Energy Principle And Nonlinear Electric-Mechanical Behavior Of Ferroelectric Ceramics

Many experimental observations have shown that a single domain in a ferroelectric material switches by progressive movement of domain walls, driven by a combination of electric field and stress. The mechanism of the domain switch involves the following steps: initially, the domain has a uniform spontaneous polarization; new domains with the reverse polarization direction nucleate, mainly at the surface, and grow though the crystal thickness; the new domain expands sideways as a new domain continues to form; finally, the domain switch coalesces to complete the polarization reversal. According to this mechanism, the volume fraction of the domain switching is introduced in the constitutive law of the ferroelectric material and used to study the nonlinear constitutive behavior of a ferroelectric body in this paper. The principle of stationary total potential energy is put forward in which the basic unknown quantities are the displacement u(i), electric displacement D-i and volume fraction rho(I) of the domain switching for the variant I. The mechanical field equation and a new domain switching criterion are obtained from the principle of stationary total potential energy. The domain switching criterion proposed in this paper is an expansion and development of the energy criterion established by Hwang et al. [ 1]. Based on the domain switching criterion, a set of linear algebraic equations for determining the volume fraction rho(I) of domain switching is obtained, in which the coefficients of the linear algebraic equations only contain the unknown strain and electric fields. If the volume fraction rho(I) of domain switching for each domain is prescribed, the unknown displacement and electric potential can be obtained based on the conventional finite element procedure. It is assumed that a domain switches if the reduction in potential energy exceeds a critical energy barrier. According to the experimental results, the energy barrier will strengthen when the volume fraction of the domain switching increases. The external mechanical and electric loads are increased step by step. The volume fraction rho(I) of domain switching for each element obtained from the last loading step is used as input to the constitutive equations. Then the strain and electric fields are calculated based on the conventional finite element procedure. The finite element analysis is carried out on the specimens subjected to uniaxial coupling stress and electric field. Numerical results and available experimental data are compared and discussed. The present theoretic prediction agrees reasonably with the experimental results.

An Efficient Front-Tracking Method For Fully Nonlinear Interfacial Waves

A fully nonlinear and dispersive model within the framework of potential theory is developed for interfacial (2-layer) waves. To circumvent the difficulties arisen from the moving boundary problem a viable technique based on the mixed Eulerian and Lagrangian concept is proposed: the computing area is partitioned by a moving mesh system which adjusts its location vertically to conform to the shape of the moving boundaries but keeps frozen in the horizontal direction. Accordingly, a modified dynamic condition is required to properly compute the boundary potentials. To demonstrate the effectiveness of the current method, two important problems for the interfacial wave dynamics, the generation and evolution processes, are investigated. Firstly, analytical solutions for the interfacial wave generations by the interaction between the barotropic tide and topography are derived and compared favorably with the numerical results. Furthermore simulations are performed for the nonlinear interfacial wave evolutions at various water depth ratios and satisfactory agreement is achieved with the existing asymptotical theories. (c) 2008 Elsevier Inc. All rights reserved.

Pull-In Instability Of Micro-Switch Actuators: Model Review

The existing three widely used pull-in theoretical models (i.e., one-dimensional lumped model, linear supposition model and planar model) are compared with the nonlinear beam mode in this paper by considering both cantilever and fixed-fixed type micro and nano-switches. It is found that the error of the pull-in parameters between one-dimensional lumped model and the nonlinear beam model is large because the denominator of the electrostatic force is minimal when the electrostatic force is computed at the maximum deflection along the beam. Since both the linear superposition model and the slender planar model consider the variation of electrostatic force with the beam's deflection, these two models not only are of the same type but also own little error of the pull-in parameters with the nonlinear beam model, the error brought by these two models attributes to that the boundary conditions are not completely satisfied when computing the numerical integration of the deflection.

Investigation Of Mode Ii Crack Growth Following A Very High Speed Impact

A recoverable plate impact testing technology has been developed for studying fracture mechanisms of mode II crack. With this technology, a single duration stress pulse with submicrosecond duration and high loading rates, up to 10(8) MPam(1/2)s(-1), can be produced. Dynamic failure tests of Hard-C 60# steel were carried out under asymmetrical impacting conditions with short stress-pulse loading. Experimental results show that the nucleation and growth of several microcracks ahead of the crack tip, and the interactions between them, induce unsteady crack growth. Failure mode transitions during crack growth, both from mode I crack to mode II and from brittle to ductile fracture, were observed. Based on experimental observations, a discontinuous crack growth model was established. Analysis of the crack growth mechanisms using our model shows that the shear crack extension is unsteady when the extending speed is between the Rayleigh wave speed c(R) and the shear wave speed c(S). However, when the crack advancing speed is beyond c(S), the crack grows at a steady intersonic speed approaching root 2c(S). It also shows that the transient mechanisms, such as nucleation, growth, interaction and coalescence among microcracks, make the main crack speed jump from subsonic to intersonic and the steady growth of all the subcracks causes the main crack to grow at a stable intersonic speed.

Derivation Of A Nonlinear Reynolds Stress Model Using Renormalization Group Analysis And Two-Scale Expansion Technique

Adopting Yoshizawa's two-scale expansion technique, the fluctuating field is expanded around the isotropic field. The renormalization group method is applied for calculating the covariance of the fluctuating field at the lower order expansion. A nonlinear Reynolds stress model is derived and the turbulent constants inside are evaluated analytically. Compared with the two-scale direct interaction approximation analysis for turbulent shear flows proposed by Yoshizawa, the calculation is much more simple. The analytical model presented here is close to the Speziale model, which is widely applied in the numerical simulations for the complex turbulent flows.

Nonlinear Mechanical Modeling Of Cell Adhesion

Cell adhesion, which is mediated by the receptor-ligand bonds, plays an essential role in various biological processes. Previous studies often described the force-extension relationship of receptor-ligand bond with linear assumption. However, the force-extension relationship of the bond is intrinsically nonlinear, which should have significant influence on the mechanical behavior of cell adhesion. In this work, a nonlinear mechanical model for cell adhesion is developed, and the adhesive strength was studied at various bond distributions. We find that the nonlinear mechanical behavior of the receptor-ligand bonds is crucial to the adhesive strength and stability. This nonlinear behavior allows more bonds to achieve large bond force simultaneously, and therefore the adhesive strength becomes less sensitive to the change of bond density at the outmost periphery of the adhesive area. In this way, the strength and stability of cell adhesion are soundly enhanced. The nonlinear model describes the cell detachment behavior better than the linear model. (C) 2007 Elsevier Ltd. All rights reserved.

Dynamic mode I perturbation solution for a moving crack unsteadily

Rice et al. (Jounal of Mechanics and Physics of Solids 42, 813-843) analyze the propagation of a planar crack with a nominally straight front in a model elastic solid with a single displacement component. Using the form of Willis er al. (Journal of the Mechanics and Physics of Solids 43, 319-341), of dynamic mode I weight functions for a moving crack, we address that problem solved by Rice ei al. in the 3D context of elastodynamic theory. Oscillatory crack tip motion results from constructive-destructive interference of stress intensity waves. Those waves, including system of the dilatational, shear and Rayleigh waves, interact on each other and with moving edge of crack, can lead to continuing fluctuations of the crack front and propagation velocity. (C) 1997 Elsevier Science Ltd.