Fundamentals in generalized elasticity and dislocation theory of quasicrystals: Green tensor,dislocation key-formulas and dislocation loops

The present work provides fundamental quantities in generalized elasticity and dislocation theory of quasicrystals. In a clear and straightforward manner, the three-dimensional Green tensor of generalized elasticity theory and the extended displacement vector for an arbitrary extended force are derived. Next, in the framework of dislocation theory of quasicrystals, the solutions of the field equations for the extended displacement vector and the extended elastic distortion tensor are given; that is, the generalized Burgers equation for arbitrary sources and the generalized Mura–Willis formula, respectively. Moreover, important quantities of the theory of dislocations as the Eshelby stress tensor, Peach–Koehler force, stress function tensor and the interaction energy are derived for general dislocations. The application to dislocation loops gives rise to the generalized Burgers equation, where the displacement vector can be written as a sum of a line integral plus a purely geometric part. Finally, using the Green tensor, all other dislocation key-formulas for loops, known from the theory of anisotropic elasticity, like the Peach–Koehler stress formula, Mura–Willis equation, Volterra equation, stress function tensor and the interaction energy are derived for quasicrystals.     

The relation between the generalised Eshelby integral and the generalised BCS and DB modelsvspace1mm

The generalised BCS dislocation group model and the generalised DB atomic cohesive force zone model have obtained the same results on nonlinear fracture study of some one-, two- and three-dimensional quasicrystals. This work reveals some inherent connection between the two models, and finds that their common basis is the generalised Eshelby integral based on the generalised Eshelby energy--momentum tensor for quasicrystals. Further applications of the theory in solving nonlinear fracture problems of the materials are also discussed.     

Derivation of governing equation for predicting thermal conductivity of composites with spherical inclusions and its applications

A governing differential equation for predicting the effective thermal conductivity of composites with spherical inclusions is shown to be simply derived by using the result of the generalized self-consistent model. By applying the equation to composites including spherical inclusions such as graded spherical inclusions, microballoons, mutiply-coated spheres, and spherical inclusions with an interphase, their effective thermal conductivities are easily predicted. The results are compared with those in the literatures to be consistent. It can be stated from the investigations that the effective thermal conductivity of composites with spherical inclusions can be estimated as long as their conductivities are expressed as a function of their radius.     

Continuum theory of the volume effect caused by point defects in hexagonal media

The volume change caused by a point defect in the center of a spherical reference volume which is embedded into the infinite medium is calculated analytically for hexagonal crystal symmetry. Two new dimensionless coefficients which we call generalized Eshelby coefficients are introduced to describe the correction of volume change which appears if that reference volume has a free, unforced surface. These coefficients play a similar role for hexagonal crystals as the Eshelby factor in the isotropic medium does. It is shown that the influence of elastic anisotropy on the Eshelby coefficients is essentially determined by the closest elastic instabilities. In the limit of an isotropic medium these coefficients reduce to the well-known Eshelby factor.     

Prediction of effective stagnant thermal conductivities of porous materials at high temperature by the generalized self-consistent method

The generalized self-consistent method is developed to deal with porous materials at high temperature, accounting for thermal radiation. An exact closed form formula of the local effective thermal conductivity is obtained by solving Laplace's equation, and a good approximate formula with uncoupled conductive and radiative effects is given. A comparison with available experimental data and theoretical predictions demonstrates the accuracy and efficiency of the present formula. Numerical examples provide a better understanding of interesting interaction phenomena of pores in heat transfer. It is found that the local effective thermal conductivity divides into two parts. One, attributed to conduction, is independent of pore radius for a fixed porosity and, furthermore, is independent of temperature (actually, it is approximately independent of the temperature) if it is non-dimensionalized by the thermal conductivity of the matrix. The other is due to thermal radiation in pores and strongly depends on the temperature and pore radius. The radiation effect can not be neglected at high temperature and in the case of relatively large pores.     

考虑界面接触热阻的一维复合结构的热整流机理

建立了考虑变截面、变热导率及界面接触热阻效应的组合热整流结构的温度场及热整流系数的理论模型和有限元解.数值算例证明了本文模型及算法的可靠性,进而通过参数影响研究确定了若干几何及材料参数对结构热整流系数的影响规律,揭示界面接触热阻对热整流效果的影响机理.研究结果表明长度比、截面半径变化率、热导率、边界条件温差和界面接触热阻等因素必须通过优化设计才能得到最大的热整流系数,同时界面接触热阻的引入也为调控热整流系数提供了一条新的途径.     

固-固接触界面热传输研究

提出了固-固接触热传导接触界面层的概念并进行了解释。接触界面层的建立,把微结构的散射和辐射热传导机制统一于界面层内,通过对接触界面层、接触界面层的厚度和界面层热导率等的讨论,初步揭示了接触界面层热传导的机制。在界面层微观传热的机制上,建立了接触界面层热阻预测模型,并把模型预测接触热阻值与扩散失陪模型(DMM)以及实验值进行了比较。结果显示该模型克服了DMM模型预测值偏低的缺陷,这些将对接触界面层的微尺度热分析有一定的帮助。     

On microcontinuum field theories: the Eshelby stress tensor and incompatibility conditions

We investigate linear theories of incompatible micromorphic elasticity, incompatible microstretch elasticity, incompatible micropolar elasticity and the incompatible dilatation theory of elasticity (elasticity with voids). The incompatibility conditions and Bianchi identities are derived and discussed. The Eshelby stress tensor (static energy momentum) is calculated for such inhomogeneous media with microstructure. Its divergence gives the driving forces for dislocations, disclinations, point defects and inhomogeneities which are called configurational forces.     

键合界面阻抗对VCSEL的电、热学特性的影响

采用一电阻层来表征键合界面处的阻抗.通过求泊松方程、电流密度方程、载流子扩散方程以及有源层结压降方程自洽解的方法，计算了VCSEL的电势分布，进而求解热传导方程，得到VCSEL的温度分布.详细分析了键合界面阻抗对晶片键合结构垂直腔面发射激光器内部的电势分布、温度分布以及有源层中的注入电流密度、载流子浓度、结压降和温度沿径向分布的影响.     

Stress distributions in diblock copolymers

We demonstrate how a generalized self-consistent field theory for polymer melts that includes elastic stress and strain fields can be applied to the study of AB diblock copolymers melts. By obtaining the stress distributions for volume conserving strain loadings where lamellar and hexagonal morphologies are stable, we show that the local stress is reduced at the domain interface but slightly enhanced in the immediate vicinity of the interface. The overall stress profile is the result of the combined effects of chain connectivity across the interface, which yields a positive contribution, and the immiscible nature of the monomers, which leads to a stress reduction because of interfacial tension.     

Correlations of Thermal Contact Conductance for Nominally Flat Metallic Contact in Vacuum

Heat transfer experiments were performed in a vacuum environment (0.045 torr) to find out solid spot contact conductance for nominally flat surfaces of copper, brass, and stainless steel with different surface roughnesses (1–5 μm) for each specimen under several load conditions (0.6–15 MPa). A precise estimation of thermal contact conductance for the interface of sets of similar materials has been carried out employing a steady-state approach. Results have been compared with the theoretical models based on plastic and elastic deformation based theories for nominally flat metallic contacts. It has been demonstrated that a dire need exists to develop an experimentally based generalized correlation of thermal contact conductance for nominally flat metallic contacts that can be used by design engineers as well as for research purposes in different fields. Along with the generalized correlation, a specific correlation for thermal contact conductance has been proposed for three sets of materials. The thermal contact conductance of each set of materials presented in the form of specific correlations for different roughness parameters is one of the most important outcomes of the present research.     

导热与弹性系统及导电的相似性

本文将导热系统与弹性力学系统以及带电系统类比,发现这三种不同类型的系统在输运方面具有一致的行为特征,有相同的数学表达方式。都是在强度量的作用下,广延量的输运过程。强度量在被传递的广延量上的累积效果由广义功反映,广义功就是传递过程中的传递能力,传递能力在过程中有损耗。定义了导热过程中的热力功,它等于传热温度与传递的热量的乘积,反映了温度在传热量上的累积效果。热力功是传递中的热量传递势容,总热力功等于系统热量传递势容的改变量,热量传递势容表示物体的导热能力。     

Homogenization of multicoated inclusion-reinforced linear elastic composites with eigenstrains: Application to thermoelastic behavior

A new micromechanical approach for arbitrary multicoated ellipsoidal elastic inclusions with general eigenstrains is developed. We start from the integral equation of the linear elastic medium with eigenstrains adopting the Green's function technique and we apply an ‘(n+1)-phase’ model with a self-consistent condition to determine the homogenized behavior of multicoated inclusion-reinforced composites. The effective elastic moduli and eigenstrains are obtained as well as the residual stresses through the local stress concentration equations. The effective eigenstrains are determined either with the concentration tensors obtained here by the present model, or, more classically, with Levin's formula. In order to assess our micromechanical model, some applications to the isotropic thermoelastic behavior of composites with and without interphase are given. In particular, ‘four-phase’ and ‘three-phase’ models are derived for isotropic homothetic spherical inclusion-reinforced materials, and the results are successfully compared to exact analytical solutions regarding the effective elastic moduli and the effective thermal expansion.     

Punktdefekte im kubischen elastischen Kontinuum

The determination of the displacement and strain fields of a point defect in a cubic crystal requires even in the framework of continuum elasticity theory numerical calculation. These fields of elastic dipoles are expanded in suitable vector and tensor fields. The coefficients of this expansion are calculated up to polynomials of 5th and 4th order in the direction cosines using the ratios of elastic constants as parameters. With this expansion the interaction of elastic dipoles in a cubic medium can be calculated. The results have been applied to the interaction of F-centres and of O₂ ^?-centres in alkali halides.     

GENERALIZATION OF ESHELBY''S METHOD TO THE ANISOTROPIC ELASTICITY THEORY OF DISLOCATIONS IN QUASICRYSTALS

The general expressions of the elastic fields induced by straight dislocations in quasicrystals have been given according to Eshelby's method which was used to treat the anisotropic elasticity of dislocations in crystals. As an example, the elastic displacement vector, the stress tensor and the elastic energy density of a screw dislocation line lying on the quasiperiodic plane of decagonal quasicrystals are calculated.     

GENERALIZATION OF ESHELBY'S METHOD TO THE ANISOTROPIC ELASTICITY THEORY OF DISLOCATIONS IN QUASICRYSTALS

The general expressions of the elastic fields induced by straight dislocations in quasicrystals have been given according to Eshelby's method which was used to treat the anisotropic elasticity of dislocations in crystals. As an example, the elastic displacement vector, the stress tensor and the elastic energy density of a screw dislocation line lying on the quasiperiodic plane of decagonal quasicrystals are calculated.     

Traces of products of angular momentum operators

Traces of products of angular momentum operators in a spherical or cartesian basis are common in the theory of atomic levels in fields, in the theory of nuclear orientation and of asymmetric top moments. Conventional angular momentum techniques lead to difficult and cumbersome calculations. In the present paper Schwinger's coupled boson representation is used in straightforward calculations of angular momentum and spherical tensor traces, of matrix elements and of asymmetric top moments. Only simple algebra, elementary multiplication and summation of integers are necessary. The method considerably simplifies calculations with angular momentum operators.     

Size-dependent effect on thermo-electro-mechanical responses of heated nano-sized piezoelectric plate

The booming development of nanotechnology motivates the widespread applications of piezoelectric nanomaterials (e.g. ZnO, ZnS, GaN) and their nanostructures (e.g. nanobelts, nanorings nanowires). It is noted that the coupled field analysis of nano-sized piezoelectric structure under non-uniform temperature in-service environment is of great importance for the fabrication and exploitation of nanoelectromechanical devices. In such situation, spatial size effect of heat conduction is necessary to be taken into account due to its important significance in characterizing the nonlocal feature of heat transport in nanosystems. In this study, thermal nonlocal effect is introduced into the thermo-electro-mechanical model based on nonlocal elasticity theory to further shed light on the size-dependent coupling behavior of thermal, electric, and elastic fields. The coupled field equations involving size-dependent parameters are derived. The solutions can be obtained using Laplace transformation methods. Parametric studies are conducted to evaluate the influences of thermal as well as elastic nonlocal parameters on the transient responses. The results indicate that the piezoelectric performance of the nanoplate is greatly improved in the presence of thermal nonlocal effect.     

Elasticity of hexagonal-closed-packed cobalt at high pressure and temperature: a quasiharmonic case

We performed high-resolution inelastic x-ray scattering measurements on a single crystal of hcp cobalt at simultaneous high pressure and high temperature, obtaining 4 of the 5 independent elements of the elastic tensor. Our experiments indicate that the elasticity of hcp-Co is well described within the quasiharmonic approximation and that anharmonic high-temperature effects on the elastic moduli, sound velocities, and elastic anisotropy are minimal at constant density. These results support the validity of Birch's law and represent an important benchmark for ab initio thermal lattice dynamics and molecular-dynamics simulations.     

Tensor spherical harmonics

The concept of vector spherical harmonics is generalized for symmetric and traceless Cartesian tensor fields of arbitrary rank. Differential relations of these functions are derived as generalizations of the gradient formula for scalar, and the divergence and curl formulas for vector spherical harmonics.