考虑内部胞元能量等效的代表体元法

具有周期性胞元的超轻质材料在制造和应用过程中,不可避免地会出现基体材料、微结构拓扑和尺寸的随机性变化.此时,评价材料的等效弹性性能需要借助基于均匀化方法(周期性边界条件)或代表体元法(周期性边界条件,均匀应力或均匀应变边界条件等)的蒙特卡洛模拟.该文首先通过算例分析和比较了不同边界条件下的数值结果,讨论了结果的尺度效应和对胞元选取的依赖性.为了提高和改善Dirichlet边界条件下的计算效率和结果,提出了一种考虑内部胞元能量等效的代表体元法.该方法能够有效削弱边界条件和胞元选取的影响,从而实现了采用较小的代表体元得到更好的结果.数值算例验证了方法在预测确定性材料和随机性材料等效模量时的有效性.     

Homogeneous films by inverse pulsed laser deposition

Recently, we proposed an alternative arrangement to traditional on- or off-axis PLD geometries, termed inverse PLD (IPLD) that is capable of producing films of improved surface morphology. Two configurations of this new target-substrate arrangement were developed, namely static and co-rotating IPLD. In the static IPLD configuration, the substrate is stationary with respect to the ablated spot; while in the co-rotating IPLD configuration the substrate is fixed to the target surface and rotates simultaneously with the target, hence offering an appealingly simple approach to homogenize film properties.Here we report the growth of CN_x and Ti films, simultaneously deposited in the co-rotating and static IPLD arrangements. The homogeneity of the co-rotating films is described by a thickness inhomogeneity index, which allows for the comparison of films of different lateral dimension. A semi-analytical, semi-numerical model is proposed to derive the radial variation of the growth rate of co-rotating IPLD films from the lateral growth rate distributions measured along the symmetry axes of static IPLD films. The laterally averaged growth rate, LAGR is used to describe how the ambient pressure affects growth in the 0.5-50 Pa domain. As an example, the absolute error between the measured and calculated radial growth rate variation, obtained at 5 Pa, was less than 3%, while the LAGR of CN_x layers grown by co-rotating IPLD was predicted with 20% accuracy.     

Asymptotics for models of non‐stationary diffusion in domains with a surface distribution of obstacles

We consider a time‐dependent model for the diffusion of a substance through an incompressible fluid in a perforated domain Ω_?, with n = 3,4. The fluid flows in a domain containing a periodical set of “obstacles” (Ω\Ω_?) placed along an inner (n ? 1)‐dimensional manifold . The size of the obstacles is much smaller than the size of the characteristic period ?. An advection term appears in the partial differential equation linking the fluid velocity with the concentration, while we assume a nonlinear adsorption law on the boundary of the obstacles. This law involves a monotone nonlinear function σ of the concentration and a large adsorption parameter. The “critical adsorption parameter” depends on the size of the obstacles , and, for different sizes, we derive the time‐dependent homogenized models. These models contain a “strange term” in the transmission conditions on Σ, which is a nonlinear function and inherits the properties of σ. The case in which the fluid velocity and the concentration do not interact is also considered for n ≥ 3.     

Stationary heat conduction in a macro- and microperiodically layered solid

Summary This paper deals with the stationary heat conduction in a solid consisting of planar, isotropic or transversely isotropic layers. The following cases are considered: (1) arbitrarily layered solid, (2) macroperiodically layered solid, consisting of equal pairs of different basic layers with finite thicknesses, (3) microperiodically layered solid, consisting of equal layer groups of two or more different basic layers of infinitesimal thicknesses. Assuming a perfect contact between the layers, exact solutions for the plane, the axisymmetric and the general three-dimensional problem of macro- and microperiodically layered semispaces, respectively, are derived using integral transforms and the transfer-matrix method. It is proved that the microperiodically layered solid with isotropic or transversely isotropic basic layers is equivalent to a homogeneous transversely isotropic solid. Received 31 March 1999; accepted for publication 21 May 1999     

Roughness-induced effects on the thermomicropolar fluid flow through a thin domain

In this paper, we study the asymptotic behavior of the thermomicropolar fluid flow through a thin channel with rough boundary. The flow is governed by the prescribed pressure drop between the channel's ends and the heat exchange through the rough wall is allowed. Depending on the limit of the ratio between channel's thickness and the wavelength of the roughness, we rigorously derive different asymptotic models clearly showing the roughness-induced effects on the average velocity and microrotation. To accomplish that, we employ the adaptation of the unfolding method to a thin-domain setting.     

多孔氧化铝薄膜横观各向同性弹性性质的研究

电化学阳极氧化生成的氧化铝薄膜含有高度有序的纳米孔阵列,本文首先假设氧化铝薄膜基体(无孔部分)为各向同性,结合其周期性孔结构特点和均匀化理论,可以得到氧化铝基体和薄膜弹性性质之间的关系。然后利用单轴拉伸结合电子散斑干涉(ESPI)的方法得到薄膜面内的杨氏模量为63.4GPa,并根据均匀化方法得到的基体与薄膜弹性性质的关系进一步推出薄膜横观各向同性的其它弹性参数,如基体杨氏模量等。为证明结果的可靠性,利用推出的弹性参数建立三维有限元模型,模拟纳米压痕实验,得到的加卸载曲线与实验曲线相吻合。     

Effective elastic shear stiffness of a periodic fibrous composite with non-uniform imperfect contact between the matrix and the fibers

In this contribution, effective elastic moduli are obtained by means of the asymptotic homogenization method, for oblique two-phase fibrous periodic composites with non-uniform imperfect contact conditions at the interface. This work is an extension of previous reported results, where only the perfect contact for elastic or piezoelectric composites under imperfect spring model was considered. The constituents of the composites exhibit transversely isotropic properties. A doubly periodic parallelogram array of cylindrical inclusions under longitudinal shear is considered. The behavior of the shear elastic coefficient for different geometry arrays related to the angle of the cell is studied. As validation of the present method, some numerical examples and comparisons with theoretical results verified that the present model is efficient for the analysis of composites with presence of imperfect interface and parallelogram cell. The effect of the non uniform imperfection on the shear effective property is observed. The present method can provide benchmark results for other numerical and approximate methods.