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.     

具有非均匀界面相的颗粒和纤维增强复合材料弹性静力学问题的解析解

通过将以位移表示的平衡方程转化为黎卡提方程,得到了具有非均匀界面相的颗粒和纤维增强复合材料非均匀界面相内弹性场的解析解·　所得的解析解是弹性模量呈幂次方变化的非均匀界面相解的通用形式·　任意给定1个幂指数,可以得到具有非均匀界面相的颗粒和纤维增强复合材料体积模量的解析表达式·　通过改变幂指数及幂次方项的系数,此解析解可适用于具有多种不同性质的非均匀界面相·　结果表明:界面相模量和厚度对复合材料模量有很大的影响,当界面相存在时,粒子将出现一种"尺寸效应"·     

残余界面应力对粒子填充热弹性纳米复合材料有效热膨胀系数的影响

根据黄筑平等人提出的基于“3个构形”的表/界面能理论,研究了热弹性纳米复合材料的有效性质,重点讨论了残余界面应力对纳米尺度夹杂填充的热弹性复合材料有效热膨胀系数的影响．首先,给出了由第一类Piola-Kirchhoff界面应力表示的热弹性界面本构关系和Lagrange描述下的Young-Laplace方程;其次,采用Hashin复合球作为代表性体积单元,推导了在参考构形下复合球内部由残余界面应力诱导的残余弹性场,并进一步计算了从参考构形到当前构形的变形场;最后,基于以上计算得到了热弹性复合材料有效体积模量和有效热膨胀系数的解析表达式．研究表明,残余表/界面应力对复合材料的热膨胀系数有重要影响．     

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。     

正交异性双材料界面裂纹尖端应力场

通过构造新的应力函数,利用复合材料断裂复变方法,对正交异性双材料界面裂纹进行了研究.在特征方程组的判别式都大于零的情形下,推出了Ⅰ型界面裂纹尖端的应力场、位移场的理论公式,其结果没有振荡奇异性及裂纹面没有相互嵌入现象.     

用界面单元法分析复合材料界面力学性能

本文利用界面单元的固有特性，将其用来模拟复合材料中纤维与基体之间的界面特征，计算了一个沿Ｘ轴方向纤维周期排列的单尾板，在横向载荷作用下的应力分布问题．给出了三相（纤维、基体和界面）特性各种配比时应力分布等高线图以及通过界面时径向应力σｒ的变化情况，反映了界面特性对应力分布的影响．     

颗粒增强复合材料相界面的动态应力分析

针对硬微粒填充高聚物复合材料因相界面脱粘开裂生成微孔洞的微损伤成核机制,取材料的代表体积单元进行动力分析,通过对粘弹性基体本构关系作Laplace变换建立了基本方程,并引入Hankel变换,得到了球对称动荷载作用下相界面应力变化规律的解析解,据此分析了惯性效应和粘性效应对界面脱粘的影响。     

压电压磁复合材料中界面裂纹对弹性波的散射

利用Schmidt方法分析了压电压磁复合材料中可导通界面裂纹对反平面简谐波的散射问题．经过富里叶变换得到了以裂纹面上的间断位移为未知变量的对偶积分方程A·D2在求解对偶积分方程的过程中,裂纹面上的间断位移被展开成雅可比多项式的形式．数值模拟分析了裂纹长度、波速和入射波频率对应力强度因子、电位移强度因子、磁通量强度因子的影响A·D2从结果中可以看出,压电压磁复合材料中可导通界面裂纹的反平面问题的应力奇异性形式与一般弹性材料中的反平面问题应力奇异性形式相同．     

压电复合材料圆形夹杂中螺型位错和界面裂纹的干涉分析

研究了无穷远纵向剪切和面内电场共同作用下,压电复合材料圆形夹杂中螺型位错与界面裂纹的电弹耦合干涉作用．运用Riemann-Schwarz 对称原理,并结合复变函数奇性主部分析方法,获得了该问题的一般解答．作为典型算例,求出了界面含一条裂纹时基体和夹杂区域复势函数和电弹性场的封闭形式解．应用广义Peach-Koehler公式,导出了位错力的解析表达式．分析了裂纹几何参数和材料的电弹性常数对位错力的影响规律．结果表明,界面裂纹对位错力和位错平衡位置有很强的扰动效应,当界面裂纹长度达到临界值时,可以改变位错力的方向．该结果可以作为格林函数研究圆形夹杂内裂纹和界面裂纹的干涉效应．其公式的退化结果与已有文献完全一致．     

空心球复合材料热弹性性质的一些精确结果

本文基于所提出的基体均匀场方法研究了空心球增强复合材料的热弹性性质·导出了均匀边界条件激发的局部热场和力学场量的关系，并进而得到了复合材料等效热弹性性质之间的精确关系·对于具有某种特定内外径比的空心球所构成的宏观各向同性复合材料，如果基体和空心球的热膨胀系数相同，可以证明其等效体积模量和线膨胀系可以精确地确定·     

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)     

Effect of anisometry of a platelike nanofiller on the elastic constants of a transversely isotropic composite

Analysis results for the elastic properties of a composite with a small amount of coplanarly arranged platelike filler particles are presented. The geometrical form of the particles is described by an oblate ellipsoid of revolution. The calculations are performed by formulas obtained by using the Eshelby approach for media with a low concentration of inclusions. The effect of anisometry of the ellipsoidal particles and of the ratio between the elastic moduli of the filler and matrix on the effective elastic constants of the composite is discussed. Calculation results are compared with experimental data for the elastic moduli of a nanocomposite containing completely exfoliated particles of an unmodified montmorillonite. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 4, pp. 493–504, July–August, 2008.     

Anisotropy of elasticity of a composite with irregularly oriented anisometric filler particles

The effects of orientation and shape of filler particles on the elastic properties of composites have been analyzed. The elastic constants of a composite with irregularly oriented filler particles were calculated by using the method of orientational averaging of the properties of a representative structural element. The elastic constants of the structural element were found according to a known generalized Eshelby solution for a finite concentration of ellipsoidal inclusions. The diagrams of elasticity anisotropy for a transversely isotropic structural element and an orthotropic composite with irregularly oriented inclusions are presented. A quantitative estimate for the degree of anisotropy of elastic properties of composites is suggested. Data on the influence of shape anisometry of inclusions on the anisotropy coefficient of filled composites are also reported.     

Explicit jump immersed interface method for virtual material design of the effective elastic moduli of composite materials

Virtual material design is the microscopic variation of materials in the computer, followed by the numerical evaluation of the effect of this variation on the material’s macroscopic properties. The goal of this procedure is an in some sense improved material. Here, we give examples regarding the dependence of the effective elastic moduli of a composite material on the geometry of the shape of an inclusion. A new approach on how to solve such interface problems avoids mesh generation and gives second order accurate results even in the vicinity of the interface. The Explicit Jump Immersed Interface Method is a finite difference method for elliptic partial differential equations that works on an equidistant Cartesian grid in spite of non-grid aligned discontinuities in equation parameters and solution. Near discontinuities, the standard finite difference approximations are modified by adding correction terms that involve jumps in the function and its derivatives. This work derives the correction terms for two dimensional linear elasticity with piecewise constant coefficients, i.e. for composite materials. It demonstrates numerically convergence and approximation properties of the method.      

Deformation of orthotropic composites with unidirectional ellipsoidal inclusions under matrix microdamages

In the present paper, a model of deformation of stochastic composites under microdamaging is developed for the case of orthotropic composite, when the microdamages are accumulated in the matrix. The composite is treated as an isotropic matrix strengthened by three-axial ellipsoidal inclusions with orthotropic symmetry of elastic properties. It is assumed that the loading process leads to accumulation of damages in the matrix. Fractured microvolumes are modeled by a system of randomly distributed quasispherical pores. The porosity balance equation and relations for determining the effective elastic moduli for the case of a composite with orthotropic components are taken as the basic relations. The fracture criterion is assumed to be given as the limit value of the intensity of average shear stresses occurring in the undamaged part of the material. Based on the analytical and numerical approach, an algorithm for the determination of nonlinear deformation properties of such a material is constructed. The nonlinearity of composite deformations is caused by the accumulation of microdamages in the matrix. Using the numerical solution, nonlinear stress-strain diagrams for the orthotropic composite in the case of biaxial extension are obtained. Published in Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 51, No. 1, pp. 121–130, January–March, 2008.     

Dynamic stresses in a compound body with circular crack under sliding contact on an interface

We have considered the three-dimensional problem of harmonic loading of a circular crack in an elastic composite consisting of two dissimilar half-spaces under sliding contact on the surface of their bonding. The defect is situated in one of the half-spaces perpendicularly to the interface of materials. Using the representations of solutions in the form of Helmholtz potentials, we have reduced the problem to a boundary integral equation for the function of dynamic defect opening. Based on the numerical solution of this equation, we have obtained the frequency dependences of mode I stress intensity factor near the crack for different relations between the elastic moduli of components of the composite and the depths of crack location with respect to the interface.     

The Eshelby tensor

The problem of the existence of a tensor that is inverse to the well-known Eshelby tensor, which connects the free homogeneous and hindered strains of an ellipsoidal elastic inclusion undergoing transformation, is investigated. It is shown that this tensor exists for inclusions in the form of oblate and prolate spheroids in isotropic elastic space. Certain applications are considered, in particular problems of determining the stresses in ellipsoidal rigid and rigid plastic inclusions.     

Deformation of composites with arbitrarily oriented orthotropic fibers under matrix microdamages

In the present work, a model of nonlinear deformation of stochastic composites under microdamaging is developed for the case of a composite with orthotropic inclusions, when microdefects are accumulated in the matrix. The composite is treated as an isotropic matrix strengthened by triaxial arbitrarily oriented ellipsoidal inclusions with orthotropic symmetry of the elastic properties. It is assumed that the process of loading leads to accumulation of damage in the matrix. Fractured microvolumes are modeled by a system of randomly distributed quasispherical pores. The porosity balance equation and relations for determining the effective elastic modules in the case of orthotropic components are taken as basic relations. The fracture criterion is specified as the limiting value of the intensity of average shear stresses acting in the intact part of the material. On the basis of the analytic and numerical approach, we propose an algorithm for the determination of nonlinear deformation properties of the investigated material. The nonlinearity of composite deformations is caused by the finiteness of deformations. By using the numerical solution, the nonlinear stress–strain diagrams are predicted and discussed for an orthotropic composite material for various cases of orientation of inclusions in the matrix.     

On bounding the effective conductivity of isotropic composite materials

In this paper inequalities for the effective conductivity of isotropic composite materials are derived. These inequalities depend on several coefficients characterizing the microstructure of composites. The obtained coefficients can be exactly calculated for models of a two-component aggregate of multisized, coated ellipsoidal inclusions, packed to fill all space. As a result, new bounds for effective conductivity, considerably narrower than those of Hashin-Shtrikman, are established for such models of composite materials.     

Thermally Stressed State of Bodies with Two Ellipsoidal Inclusions

Solutions are obtained for the interaction of two ellipsoidal inclusions in an elastic isotropic matrix with polynomial external athermal and temperature fields. Perfect mechanical and temperature contact is assumed at the phase interface. A solution to the problem is constructed. When the perturbations in the temperature field and stresses in the matrix owing to one inclusion are re-expanded in a Taylor series about the center of the second inclusion, and vice versa, and a finite number of expansion terms is retained, one obtains a finite system of linear algebraic equations in the unknown constants. The effect of a force free boundary of the half space on the stressed state of a material with a triaxial ellipsoidal inhomogeneity (inclusion) is investigated for uniform heating. Here it was assumed that the elastic properties of the inclusions and matrix are the same, but the coefficients of thermal expansion of the phases differ. Studies are made of the way the stress perturbations in the matrix increase and the of the deviation from a uniform stressed state inside an inclusion as it approaches the force free boundary.