An eigen theory of waves in piezoelectric solids

Based on the standard spaces of the physical presentation, both the quasi-static mechanical approximation and the quasi-static electromagnetic approximation of piezoelectric solids are studied here. The complete set of uncoupled elastic wave and electromagnetic wave equations are deduced. The results show that the number and propagation speed of elastic waves and electromagnetic waves in anisotropic piezoelectric solids are determined by both the subspaces of electromagnetically anisotropic media and ones of mechanically anisotropic media. Based on these laws, we discuss the propagation behaviour of elastic waves and electromagnetic waves in the piezoelectric material of class 6 mm.     

ON THE LAW OF ENERGY CONSERVATION IN THE CLASSICAL ELECTRODYNAMICS OF DEFORMABLE MEDIA——A GENERALIZATION OF THE POYNTING THEOREM

This paper establishes the generalized Poynting theorem for the electrodynamics of deformable media with a view to shedding some light on the detailed mechanism of energy transfer between the electromagnetic field and the deformable media. Global field equations are chosen as the starting point and specialized forms of the theorem are derived based on the special postulates for the electromagnetic body force.     

Method of reverberation ray matrix for static analysis of planar framed structures composed of anisotropic Timoshenko beam members

Based on the method of reverberation ray matrix(MRRM), a reverberation matrix for planar framed structures composed of anisotropic Timoshenko(T) beam members containing completely hinged joints is developed for static analysis of such structures.In the MRRM for dynamic analysis, amplitudes of arriving and departing waves for joints are chosen as unknown quantities. However, for the present case of static analysis, displacements and rotational angles at the ends of each beam member are directly considered as unknown quantities. The expressions for stiffness matrices for anisotropic beam members are developed. A corresponding reverberation matrix is derived analytically for exact and unified determination on the displacements and internal forces at both ends of each member and arbitrary cross sectional locations in the structure. Numerical examples are given and compared with the finite element method(FEM) results to validate the present model. The characteristic parameter analysis is performed to demonstrate accuracy of the present model with the T beam theory in contrast with errors in the usual model based on the Euler-Bernoulli(EB) beam theory. The resulting reverberation matrix can be used for exact calculation of anisotropic framed structures as well as for parameter analysis of geometrical and material properties of the framed structures.     

Three-dimensional steady-state closed form solution for multilayered fluid-saturated anisotropic finite media due to surface/internal point source

A three-dimensional(3 D)steady-state solution of fluid saturated anisotropic finite media is presented.The eigenequation method and the pseudo-Stroh formalism are used to obtain the exact solution for homogeneous saturated finite media.The propagator matrix method is introduced to deal with the corresponding multilayered poroelastic media.The poroelastic solutions due to surface or internal point fluid source are obtained.The comparison of the results of the saturated isotropic media in a half space and those obtained by the finite element method is given to illustrate the accuracy of the solution in a finite domain.Numerical solutions of a sandwich poroelastic medium are presented to analyze its hydromechanical behaviors.Two ratios of the horizontal permeability to vertical permeability and different source positions are investigated.The results show that the fluid parameters and source positions have great influence on the hydromechanical behaviors of the layered media.     

PRODUCTION OF PIGMENT NANOPARTICLES USING A WET STIRRED MILL WITH POLYMERIC MEDIA

Pigment nanoparticles with a size range of 10-100 nm were produced from large agglonmerates via a stirred media mill operating in the wet-batch mode and using polymeric media,The effects of several operating variables such as the surfactant concentration,polystyrene media loading.and media size on the pigment size distribution of the product were studied.The process dynamics was also investigated.Dynamic light scattering and electron microscopy were used as the characerization techniques.The polymeric grinding media are found to be effective for the production of pigment nanoparticles.The experimental results suggest the existence of an optimum media size and surfactant concentration,A population balance model of the process reveals a transition from first-order breakage kinetice for rela-large agglomerates split in a first-order kinetics,with a delay period,for the smaller particles.The model implies that large agglomerates split in a first-order fashion whereas the breakage of individual naoparticles may depend on induced fatigue of the particles.     

SINGULARITIES AND EXPLICIT SOLUTIONS OF COLLINEAR CRACK PROBLEM IN ANISOTROPIC MEDIA

The singularities of collinear cracks both in anisotropic single mediumand at the interface of anisotropie bimaterials are studied by combining Stroh formalismand the analytic function method.The formulae for calculating the field potential andstress intensity factor(SIF)are obtained.It is found that the field potentials areexplicitly related to material matrix L and the in-plane and anti-plane fields can beseparately calculated when orthotropic bimaterials are considered.     

HEAT TRANSFER CHARACTERISTICS OF CONDUCTIVE MATERIAL UNDER INNER NON-UNIFORM ELECTROMAGNETIC FIELDS

Electronic transport properties can be influenced by the applied electromagnetic fields in conductive materials. The change of the electron distribution function evoked by outfields obeys the Boltzmann equation. In this paper, a general law of heat conduction considering the non-uniform electromagnetic effect is developed from the Boltzmann equation. An analysis of the equation leads to the result that the electric field gradient and the magnetic gradient in the conductive material are responsible for the influences of electromagnetic fields on the heat conduction process. A physical model is established and finite element numerical simulation reveals that heat conduction can be increased or delayed by the different directions of the electric field gradient, and the existence of the magnetic gradient always hinders heat conduction.     

SUPPLEMENTARY STUDY ON ANISOTROPIC PLASTIC STRESS FIELDS AT A STATIONARY PLANE-STRESS CRACK-TIP

The results in Ref.[1]are not suitable for the cases of a≥2 .For this reason,we use the method in Ref.[1]to derive the general expressions of the anisotropic plastic stress fields at a stationary plane-stress crack-tip for both of the cases of a=2 and a>2 .As an example,we give the analytical expressions of the anisotropic plastic stress fields at the stationary tips of modeⅠand modeⅡplane-stress cracks for the case of a=2.     

ANALYSIS OF DAMAGE NEAR A CONDUCTING CRACK IN A PIEZOELECTRIC CERAMIC

The finite element formulation for analyzing static damage near a conducting crack in a thin piezoelectric plate is established from the virtual work principle of piezoelectricity. The damage fields under various mechanical and electrical loads are calculated carefully by using an effective iterative procedure. The numerical results show that all the damage fields around a crack tip are fan-shaped and the electric field applied has great influence on the mechanical damage,which is related to the piezoelectric properties.     

Piezoelectric study on singularities interacting with interfaces in an anisotropic media

In this work, the singularity problem of a three-phase anisotropic piezoelectric media is studied using the extended Stroh formalism. Based on the method of analytical continuation in conjunction with alternating technique, the general expressions for the complex potentials are derived in each medium of a three-phase anisotropic piezoelectric media. This approach has a clear advantage in deriving the solution to the heterogeneous problem in terms of the solution for the corresponding homogeneous problem. The presented series solutions have rapid convergence which is guaranteed numerically. Stress and electric fields which are dependent on the mismatch in the material constants, the location of singularities and the magnitude of electromechanical loadings are studied in detail. Numerical results demonstrate that the continuity conditions at the interfaces are indeed satisfied and show the effects of material mismatch on the stress and electric displacement fields. The image forces exerted on a dislocation due to the interfaces are also calculated by means of the generalized Peach–Koehler formula.     

Theory of averaging of elastic fields in media with a monoclinic structure

Conclusions The proposed relations of averaging theory, together with complex Kolosov-Muskhelishvili potentials for isotropic matrices and Lekhnitskii potentials for rectilinearly anisotropic matrices with prismatic fillers, constitute a closed system of equations in the problem of determining the internal fields and the complete set of effective elastic constants of composite media with uniform external static stresses.By combining relations of the averaging theory and well-known solutions of boundary-value problems on the stress-state of an infinite medium with an individual inclusion, we can directly construct the solution of the problem of determining the macroscopic parameters of a composite system with an arbitrary structure.Conformal mapping of the external boundary of the determining element onto a unit circle is an efficient method of calculating contour integrals in averaging theory with a high degree of accuracy.When the initial terms are retained in an expansion of the complex potentials in degrees of inclusion interaction, it is possible to obtain approximate analytic formulas for all of the effective constants. In special cases, these formulas coincide with the asymptotic formulas found from the exact solutions.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 23, No. 1, pp. 3–18, January, 1987.     

Dynamic crack tip fields and dynamic crack propagation characteristics of anisotropic material

Based on mechanics of anisotropic material, the dynamic crack propagation problem of I/II mixed mode crack in an infinite anisotropic body is investigated. Expressions of dynamic stress intensity factors for modes I and II crack are obtained. Components of dynamic stress and dynamic displacements around the crack tip are derived. The strain energy density theory is used to predict the dynamic crack extension angle. The critical strain energy density is determined by the strength parameters of anisotropic materials. The obtained dynamic crack tip fields are unified and applicable to the analysis of the crack tip fields of anisotropic material, orthotropic material and isotropic material under dynamic or static load. The obtained results show Crack propagation characteristics are represented by the mechanical properties of anisotropic material, i.e., crack propagation velocity M and fiber direction α. In particular, the fiber direction α and the crack propagation velocity M give greater influence on the variations of the stress fields and displacement fields. Fracture angle is found to depend not only on the crack propagation but also on the anisotropic character of the material.     

Incremental elastic motions superimposed on a finite deformation in the presence of an electromagnetic field

The equations describing the interaction of an electromagnetic sensitive elastic solid with electric and magnetic fields under finite deformations are summarized, both for time-independent deformations and, in the non-relativistic approximation, time-dependent motions. The equations are given in both Eulerian and Lagrangian form, and the latter are then used to derive the equations governing incremental motions and electromagnetic fields superimposed on a configuration with a known static finite deformation and time-independent electromagnetic field. As a first application the equations are specialized to the quasimagnetostatic approximation and in this context the general equations governing time-harmonic plane-wave disturbances of an initial static configuration are derived. For a prototype model of an incompressible isotropic magnetoelastic solid a specific formula for the acoustic shear wave speed is obtained, which allows results for different relative orientations of the underlying magnetic field and the direction of wave propagation to be compared. The general equations are then used to examine two-dimensional motions, and further expressions for the wave speed are obtained for a general incompressible isotropic magnetoelastic solid.     

Anti-plane shear of kinked interface crack in bonded dissimilar anisotropic solid

Complex potentials are derived to describe the anti-plane singular shear stress fields around a kinked crack, the main portion of which is embedded along the interface of two dissimilar anisotropic elastic media. This is accomplished by formulating the problem as singular integral equations with generalized Cauchy kernels. The shear stress singularity at the kink differs from the familiar inverse square root of the local distance; it is found to influence the magnitude of the Mode III crack tip stress intensity factor, K₃. Numerical results of K₃ are obtained and displayed in graphical forms for different degree of material anisotropy and crack dimensions.     

基于Hamilton体系的辛半解析法在各向异性电磁波导中的应用

力学中的Hamilton体系使用对偶变量来描述问题，而电磁场正好有电场和磁场这一对对偶变量。本文将力学中的Hamilton体系应用到电磁波导问题。根据电磁波导的Hamilton体系理论，辛几何可用于任意各向异性材料。将横向的电场和磁场构成对偶向量，基于Hamilton变分原理做半解析横向离散，并保持结构辛体系。本文以各向异性材料电磁波导为例，求解了问题的辛本征值，得到了镜像线的色散曲线。     

A Unified Two-Phase Potential Method for Elastic Bi-material: Planar Interfaces

This paper gives a unified approach to analyze two-dimensional elastic deformations of a composite body consisting of two dissimilar anisotropic or isotropic materials perfectly bonded along a planar interface. The Eshelby et al. formalism of anisotropic elasticity is linked with that of Kolosov-Muskhelishvili for isotropic elasticity by means of two complex matrix functions describing completely the arising elastic fields. These functions, whose elements are holomorphic functions, are defined as the two-phase potentials of the bimaterial. The present work is concerned with bi-materials whose constituent materials occupy the whole space and are connected by a planar interface. The elastic fields arising in such a bimaterial are given by universal relationships in terms of the two-phase potentials. Then, the general results obtained are implemented to study two interesting bimaterial problems: the problem of a uniformly stressed bimaterial with a perfect interfacial bonding, and the interface crack problem of a bimaterial with a general loading. For both problems, all combinations of the elastic properties of the constituent materials are considered. For the first problem, the constraints, which must be imposed between the components of the applied uniform stress fields, are established, so that they are admissible as elastic fields of the bimaterial. For the interface crack problem, the solution is obtained for a general loading applied in the body. Detailed results are given for the case of a remote uniform stress field applied to the bimaterial constituents.     

Some recent developments in elastic waves in solids

Three topics on recent developments in elastic waves which are of special interest to researchers in experimental mechanics are discussed. They are: (1) the elastic waves in anisotropic media with particular reference to waves in fiber-reinforced composite materials; (2) the coupled thermoelastic waves in isotropic or anisotropic media; and (3) the interaction of elastic waves with magnetic fields in nonferrous metals, polycrystalline ferromagnetic alloys and saturated ferrimagnetic crystals.     

电磁场?渗流场耦合作用下离子液体多孔介质流动模型

离子液体是一类可调控、多功能的绿色环保材料, 具有良好的电磁场响应, 有望应用于调控水驱油路径. 在分析离子液体在毛细管中电磁场响应机理的基础上, 建立了电磁场?渗流场耦合作用下离子液体多孔介质流动模型. 通过理论推导与数值分析发现: 电磁场?渗流场耦合作用下毛细管流量大小主要由离子液体电导率与黏度的比值(内因)、电磁场强度与压力梯度(外因)两方面决定; 电磁场产生的洛伦兹力对离子液体施加一个电磁驱动压强, 形成一个类似压力梯度的电磁驱动等效压力梯度, 从而改变离子液体的流量, 当电磁场强度为2.0 × 104 V/m·T时, 电磁场在电导率为0.5 S/m的离子液体上可形成10 kPa/m电磁驱动等效压力梯度. 通过调整电磁场方向即可控制离子液体在多孔介质中的流动方向, 解决常规注水利用压力差难以控制流动路径的难题, 为离子液体智能驱油提供理论依据, 且电磁场产生的热效应会影响离子液体的流动能力及潜在驱油效率.