Long-range topological correlations of real polycrystalline grains in two dimensions

The topological and geometric properties of real polycrystalline grains in two dimensions are investigated on the basis of a large dataset (14,810 grains). The distribution of grain edges, the grain topology–size relationship and the short- and long-range topological correlations between neighboring grains are characterized quantitatively. The results show a strong short-range topological correlation between a center grain and its first nearest neighbors, and a trivial long-range topological correlation beyond the first nearest neighbors (on average). Both the short- and long-range relations are well described by a generalized Aboav–Weaire law reported recently. Meanwhile, it is the perimeter law, rather than the Lewis law, that describes appropriately the relationship between the topology and geometry of metallurgical grains.     

Rotating correlations in partially coherent fields

Abstract

Partially coherent optical fields whose cross-spectral density functions rotate on propagation are examined. The general theory for rotating partially coherent fields in the space-frequency domain is derived for both scalar and electromagnetic approaches. Differences between the results obtained with full and partial coherence is discussed. A numerical example is given for rotating intensity distributions.     

Quantum correlations in cavity QED networks

We present a review of the dynamical features such as generation, propagation, distribution, sudden transition and freezing of the various quantum correlation measures, as Concurrence, Entanglement of Formation, Quantum Discord, as well their geometrical measure counterparts within the models of Cavity Quantum Electrodynamics Networks. Dissipation and thermal effects are discussed both in the generation of quantum correlations as well as their effect on the sudden changes and freezing of the classical and quantum correlations in a cavity quantum electrodynamical network. For certain initial conditions, double transitions in the Bures geometrical discord are found. One of these transitions tends to disappear at a critical temperature.     

A fast algorithm for the elastic fields due to a single fiber break in a periodic fiber-reinforced composite

The stress state in a shear-lag model of a unidirectional fiber composite with an arbitrary configuration of fiber breaks is obtained by the weighted superposition of the stress state due to a single broken fiber. In a periodic patch comprised of N fibers located at the points of a regular lattice, a method to determine the stress state due to a single break was proposed by Landis et al. (J Mech Phys Solids 48(3):621–648, 2000). This method entails the determination of the eigenspace of an \(N\times N\) matrix, at a computational cost of \(O(N^3)\). In the present work, an alternative algorithm is proposed. This algorithm exploits the circulant structure of the matrix describing the inter-fiber interactions. The asymptotic computational complexity of the present algorithm equals that of the discrete Fourier transform: \({O}(N \log N)\). Run times of the present method with the eigensolution based method are compared, and shown to be very favorable for the present method, even for small N. Power-law scaling of the overloads due to a single break to much larger distances than previously possible has been verified using the present method.     

Universal features of elastic notch-tip stress fields

The results of linear elastic analyses of stress distributions near a wide variety of notches are presented. Notches under tension, tension and bending, and pure bending have been considered. It is demonstrated that notch-tip stress fields are similar to each other regardless of the notch geometry and the loading system. Universal functions describing the stress field in the notch-tip neighbourhood have been derived and tested againts available analytical, numerical and experimental data. The universal expressions can be used to calculate stresses in the region x⩽ 3ρ from the notch tip. These expressions can be particularly useful when using the weight function method to calculate stress intensity factors for cracks emanating from notches.     

硬弹性聚丙烯中空纤维的形成

通过应力场下聚丙烯熔体结晶制备出硬弹性聚丙烯中空纤维 .利用对样品弹性回复率及力学性能测试等手段 ,研究了硬弹性聚丙烯中空纤维的形成 .结果表明 :纺丝温度下降、熔体拉伸比增加及热处理等均有利于硬弹性聚丙烯中空纤维的形成 ,聚丙烯原料的分子量、纺丝冷却条件等对硬弹性的形成也有影响 .所制备的硬弹性中空纤维具有典型的应力 -应变行为 .     

Equilibrium analysis of finitely deformed elastic networks

A specialized membrane theory is used to analyze equilibrium configurations of finitely deformed elastic networks. The effects of wrinkling of the network are incorporated by using a certain relaxed strain energy function derived from minimum energy considerations. The stresses derived from this function are non-compressive at all values of the strain. In particular, a fibre strain associated with vanishing fibre stress may be viewed as resulting from fine-scale wrinkling of the fibre. In this way destabilizing compressive stresses are automatically excluded from the solution of an equilibrium boundary value problem.The properties of the relaxed strain energy are used to show that all equilibrium configurations are absolute minimizers of the total potential energy, for certain classes of boundary data. The equilibrium equations are discretized by a differencing method derived from Green's theorem, and artificial mass, damping and time are incorporated. Equilibrium configurations are then obtained in the long-time limit of a damped dynamical problem. Several examples of two- and three-dimensional deformations are presented, and comparisons with analytical solutions are made wherever possible.     

Discrimination of globally unpolarized fields through Stokes vector element correlations

In a previous publication [J. Opt. Soc. Am. A 21, 988 (2004)], we examined theoretically joint probability distributions of Stokes vector elements and suggested the existence of various types of globally unpolarized light that could be discriminated through measurement of the Stokes vector element correlations. We now study the joint distribution of the degree of polarization and the three Stokes parameters as it relates to material properties in highly scattering, depolarizing random media. We describe numerical and experimental results of second-order Stokes vector element correlations, demonstrating the existence of various types of nonclassical, globally unpolarized light, and we suggest experimental means for discriminating between such field distributions. We also discuss the usefulness of the Stokes vector element correlations as an experimental tool for discriminating between different globally unpolarized fields and for verifying the assumption of Gaussian statistics usually invoked in the context of multiple light scattering.     

Eshelby tensors for a spherical inclusion in microelongated elastic fields

Eshelby tensors are found for a spherical inclusion in a microelongated elastic field. Here, a special micromorphic model is introduced to describe the damaged material which defines the damage as the formation and the growth of microcracks and microvoids occurred in the material at the microstructural level. To determine the new material coefficients of the model, an analogy is established between the damaged body and the composite materials and then Mori–Tanaka homogenization technique is considered to obtain overall material moduli. Following this idea, the determination of the Eshelby tensors which establish the relation between the strains of the matrix material and of the inclusion becomes the first task. Introducing the concept of eigenstrain and microeigenstrain, the general constitutive theory is given for a homogeneous isotropic centrosymmetric microelongated media with defects. Then by the use of Green’s functions, micro and macro elastic fields are presented for the case of spherical inclusions embedded in an infinite microelongated material. Thus, the Eshelby tensors are obtained for a microelongated elastic field with a spherical inclusion and it is also shown that the classical Eshelby tensors can be obtained as a limit case of the microelongation.     

Distributions of electric and elastic fields at domain boundaries

In this paper we describe the application of the finite element method (FEM) in modelling spatial distributions of electric and elastic fields in a ferroelectric crystals with two domains separated by a 90° domain wall. The domain boundary is idealized as a two-dimensional defect in an electro-elastic continuum. It represents the source of inhomogenity and internal distortion in both elastic and electric fields. The main results are distributions of electric field, strain and mechanical force along the domain boundary.     

Dominance of asymptotic crack tip fields in elastic functionally graded materials

The stress field surrounding an edge crack in an elastic functionally graded plate is calculated using two dimensional finite element analysis. The property gradient direction is parallel to the crack line and loading is constrained to be symmetric such that a pure mode I situation is achieved. The extent of dominance of asymptotic fields is evaluated by comparing the stress field calculated from the finite element analysis to that calculated by asymptotic equations. Two separate forms of the asymptotic stress fields, one for homogeneous materials and another for continuously nonhomogeneous materials are used. The shape and extent of the dominance regions of each asymptotic field and their dependence on crack length and material nonhomogeneity is also presented. Under the pure mode I conditions considered here, it is seen that both asymptotic fields exist around the crack tip with the one for homogeneous materials in general being embedded in the one for continuously nonhomogeneous materials. The ligament length is seen to primarily control the extent of development of the asymptotic stress field for nonhomogeneous materials. The steepness of the material gradient affects the relationship between the two asymptotic stress fields and therefore the extent of their dominance.     

Transverse elastic moduli of unidirectional fiber composites with fiber/matrix interfacial debonding

An elastic contact model is developed to predict the transverse Young's modulus, Poisson's ratio and shear modulus of unidirectional fiber composites with interfacial debonding. The elastic deformation formulae of the fiber under contact pressure are derived by the use of elasticity theory. These results are then used in the formulation of an analytic boundaryelement method for solving the interfacial debonding problem. The two extreme cases of perfect bonding and the fiber-like void are also studied. On the basis of this theory, the upper and lower bounds of the transverse moduli for unidirectional fiber composites with imperfect fiber/matrix interfaces are provided. Numerical calculations of parametric studies are conducted for four composites, and some basic characteristics of the transverse elastic moduli of unidirectional fiber composites with interfacial debonding are presented.     

Attenuation of coupled waves in antiferromagnetic elastic conductors in weak magnetic fields

Following along the same line of approach as in a previous paper in which dissipative mechanisms were ignored, the present paper discusses the attenuation of coupled magnetoelastic oscillations in a simple deformable antiferromagnet of which the material symmetry has been broken by a relatively weak bias magnetic field. The linearized equations needed in the analysis are deduced from a fully dynamical nonlinear, rotationally invariant and thermodynamically admissible theory of deformable antiferromagnets. Three types of dissipative mechanisms are taken into account: viscosity, Spin-lattice relaxation and electrical conduction. While all these mechanisms affect to a greater or lesser degree the propagation of essentially transverse elastic modes outside resonance regions, electrical conduction modifies the absorption of spin waves due to spin-lattice relaxation and both viscosity and spin-lattice relaxation are shown to contribute, collaboratively and equally, to the damping of mixed elastic-spin modes in the two magnetoacoustic resonance regions which correspond to the interaction of left-circularly polarized transverse elastic waves and an upper spin-wave branch and right-circularly polarized transverse elastic waves and a lower spin-wave branch, respectively. The analytical discussion of the resulting dispersive and attenuated coupled modes is achieved in terms of characteristically small parameters in a quasi-magnetostatic approximation. The phenomenon of heat conduction, important as it may be, is left out of the analysis.     

Phase correlations at neighboring intensity critical points in gaussian random wave fields

Phase correlations are studied for neighboring critical points of the intensity in an isotropic Gaussian random wave field. Significant correlations and anticorrelations are found that extend out to at least the fifth nearest neighbors. A theoretical interpretation of the empirical data is attempted within the framework of the phase autocorrelation and the probability-density functions of extended two-dimensional random phase fields. It is found, however, that adaptations of these theoretical models are unable to account satisfactorily, or even qualitatively, for the extensive phase correlations that are present in these fields.     

Multi-modal social networks for modeling scientific fields

This paper analyzes whether methods from social network analysis can be adopted for the modeling of scientific fields in order to obtain a better understanding of the respective scientific area. The approach proposed is based on articles published within the respective scientific field and certain types of nodes deduced from these papers, such as authors, journals, conferences and organizations. As a proof of concept, the techniques discussed here are applied to the field of ‘Mobile Social Networking’. For this purpose, a tool was developed to create a large data collection representing the aforementioned field. The paper analyzes various views on the complete network and discusses these on the basis of the data collected on Mobile Social Networking. The authors demonstrate that the analysis of particular subgraphs derived from the data collection allows the identification of important authors as well as separate sub-disciplines such as classic network analysis and sensor networks and also contributes to the classification of the field of ‘Mobile Social Networking’ within the greater context of computer science, applied mathematics and social sciences. Based on these results, the authors propose a set of concrete services which could be offered by such a network and which could help the user to deal with the scientific information process. The paper concludes with an outlook upon further possible research topics.     

Effect of fiber orientation on the non-affine deformation of random fiber networks

The study of fiber networks is essential in understanding the mechanical properties of many polymeric and biological materials. These systems deform non-affinely, i.e. the local deformation is different than the applied far-field. The degree of non-affinity increases with decreasing scale of observation. Here, we show that this relationship is a power law with a scaling exponent independent of the type of applied load. Preferential fiber orientation influences non-affinity in a significant way: this parameter generally increases upon increasing orientation. However, some components of non-affinity, such as that associated with the normal strain in the direction of the preferential fiber orientation, decrease. In random networks, the nature of the far-field has little influence on the level of non-affinity. This is not the case in oriented networks.     

A model for crack initiation in elastic/plastic indentation fields

A model is proposed for the initiation of microfracture beneath sharp indenters. Using a simple approximation for the tensile stress distribution in the elastic/plastic indentation field, in conjunction with the principle of geometrical similarity, fracture mechanics procedures are applied to determine critical conditions for the growth of penny-like median cracks from sub-surface flaws. The analysis provides a functional relationship between the size of the critical flaw and the indentation load necessary to make this flaw extend. Initiation is well defined (unstable) only if the critical flaw lies within a certain size range; outside this range, large flaws can extend stably but small flaws can not extend at all. No flaws can extend below a characteristic minimum load, values of the indentation variables at this load accordingly providing useful threshold parameters. These quantities involve the intrinsic deformation/fracture parameters, hardness and toughness, in a fundamental way, thereby establishing a basis for materials selection in fracture-sensitive applications.     

Three-dimensional elastic stress fields ahead of blunt V-notches in finite thickness plates

Based on detailed three-dimensional (3D) finite element analyses, elastic fields in front of blunt V-notches in finite thickness plates subjected to uniaxial far-end tensile stress have been investigated. By comparison with the corresponding planar V-notch fields and 3D through-thickness sharp crack fields, various aspects of the 3D fields of the blunt V-notches in finite thickness plates are revealed: (1) The plate thickness and notch angle have obvious effects on the stress concentration factor (SCF) K _t, which is higher in finite thickness plates than in the plane stress and plane strain cases. When the notch angle is smaller than 90°, the SCF is insensitive to the notch angle, but has close relation with the dimensionless plate thickness. With the notch angle increasing further, the SCF decreases and the effect of dimensionless plate thickness on it becomes weaker. (2) For any notch angle considered, the variation of the opening stress _yy normalized by its value _yy0 at the notch-root with the distance x from the root normalized by the root-radius , is insensitive to the plate thickness and coincides well with the two-dimensional (2D) planar solution. (3) The 3D distribution of the out-of-plane constraint factor T _z=_zz/(_yy+_xx) is controlled by the plate thickness (B), the notch-radius () as well as the notch angle (), but for deeper V-notches with 90°, the distribution of T _z coincides well with that of a U-notch as well as a sharp 3D through-thickness crack and an explicit empirical expression of T _z is presented. (4) The distribution of the in-plane stress ratio T _x=_yy/_xx in front of the 3D V-notch is nearly independent of the plate thickness and coincides well with the corresponding 2D solutions when the opening angle is smaller than 120°. (5) The gradient of the out-of-plane strain _zz is significant near the free surface in finite thickness plates. On the free surface, the _zz can be 3.5 times the value on the mid-plane, and the through-thickness gradient of the _zz increases with decreasing notch angle. It is of interest to note that most of the field quantities ahead of V-notches are insensitive to the notch angles when the notch angle is smaller than 90°.     

Computational homogenization of nonlinear elastic materials using neural networks

In this work, a decoupled computational homogenization method for nonlinear elastic materials is proposed using neural networks. In this method, the effective potential is represented as a response surface parameterized by the macroscopic strains and some microstructural parameters. The discrete values of the effective potential are computed by finite element method through random sampling in the parameter space, and neural networks are used to approximate the surface response and to derive the macroscopic stress and tangent tensor components. We show through several numerical convergence analyses that smooth functions can be efficiently evaluated in parameter spaces with dimension up to 10, allowing to consider three‐dimensional representative volume elements and an explicit dependence of the effective behavior on microstructural parameters like volume fraction. We present several applications of this technique to the homogenization of nonlinear elastic composites, involving a two‐scale example of heterogeneous structure with graded nonlinear properties. Copyright © 2015 John Wiley & Sons, Ltd.     

碳纤维技术在不同应用领域中的发展状况研究

通过对德温特专利数据库收录的1963~2015年全球范围内申请的碳纤维技术相关专利的分析,从应用的角度研究了碳纤维技术在航空航天、交通、电缆、风力发电以及文体用品等领域的发展状况和趋势。研究表明,我国在文体用品、风力发电领域专利数量巨大,但在航空航天、交通领域的技术实力还比较弱,与国际领先水平差距较大。因技术实力落后,国外企业在中国专利布局也很少。可见,我国打造碳纤维产业还有很长的路要走。