Search Results (18)

This study investigates the two-dimensional (2D) steady-state frictional contact behavior of functionally graded piezoelectric material (FGPM) coatings under a high-speed rigid cylindrical punch. An electromechanical coupled contact model considering inertial effects is established, while a layered model is employed to simulate arbitrarily varying material parameters. Based on piezoelectric elasticity theory, the steady-state governing equations for the coupled system are derived. By utilizing the transfer matrix method and the Fourier integral transform, the boundary value problem is converted into a system of coupled Cauchy singular integral equations of the first and second kinds in the frequency domain. These equations are solved semi-analytically, using the least squares method combined with an iterative algorithm. Taking a power-law gradient distribution as a case study, the effects of the gradient index, relative sliding speed, and friction coefficient on the contact pressure, in-plane stress, and electric displacement are systematically analyzed. Furthermore, the contact responses of FGPM coatings with power-law, exponential, and sinusoidal gradient profiles are compared. The findings provide a theoretical foundation for the optimal design of FGPM coatings and for enhancing their operational reliability under high-speed service conditions. Full article

Piezoelectric materials have garnered significant attention due to their diverse applications in technologies such as sensors, actuators, and energy-harvesting systems. This study focuses on the growth and characterization of Tb³⁺-doped La₃Ga₅SiO₁₄ (LGS) crystals. A novel 10% Tb³⁺-doped single LGS crystal was successfully grown using the Czochralski method. The crystal structure and fluorescence properties were determined, and the electro-elastic properties were evaluated by the impedance method, which assessed dielectric, piezoelectric, and elastic constants. The Tb³⁺-doped crystal was observed to crystallize in the trigonal system, with the concentration of the Tb³⁺ ion in the crystal determined to be 2.50 wt%. The piezoelectric coefficients were measured as d₁₁ = 5.41 pC/N and d₁₄ = −5.52 pC/N, and the dielectric constants were found to be 19.60 and 52.75, respectively. The temperature-dependent behavior of Tb:LGS crystals was investigated, particularly concerning their elastic constants, demonstrating favorable thermal stability. This study provides valuable insights into the relationship between the crystals’ structural characteristics and performance. Additionally, the fluorescence properties were measured; a long lifetime (τ = 1.655 ms) indicated the potential applications of Tb:LGS crystals in laser technology. Full article

As a category of polymeric materials, soft dielectrics, such as most elastomers and rubber-like materials, have shown great potential for extensive applications in various fields. Owing to their intriguing electromechanical coupling behaviors, the morphological instabilities in soft dielectrics have been an active research field in recent years. In this work, the recent progress in experimental and theoretical research on their electromechanical morphological instabilities is reviewed, especially regarding the theoretical aspect. First, we revisit the theoretical framework for the electroelasticity of soft dielectrics. Then, the typical configurations of soft dielectric membranes used to generate two typical types of surface instabilities, namely wrinkles and creases, are introduced. Three commonly used modeling approaches (i.e., the stress balance method, the incremental method, and the energy method) for surface instabilities are reviewed with specific examples. Moreover, discussions on the difference between these methods and the corresponding critical loading conditions are presented. Furthermore, this review also covers the relation and transition between wrinkling and creasing phenomena. Full article

Dielectric elastomers have attracted considerable attention both from academia and industry alike over the last two decades due to their superior mechanical properties. In parallel, research on the mechanical properties of dielectrics has been steadily advancing, including the theoretical, experimental, and numerical aspects. It has been recognized that the electromechanical coupling property of dielectric materials can be utilized to drive deformations in functional devices in a more controllable and intelligent manner. This paper reviews recent advances in the theory of dielectrics, with specific attention focused on the theory proposed by Dorfmann and Ogden. Additionally, we provide examples illustrating the application of this theory to analyze the electromechanical deformations and the associated bifurcations in soft dielectrics. We compared the bifurcations in elastic and dielectric materials and found that only compressive bifurcation modes exist in elastic structures, whereas both compressive and tensile modes coexist in dielectric structures. We summarize two proposed ways to suppress and prevent the tensile bifurcations in dielectric materials. We hope that this literature survey will foster further advancements in the field of the electroelastic theory of soft dielectrics. Full article

To significantly reduce the amplitude of longitudinal vibrations of the beam in the vicinity of its natural frequencies, a fundamentally new method of damping vibrations is used. For this purpose, the beam surfaces are covered with layers of polarized piezoceramics with a strong piezoelectric effect. We will use two types of electrical conditions on the electrodes of the piezoelectric layers: short-circuited electrodes and disconnected electrodes. On short-circuited electrodes, the electric potential is zero. As a result of the piezoelectric effect, an electric charge appears on the disconnected electrodes when the beam is deformed. The electroelastic state of a beam with different electrical conditions is described by different boundary value problems. A new approach to damping vibrations in the vicinity of natural frequencies is based on the following rule for controlling the dynamic characteristics of a structure: when the beam vibration frequency approaches its natural vibration frequency, we change the electrical conditions on the electrodes of the piezoelectric layers, thereby changing the spectrum of its natural frequencies. Let, for example, the vibration frequency of a beam with short-circuited electrodes approach its natural frequency. In this case, the amplitudes of the sought quantities grow without limit. The natural frequency spectrum of a beam with disconnected electrodes will differ from the spectrum of a beam with short-circuited electrodes. As a result, the amplitudes of the sought quantities will decrease. It is shown that the efficiency of vibration damping can be significantly increased by choosing the direction of the preliminary polarization of the piezoelectric material and the location of its electrodes. Numerical examples are given that demonstrate the effectiveness of the proposed method. The advantage of the method lies in its simplicity and the low cost of the piezoelectric material, which serves as a non-inertial damper. Full article

In the framework of electro-elasticity theory and the finite element method (FEM), a model is set up for the computation of quantities in surface acoustic wave (SAW) devices accounting for nonlinear effects. These include second-order and third-order intermodulations, second and third harmonic generation and the influence of electro-acoustic nonlinearity on the frequency characteristics of SAW resonators. The model is based on perturbation theory, and requires input material constants, e.g., the elastic moduli up to fourth order for all materials involved. The model is two-dimensional, corresponding to an infinite aperture, but all three Cartesian components of the displacement and electrical fields are accounted for. The first version of the model pertains to an infinite periodic arrangement of electrodes. It is subsequently generalized to systems with a finite number of electrodes. For the latter version, a recursive algorithm is presented which is related to the cascading scheme of Plessky and Koskela and strongly reduces computation time and memory requirements. The model is applied to TC-SAW systems with copper electrodes buried in an oxide film on a LiNbO₃ substrate. Results of computations are presented for the electrical current due to third-order intermodulations and the displacement field associated with the second harmonic and second-order intermodulations, generated by monochromatic input tones. The scope of this review is limited to methodological aspects with the goal to enable calculations of nonlinear quantities in SAW devices on inexpensive and easily accessible computing platforms. Full article

Models of dielectric solids subject to large deformations are established by following a thermodynamic approach. The models are quite general in that they account for viscoelastic properties and allow electric and thermal conduction. A preliminary analysis is devoted to the selection of fields for the polarization and the electric field; the appropriate fields are required to comply with the balance of angular momentum and to enjoy the Euclidean invariance. Next, the thermodynamic restrictions for the constitutive equations are investigated using a wide set of variables allowing for the joint properties of viscoelastic solids, electric and heat conductors, dielectrics with memory, and hysteretic ferroelectrics. Particular attention is devoted to models for soft ferroelectrics, such as BTS ceramics. The advantage of this approach is that a few constitutive parameters provide a good fit of material behaviour. A dependence on the gradient of the electric field is also considered. The generality and the accuracy of the models are improved by means of two features. The entropy production is regarded as a constitutive property per se, while the consequences of the thermodynamic inequalities are made explicit by means of representation formulae. Full article

The generalized eigenvalue problem for a symmetric definite matrix pencil obtained from finite-element modeling of electroelastic materials is solved numerically by the Lanczos algorithm. The mass matrix is singular in the considered problem, and therefore the process proceeds with the semi-inner product defined by this matrix. The shift-and-invert Lanczos algorithm is used to find multiple eigenvalues closest to some shift and the corresponding eigenvectors. The results of the numerical experiments are presented. Full article

Spin-crossover solids have been studied for many years for their promising applications as optical switches and reversible high-density memories for information storage. This study reports the effect of random metal dilution on the thermal and structural properties of a spin-crossover single crystal. The analysis is performed on a 2D rectangular lattice using an electro-elastic model. The lattice is made of sites that can switch thermally between the low-spin and high-spin states, accompanied by local volume changes. The model is solved by Monte Carlo simulations, running on the spin states and atomic positions of this compressible 2D lattice. A detailed analysis of metal dilution on the magneto-structural properties allows us to address the following issues: (i) at low dilution rates, the transition is of the first order; (ii) increasing the concentration of dopant results in a decrease in cooperativity and leads to gradual transformations above a threshold concentration, while incomplete spin transitions are obtained for big dopant sizes. The effects of the metal dilution on the spatiotemporal aspects of the spin transition along the thermal transition and on the low-temperature relaxation of the photo-induced metastable high-spin states are also studied. Significant changes in the organization of the spin states are observed for the thermal transition, where the single-domain nucleation caused by the long-range elastic interactions is replaced by a multi-droplet nucleation. As to the issue of the relaxation curves: their shape transforms from a sigmoidal shape, characteristic of strong cooperative systems, into stretched exponentials for high dilution rates, which is the signature of a disordered system. Full article

Sodium bismuth titanate (Bi_0.5Na_0.5TiO₃, BNT) has attracted much attention because of its excellent dielectric, piezoelectric and electromechanical properties. The microstructure of sodium bismuth titanate-doped ferrum niobium material (Bi_0.5Na_0.5TiO₃ doped (Fe_0.5Nb_0.5)⁴⁺, BNT-xFN) shows a triangle as its typical defect shape. Since piezoelectric devices usually operate under dynamic loads, they fail easily owing to dynamic stress concentration or dynamic fracture. Elastic waves can simulate many types of dynamic loads, and the dynamic stress concentration caused by an anti-plane shear wave is the basis for the calculation of the stress field strength factor of type Ⅲ-dynamic fractures. In this study, the electroelastic coupled-wave diffraction and dynamic stress concentration of BNT-xFN materials with triangular defects under the incidence of anti-plane shear waves were studied. Maxwell equations are decoupled by auxiliary functions, and the analytical solutions of the elastic wave field and electric field are obtained. Based on the conformal mapping method, the triangle defect was mapped to the unit circle defect, and the dynamic stress concentration coefficient around the triangle defect was obtained by calculating the undetermined mode coefficients in the expression through boundary conditions. The numerical calculation shows that the size of the triangular hole, the frequency of the applied mechanical load, the incidence angle of mechanical load and the amount of FN doping have a great influence on the stress concentration of BNT-xFN materials. Full article

In this paper, the calculation method of dynamic stress concentration around piezoelectric ceramics containing regular n-sided holes under the action of electroelastic coupling wave was studied, and it was applied to promising barium calcium zirconate titanate material. First, electroelastic governing equations were decomposed by using the auxiliary function method, and the solution forms of the elastic wave field and electric field were obtained by using the wave function expansion method. Then, the triangular boundary was simplified to a circular boundary using the mapping function, and the corresponding modal coefficients were determined according to simplified boundary conditions. Finally, the dynamic stress-concentration factor was calculated to characterize the dynamic stress concentration. We performed numerical simulations with a correlation coefficient of (1 − x)[(Ba_0.94Ca_0.06) (Ti_0.92Sn_0.08)]-xSm₂O₃-0.06 mol% GeO₂ (abbreviated as (1 − x)BCTS-xSm-0.06G). The numerical calculation results show that the incident wave number, piezoelectric properties, shape parameters of the hole, and deflection angle have a great influence on the dynamic stress around the defect, and some significant laws are summarized through analysis. Full article

In this paper, a method to calculate the dynamic stress concentration around the triangular defect of piezoelectric material under electroelastic coupling is studied and applied to the promising barium calcium zirconate titanate. Firstly, the electroelastic governing equation is decomposed by decoupling technique, and the analytical solutions of elastic wave field and electric field are obtained by wave function expansion method. Then, the conformal transformation is used to simplify the triangle boundary into a circular boundary, and the corresponding modal coefficients are determined according to the simplified boundary conditions. Finally, the analytical solution of the dynamic stress concentration factor can be obtained according to the constitutive equation. Substitute the relevant material parameters of (Ba_0.85Ca_0.15)(Zr_0.1Ti_0.9)O₃ and set different temperatures, Ce doping amount, and incident wave number for numerical simulation. The numerical results show that the incident wave number, piezoelectric properties, and the shape parameters and deflection angle of the triangular defect have a great influence on the dynamic stress around the defect, and some meaningful laws are summarized through analysis. Full article

Lithium niobate crystals (LiNbO₃, LN) are multifunctional crystal materials with many outstanding properties. In this work, the electro-elastic properties of LN single crystals were explored at temperatures from −150 °C to 150 °C. The temperature dependences of dielectric permittivities, elastic compliances, electromechanical coupling factors and piezoelectric coefficients were determined using the impedance method. The LN crystals possessed large dielectric permittivities, the ${\epsilon }_{11}^T/{\epsilon }_0$ and ${\epsilon }_{33}^T/{\epsilon }_0$ were 83.2 and 29.4 at room temperature, respectively. The elastic compliances s₁₁, s₁₃, s₃₃ and s₄₄ presented a positive increase as the temperature increased, and the variations were 5.0%, 8.2%, 4.6% and 5.4%, respectively, showing a good temperature stability. Moreover, the temperature dependence of the electromechanical coupling factors and piezoelectric coefficients for different vibration modes were studied with a temperature range from −150 °C to 150 °C, where the thickness shear vibration mode d₁₅ presented a large piezoelectric response and minimal temperature variation. Full article

Electroelastic materials, as for example, 3M VHB 4910, are attracting attention as actuators or generators in some developments and applications. This is due to their capacity of being deformed when submitted to an electric field. Some models of their actuation are available, but recently, viscoelastic models have been proposed to give an account of the dissipative behaviour of these materials. Their response to an external mechanical or electrical force field implies a relaxation process towards a new state of thermodynamic equilibrium, which can be described by a relaxation time. However, it is well known that viscoelastic and dielectric materials, as for example, polymers, exhibit a distribution of relaxation times instead of a single relaxation time. In the present approach, a continuous distribution of relaxation times is proposed via the introduction of fractional derivatives of the stress and strain, which gives a better account of the material behaviour. The application of fractional derivatives is described and a comparison with former results is made. Then, a double generalisation is carried out: the first one is referred to the viscoelastic or dielectric models and is addressed to obtain a nonsymmetric spectrum of relaxation times, and the second one is the adoption of the more realistic Mooney–Rivlin equation for the stress–strain relationship of the elastomeric material. A modified Mooney–Rivlin model for the free energy density of a hyperelastic material, VHB 4910 has been used based on experimental results of previous authors. This last proposal ensures the appearance of the bifurcation phenomena which is analysed for equibiaxial dead loads; time-dependent bifurcation phenomena are predicted by the extended Mooney–Rivlin equations. Full article

The jungle of experimental behaviors of spin-crossover materials contains a tremendous number of unexpected behaviors, among which, the unsymmetrical hysteresis loops having different shapes on heating and cooling, that we often encounter in literature. Excluding an extra effect of crystallographic phase transitions, we study here these phenomena from the point of view of elastic modeling and we demonstrate that a simple model accounting for the bond lengths misfits between the high-spin and low-spin states is sufficient to describe the situation of unsymmetrical hysteresis showing plateaus at the transition only on cooling or on heating branches. The idea behind this effect relates to the existence of a discriminant elastic frustration in the lattice, which expresses only along the high-spin to low-spin transition or in the opposite side. The obtained two-step transitions showed characteristics of self-organization of the spin states under the form of stripes, which we explain as an emergence process of antagonist directional elastic interactions inside the lattice. The analysis of the spin state transformation inside the plateau on cooling in terms of two sublattices demonstrated that the elastic-driven self-organization of the spin states is accompanied with a symmetry breaking. Full article