球形涂层粒子增强复合材料的有效模量

本文通过四相球模型和复合材料的等效介质理论,研究了球形涂层粒子增强复合材料的有效模量性质,得到了这种增强复合材料的有效体积模量和有效剪切模量的理论预测公式。这些结果在特殊情况下,可退化到三相球模型确定的球形粒子增强复合材料的有效模量公式。     

Effective bulk moduli of materials containing stochastically distributed nano-inhomogeneities with surface stresses

In the present contribution, a mathematical model for the investigation of the effective properties of a material with randomly distributed nano-particles is proposed. The surface effect is introduced via Gurtin-Murdoch equations describing properties of the matrix/nano-particle interface. They are added to the system of stochastic differential equations formulated within the framework of linear elasticity. The homogenization problem is reduced to finding a statistically averaged solution of the system of stochastic differential equations. These equations are based on the fundamental equations of linear elasticity, which are coupled with surface/interface elasticity accounting for the presence of surface tension. Using Green's function this system is transformed to a system of statistically non-linear integral equations. It is solved by the method of conditional moments. Closed-form expressions are derived for the effective moduli of a composite consisting of a matrix with randomly distributed spherical inhomogeneities. The radius of the nano-particles is included in the expression for the bulk moduli. As numerical examples, nano-porous aluminum and nano-porous gold are investigated assuming that only the influence of the interface effects on the effective bulk modulus is of interest. The dependence of the normalized bulk moduli of nano-porous aluminum on the pore volume fraction (for certain radii of nano-pores) are compared to and discussed in the context of other theoretical predictions. The effective Young's modulus of nano-porous gold as a function of pore radius (for fixed void volume fraction) and the normalized Young's modulus vs. the pore volume fraction for different pore radii are analyzed. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Three‐dimensional blockmodels

In the classic blockmodel formulation, a social network among members of a population with n actors and k relations (types of tie) is arrayed as k n X n matrices. Though this is a three‐dimensional data structure, it is typically reduced to a two‐way analysis. In this paper, a three‐way procedure for analyzing multigraph data is developed. Specifically, in addition to applying the rule of structural equivalence to collapse actors, it is also applied to the relations (the third dimension), and structurally equivalent sets of relations are collapsed. The result is a three‐dimensional blockmodel (image) of social structure that is a more parsimonious representation of social structure than the classic two‐dimensional blockmodel images. The three‐dimensional approach is illustrated by application to three case studies: Homan's Bank Wiring Room, Sampson's monastery, and a local economy of hospital services. The structural equivalence approach to relations is further explored by applying it to the individual‐level Liking and Antagonism relations and their compounds (of length four or less) in the Bank Wiring Room. This application demonstrates that the structural equivalence approach can be used to identify equality equations for primitive and compound relations.     

Modeling viscoelastic response of particulate polymeric composites with high volume fractions of fillers

A generalized self-consistent method is extended to particulate viscoelastic composites with elastomeric matrices and high volume fractions of elastic inclusions. It is shown that the effective bulk modulus of a composite coincides with the bulk modulus of particles. A quadratic operator equation is derived for an analog of the effective shear relaxation kernel. This equation is explicitly solved using the Laplace transform method. The influence of material and geometrical parameters of a composite on its effective viscoelastic moduli is analyzed numerically.     

Determination of shear and bulk characteristics of materials

A method is proposed for the determination of shear and bulk influence functions, and also the bulk and shear moduli and Poisson's ratio, based on experiments for creep of monaxially stretched (compressed) samples.

     

On the integral representation formula for a two‐component elastic composite

The aim of this paper is to derive, in the Hilbert space setting, an integral representation formula for the effective elasticity tensor for a two‐component composite of elastic materials, not necessarily well‐ordered. This integral representation formula implies a relation which links the effective elastic moduli to the N‐point correlation functions of the microstructure. Such relation not only facilitates a powerful scheme for systematic incorporation of microstructural information into bounds on the effective elastic moduli but also provides a theoretical foundation for inverse‐homogenization. The analysis presented in this paper can be generalized to an n‐component composite of elastic materials. The relations developed here can be applied to the inverse‐homogenization for a special class of linear viscoelastic composites. The results will be presented in another paper. Copyright © 2005 John Wiley & Sons, Ltd.     

预测纳米纤维复合材料有效弹性性能的界面模型和界面相模型北大核心CSCD

基于广义自洽法,同时采用Gurtin-Murdoch界面模型和界面相模型研究了纳米纤维复合材料的有效弹性性能,获得了两种模型下有效体积模量的封闭解析解和计算有效面内剪切模量数值解的全部公式.基于界面模型的解答,讨论了有效体积模量和有效面内剪切模量的界面效应.证明了界面模型的解答可由界面相模型的解答退化得到,其中有效体积模量可以实现解析退化,有效面内剪切模量则可以数值退化.以含纳米孔洞的金属铝为例,比较了两种模型计算结果的差异.结果表明,当纳米孔洞半径较小时,两个模型的结果存在很大差异,而当半径较大时两个模型的结果差别不大.     

Stability conditions and extremal contractions

We study extremal contractions from smooth projective varieties via a moduli theoretic approach. In the two dimensional case, we show that any extremal contraction appears as a moduli space of Bridgeland stable objects in the derived category of coherent sheaves. In the three dimensional case, we show that a a similar result holds with respect to conjectural Bridgeland stability conditions.     

Asymptotic expansions for the voltage potentials with two‐dimensional and three‐dimensional thin interfaces

We derive asymptotic formulae for two‐dimensional and three‐dimensional steady state voltage potentials associated with thin conductivity imperfections having no uniform thickness. These formulae recover highly conducting inclusions and those with interfacial resistance. Our calculations are rigorous and based on layer potential techniques. Copyright © 2011 John Wiley & Sons, Ltd.     

Numerical simulation of generalized newtonian blood flow past a couple of irregular arterial stenoses

This paper looked at the numerical investigations of the generalized Newtonian blood flow through a couple of irregular arterial stenoses. The flow is treated to be axisymmetric, with an outline of the stenoses obtained from a three dimensional casting of a mild stenosed artery, so that the flow effectively becomes two‐dimensional. The Marker and Cell (MAC) method is developed for the governing unsteady generalized Newtonian equations in staggered grid for viscous incompressible flow in the cylindrical polar co‐ordinates system. The derived pressure‐Poisson equation was solved using Successive‐Over‐Relaxation (S.O.R.) method and the pressure‐velocity correction formulae have been derived. Computations are performed for the pressure drop, the wall shear stress distribution and the separation region. The presented computations show that in comparison to the corresponding Newtonian model the generalized Newtonian fluid experiences higher pressure drop, lower peak wall shear stress and smaller separation region. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 960–981, 2011     

Homogenization of Unidirectional and Arbitrarily Oriented Fiber-Reinforced Materials by the Method of Conditional Moments

In this paper the method of conditional moments is developed for the case of a two–component matrix composite with randomly distributed unidirectional and arbitrarily oriented ellipsoidal inclusions. The algorithm for determination of the effective elastic properties of composites from the given elastic constants of the components and geometrical parameters and orientation of inclusions is discussed. It is assumed that the components of the composite show orthotropic symmetry of thermoelastic properties. As a numerical example arbolite (straw particle inclusions in a cement matrix) is considered. The dependencies of Young's moduli, Poisson's ratios and shear moduli from the concentration of inclusions and for certain orientations of the inclusions are predicted and discussed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The effective shear modulus for an n-layered composite sphere

This work presents the derivation of the effective shear modulus for a heterogeneous material composed of multi-layered composite spheres embedded in a linear elastic matrix. It is based on the composite spheres model known from the literature. In contrast to previous publications the effective shear modulus is obtained by equating the results of two models: In the first model, a heterogeneous sphere is embedded in an equivalent homogeneous material, whereas in the second model, the heterogeneous sphere is replaced by an equivalent homogeneous sphere. In the context of both, a shear stress approach and a shear deformation approach, this results into an overdetermined system of equations which is solved with the least squares method. In a numerical study our results are compared to effective moduli and bounds from the literature. Furthermore, a convincing agreement with experimental data for glass microspheres embedded in a polyester matrix is demonstrated. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the representation formula for well‐ordered elastic composites: a convergence of measure approach

The aim of this paper is to derive an integral representation formula for the effective elasticity tensor for a two‐component well‐ordered composite of elastic materials without using a third reference medium and without assuming the completeness of the eigenspace of the operator ? defined in (2.16) in (J. Mech. Phys. Solids 1984; 32 (1):41–62). As shown in (J. Mech. Phys. Solids 1984; 32 (1):41–62) and (Math. Meth. Appl. Sci. 2006; 29 (6):655–664), this integral representation formula implies a relation which links the effective elastic moduli to the N‐point correlation functions of the microstructure. Such relation not only facilitates a powerful scheme for systematic incorporation of microstructural information into bounds on the effective elastic moduli but also provides a theoretical foundation for de‐homogenization. The analysis presented in this paper can be generalized to an n‐component composite of elastic materials. The relations developed here can be applied to the de‐homogenization for a special class of linear viscoelastic composites. The results will be presented in another paper. Copyright © 2006 John Wiley & Sons, Ltd.     

Transparent boundary conditions based on the pole condition for time‐dependent,two‐dimensional problems

The pole condition approach for deriving transparent boundary conditions is extended to the time‐dependent, two‐dimensional case. Nonphysical modes of the solution are identified by the position of poles of the solution's spatial Laplace transform in the complex plane. By requiring the Laplace transform to be analytic on some problem‐dependent complex half‐plane, these modes can be suppressed. The resulting algorithm computes a finite number of coefficients of a series expansion of the Laplace transform, thereby providing an approximation to the exact boundary condition. The resulting error decays super‐algebraically with the number of coefficients, so relatively few additional degrees of freedom are sufficient to reduce the error to the level of the discretization error in the interior of the computational domain. The approach shows good results for the Schrödinger and the drift‐diffusion equation but, in contrast to the one‐dimensional case, exhibits instabilities for the wave and Klein–Gordon equation. Numerical examples are shown that demonstrate the good performance in the former and the instabilities in the latter case. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013     

Assessment of transmission of the shear stress in potted anchors for composite rods 3. Bipotted anchor

Our previous investigation into the means for decreasing the peak interfacial shear stress in bond-type anchors for fiber-reinforced polymer rods [1, 2] is extended to include the case where the bonded length of the rod is divided into two regions, each having a potting material with a different elastic modulus. Based on the analytical model developed earlier, a detailed parametric analysis of the influence of such parameters of a bipotted anchor as the relative lengths of anchorage zones and the pottant moduli is carried out for two schemes of anchor loading.     

Shatalov‐Sternin's construction of complex WKB solutions and the choice of integration paths

We re‐examine Shatalov‐Sternin's proof of existence of resurgent solutions of a linear ODE. In particular, we take a closer look at the “Riemann surface” (actually, a two‐dimensional complex manifold) whose existence, endless continuability and other properties are claimed by those authors. We present a detailed argument for a part of the “Riemann surface” relevant for the exact WKB method.     

The quasi‐reversibility method for a final value problem of the time‐fractional diffusion equation with inhomogeneous source

This paper is devoted to discuss a multidimensional backward heat conduction problem for time‐fractional diffusion equation with inhomogeneous source. This problem is ill‐posed. We use quasi‐reversibility regularization method to solve this inverse problem. Moreover, the convergence estimates between regularization solution and the exact solution are obtained under the a priori and the a posteriori choice rules. Finally, the numerical examples for one‐dimensional and two‐dimensional cases are presented to show that our method is feasible and effective.     

Investigation of constrained-layer technique using exact elasticity theory

It is possible to damp flexural waves in metal plates by means of a layer of elastomeric material with high loss factor. It was found that adding a third layer of metal enhances the damping effect. This may be explained by observing that the constraining layer increases shear in the elastomer layer, and thus increases energy loss due to the loss factor in its shear modulus.The purpose of the present investigation is to extend computational techniques by which one may decide on optimum combinations of layer thickness and material properties for a given damping application. A model proposed by Kerwin in 1959 shows the effect of the various parameters on the attenuation, but it uses thin-plate theory for the base plate and does not account for extensional waves. Kerwin's model is extended to include extentional waves. A hybrid model is presented whereby the base plate is described by exact elasticity theory. Comparison of the results from the hybrid model with those from the extended model shows the consequences of the use of exact elasticity theory.     

Uniqueness of Tangent Cones for Two‐Dimensional Almost‐Minimizing Currents

We consider two‐dimensional integer rectifiable currents that are almost area minimizing and show that their tangent cones are everywhere unique. Our argument unifies a few uniqueness theorems of the same flavor, which are all obtained by a suitable modification of White's original theorem for area‐minimizing currents in the euclidean space. This note is also the first step in a regularity program for semicalibrated two‐dimensional currents and spherical cross sections of three‐dimensional area‐minimizing cones.© 2017 Wiley Periodicals, Inc.     

A NEW STEPSIZE FOR THE STEEPEST DESCENT METHOD

The steepest descent method is the simplest gradient method for optimization. It is well known that exact line searches along each steepest descent direction may converge very slowly. An important result was given by Barzilar and Borwein, which is proved to be superlinearly convergent for convex quadratic in two dimensional space, and performs quite well for high dimensional problems. The BB method is not monotone, thus it is not easy to be generalized for general nonlinear functions unless certain non-monotone techniques being applied. Therefore, it is very desirable to find stepsize formulae which enable fast convergence and possess the monotone property. Such a stepsize αk for the steepest descent method is suggested in this paper. An algorithm with this new stepsize in even iterations and exact line search in odd iterations is proposed. Numerical results are presented, which confirm that the new method can find the exact solution within 3 iteration for two dimensional problems. The new method is very efficient for small scale problems. A modified version of the new method is also presented, where the new technique for selecting the stepsize is used after every two exact line searches. The modified algorithm is comparable to the Barzilar-Borwein method for large scale problems and better for small scale problems.