     

Single-frequency vibrations and vibrational heating of a piezoelectric circular sandwich plate under monoharmonic electromechanical loading

The forced monoharmonic bending vibrations and dissipative heating of a piezoelectric circular sandwich plate under monoharmonic mechanical and electrical loading are studied. The core layer is passive and viscoelastic. The face layers (actuators) are piezoelectric and oppositely polarized over the thickness. The plate is subjected to harmonic pressure and electrical potential. The viscoelastic behavior of the materials is described by complex moduli dependent on the temperature of heating. The coupled nonlinear problem is solved numerically. A numerical analysis demonstrates that the natural frequency, amplitude of vibrations, mechanical stresses, and temperature of dissipative heating can be controlled by changing the area and thickness of the actuator. It is shown that the temperature dependence of the complex moduli do not affect the electric potential applied to the actuator to compensate for the mechanical stress __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 1, pp. 79–89, January 2008.     

Phase-field modeling of crack propagation in piezoelectric and ferroelectric materials with different electromechanical crack conditions

We present a family of phase-field models for fracture in piezoelectric and ferroelectric materials. These models couple a variational formulation of brittle fracture with, respectively, (1) the linear theory of piezoelectricity, and (2) a Ginzburg–Landau model of the ferroelectric microstructure to address the full complexity of the fracture phenomenon in these materials. In these models, both the cracks and the ferroelectric domain walls are represented in a diffuse way by phase-fields. The main challenge addressed here is encoding various electromechanical crack models (introduced as crack-face boundary conditions in sharp models) into the phase-field framework. The proposed models are verified through comparisons with the corresponding sharp-crack models. We also perform two dimensional finite element simulations to demonstrate the effect of the different crack-face conditions, the electromechanical loading and the media filling the crack gap on the crack propagation and the microstructure evolution. Salient features of the results are compared with experiments.     

Modeling and simulation of magnetic-shape-memory polymer composites

Composites of small magnetic-shape-memory (MSM) particles embedded in a polymer matrix have been proposed as an energy damping mechanism and as actuators. Compared to a single crystal bulk material, the production is simpler and more flexible, as both type of the polymer and geometry of the microstructure can be tuned. Compared to polycrystals, in composites the soft polymer matrix permits the active grains to deform to some extent independently; in particular the rigidity of grain boundaries arising from incompatible orientations is reduced. We study the magnetic-field-induced deformation of composites, on the basis of a continuous model incorporating elasticity and micromagnetism, in a reduced two-dimensional, plane-strain setting. The aim is to give conceptual guidance for the design of composite materials independent of the concrete macroscopic device. Thus, on the background of homogenization theory, we determine the macroscopic behavior by studying an affine-periodic cell problem. An energy descent algorithm is developed, whose main ingredients are a boundary element method for the computation of the elastic and magnetic field energies; and a combinatorial component reflecting the phase transition in the individual particles, which are assumed to be of single-domain type. Our numerical results demonstrate the behavior of the macroscopic material properties for different possible microstructures, and give suggestions for the optimization of the composite.     

二次非线性粘弹性圆板的2/1+3/1超谐解

计及材料的非线性弹性和粘性性质，研究了圆板在简谐载荷作用下的2／1＋3／1超谐解，导出了相应的非线性动力方程。提出一类强非线性动力系统的叠加－叠代谐波平衡法。将描述动力系统的二阶常微分方程，化为基本解为未知函数的基本微分方程；及分岔解为未知函数的增量微分方程。通过叠加－迭代谐波平衡法得出了圆板的2／1＋3／1超谐解。对叠加迭代谐波平衡法和数值积分法进行了比较，两者结果吻合很高。并且讨论了2／1＋3／1超谐解的渐近稳定性。     

Graded piezoelectric cylinders subjected to high electric fields and comparison of their frequency response with piezoelectric plates

In this paper we investigated a radially polarized piezoceramic cylinder with graded piezoelectric properties, and used a nonlinear model for piezoceramics subjected to high electric fields. We investigated the nonlinear behavior of this material by examining changes in its electric-field-dependent dielectric and piezoelectric coefficients caused by domain wall motion. The Galerkin finite-element method was used to solve the governing equations of the axisymmetrically loaded heterogeneous piezoceramic medium subjected to harmonic electrical loading. Stress, displacement, resonance, and frequency responses were compared for homogeneous and graded cylinders; additionally, we compared the results of linear and nonlinear studies. We showed that the effective stress was higher within the graded cylinder than within the homogeneous cylinder, and that the nonlinearity caused by domain wall motion was less pronounced for the graded cylinder than for the homogeneous cylinder. The frequency responses of homogeneous and heterogeneous piezocylinders were also compared with those of piezoelectric plates. We concluded that—unlike for graded plates, which have a more desirable frequency response than homogeneous plates—graded cylinders are not superior to homogeneous cylinders. The finite-element solution in this paper is verified by simulations using COMSOL Multiphysics software.     

Cyclic viscoelastoplasticity and low-cycle fatigue of polymer composites

Observations are reported on a polymer composite (polyamide-6 reinforced with short glass fibers) in tensile relaxation tests with various strains, tensile creep tests with various stresses, and cyclic tests with a stress-controlled program (ratcheting with a fixed maximum stress and various minimum stresses). Constitutive equations are developed in cyclic viscoelastoplasticity of polymer composites. Adjustable parameters in the stress–strain relations are found by fitting observations in relaxation tests and cyclic tests (16 cycles of loading–unloading). It is demonstrated that the model correctly predicts experimental data in creep tests and dependencies of maximum and minimum strains per cycle on number of cycles up to fatigue fracture of specimens. The influence of strain rate and minimum stress on number of cycles to failure is studied numerically.     

Thermal effects on interfacial stress transfer characteristics of carbon nanotubes/polymer composites

The paper presents an analytical method to investigate thermal effects on interfacial stress transfer characteristics of single/multi-walled carbon nanotubes/polymer composites system under thermal loading by means of thermoelastic theory and conventional fiber pullout models. In example calculations, the mechanical properties and the thermal expansion coefficients of carbon nanotubes and polymer matrix are, respectively, treated as the functions of temperature change. Numerical examples show that the interfacial shear stress transfer behavior can be described and affected by several parameters such as the temperature field, volume fraction of CNT, and numbers of wall layer and the outermost radius of carbon nanotubes. From the results carried out it is found that mismatch of thermal expansion coefficients between the carbon nanotubes and polymer matrix may be more important in governing interfacial stress transfer characteristics of carbon nanotubes/polymer composite system.     

Spontaneous bending of piezoelectric nanoribbons: Mechanics, polarization, and space charge coupling

A theory is developed to explain the spontaneous bending of polar faceted wurtzite nanoribbons, including the widely studied case of zinc oxide (ZnO) nanoarcs and nanorings. A rigorous thermodynamic treatment shows that bending of these nanoribbons can be primarily attributed to the coupling between piezoelectric effects, electric polarization, and the motion of free charge originating from point defects and/or dopants. The present theory explains the following experimental observations: the magnitude and sign of curvature and how this curvature depends on film thickness and dopant concentration. Good agreement between theory and experiment is obtained with no adjustable parameters. We identify three regimes of bending behavior with distinct thickness dependence for bending radius that depend on free carrier density, film thickness, and elastic, piezoelectric and dielectric constants.