基于均匀化理论的页岩微观多孔黏土强度特性

页岩强度是页岩油气开发所必需的基础技术参数之一,对页岩强度的研究贯穿于钻完井、压裂工艺施工的全过程.常规宏观室内实验存在试样获取困难、耗时较长,受井下工矿制约,地球物理方法获取资料品质欠佳且增加了井下设备卡、埋风险.因此,提出基于均匀化理论评价页岩微观多孔黏土强度的方法,进行多孔黏土组成与力学分析.基于耗散能原理和Drucker-Prager准则,开展了微观多孔黏土的强度与$\pi$函数的应变求解分析;讨论黏土颗粒与粒间孔隙的力学特性,建立多孔黏土的均匀化应变能;采用强度均匀化理论构建微观非线性函数模型,建立与多孔黏土组成、摩擦系数、内聚系数等参数相关的均匀化函数模型;基于纳米力学实验、量纲分析和有限元模拟,分析多孔黏土硬度、强度与组成的内在关系.研究结果表明,页岩微观多孔黏土的弹性模量和硬度与黏土堆积密度正相关,当黏土堆积密度一定时,硬度与内聚系数的比值受摩擦系数影响较大,为非线性递增;通过量纲分析和有限元模拟,求解页岩微观多孔黏土关于硬度--强度--堆积密度的$\pi$函数,揭示页岩微观黏土矿物的组成与力学性质的关系,为进一步深入研究页岩细观强度参数和宏观强度预测奠定基础.      

基于降阶均匀化理论的混凝土双尺度力学性能分析

混凝土材料细观特性对宏观力学性能有着重要影响。为进一步分析混凝土细观特性对宏观力学行为的影响规律,将混凝土材料简化为由骨料、砂浆和界面三相组成,编制了随机凸多面体骨料生成、投放和网格剖分算法,建立可用于有限元计算的满足级配要求的随机细观模型。针对直接使用细观力学模型计算量较大的问题,采用降阶均匀化理论,对混凝土细观胞元模型进行预处理并编制了相应的双尺度计算程序。对不同强度混凝土进行了单轴静态压缩双尺度计算,与实验数据和细观力学模拟结果符合较好。研究表明,降阶均匀化理论在加快求解速度的同时具有较高的精度,可以用于混凝土的多尺度力学性能分析。     

多尺度方法在复合材料力学分析中的研究进展

简要介绍了多尺度方法的分类及各自的适用范围,重点阐述了主要的多尺度分析方法------均匀化理论,详细论述了多尺度分析方法在纤维增强复合材料弹性、黏弹性、塑性、失效退化、热力学等力学性能中的研究进展,最后对多尺度分析方法的前景进行了展望.      

On the homogenization of weakly nonlinear divergent operators in a perforated cube

In the present paper we consider a second order weakly nonlinear elliptic equation of divergent form with a lower term growing at infinity (with respect to the unknown function) as a power function. It is proved that a sequence of solutions in the perforated cubes converges to a solution in the nonperforated cube as the diameters of the holes tends to zero, and the rate of convergence depends on the power exponent of the lower term. Translated fromMatematicheskie Zametki, Vol. 68, No. 3, pp. 390–398, September, 2000.     

Homogenization of Wall-Slip Gas Flow Through Porous Media

The permeability of reservoir rocks is most commonly measured with an atmospheric gas. Permeability is greater for a gas than for a liquid. The Klinkenberg equation gives a semi-empirical relation between the liquid and gas permeabilities. In this paper, the wall-slip gas flow problem is homogenized. This problem is described by the steady state, low velocity Navier–Stokes equations for a compressible gas with a small Knudsen number. Darcy's law with a permeability tensor equal to that of liquid flow is shown to be valid to the lowest order. The lowest order wall-slip correction is a local tensorial form of the Klinkenberg equation. The Klinkenberg permeability is a positive tensor. It is in general not symmetric, but may under some conditions, which we specify, be symmetric. Our result reduces to the Klinkenberg equation for constant viscosity gas flow in isotropic media.     

TEM Investigation of Stacking Faults in the Superconducting Compound YNi2B2C

To evaluate the influence of composition and high-temperature heat treatment on the occurrence of stacking faults and intergrowths in the layered superconducting compound YNi₂B₂C a series of polycrystalline samples and a single crystal were investigated by TEM. Stacking faults were found in the most inhomogeneous sample only, which was annealed at 1100°C. Homogenisation at temperatures of 1450°C and higher results in a recovery of stacking faults. The observed faults should develop during crystallisation by formation of extra planes of YC or Ni₂B, resulting in a local deviation from the stoichiometric composition. In highly faulted areas the distance of stacking faults was about 50nm. These faults have apparently no influence on the superconduction transition temperature T_c.     

高密度封装倒装焊的新简化模型及疲劳寿命分析

高密度封装结构中存在大量焊球,在进行有限元建模时,考虑到焊球数量多且尺寸小的特点,需简化焊球层模型．本文针对高密度封装结构中倒装焊及底填胶,提出了一种新的简化模型,采用非重点部位简化和材料均匀化相结合的方法,将内部焊球层和底填胶简化为均匀层,只保留外圈几层焊球．通过建立代表性体积单元,计算得到均匀化层的材料参数．讨论了外层焊球圈数对焊球层危险点应力的影响,发现保留外圈两层焊球就能得到非常精确的结果．利用新简化模型计算了高密度封装结构的疲劳寿命,所获得的结果与未均匀化模型结果误差在0.3%以内．     

多孔格栅均匀化模型平压仿真分析

为了研究均匀化方法在一种多孔格栅结构中的应用,从格栅单胞尺度入手,建立了一种适用于有限元仿真分析的三维周期性边界条件.以ABAQUS作为分析平台,对周期性边界条件下的格栅单胞模型进行了平压仿真分析,并将仿真结果与文献实验结果对比,验证了该边界条件的可靠性.利用均匀化理论建立了格栅单胞力学平衡方程,得到了格栅均匀化模型....     

Analytical procedure for determining the linear and nonlinear effective properties of the elastic composite cylinder

In this work we consider a cylindrical structure composed of a nonlinear core (inhomogeneity) surrounded by a different nonlinear shell (matrix). We elaborate a technique for determining its linear elastic moduli (second order elastic constants) and the nonlinear elastic moduli, which are called Landau coefficients (third order elastic constants). Firstly, we develop a nonlinear perturbation method which is able to turn the initial nonlinear elastic problem into a couple of linear problems. Then, we prove that only the solution of the first linear problem is necessary to calculate the linear and nonlinear effective properties of the heterogeneous structure. The following step consists in the exact solution of such a linear problem by means of the complex elastic potentials. As result we obtain the exact closed forms for the linear and nonlinear effective elastic moduli, which are valid for any volume fraction of the core embedded in the external shell.     

Overall longitudinal shear elastic modulus of a 1–3 composite with anisotropic constituents

The overall properties of a binary elastic periodic fiber-reinforced composite, with transversely isotropic constituents in an anti-plane-strain deformation state, are studied here for a cell periodicity of square type. This analysis considers four different orientations of the axis of transverse isotropy of constituents with respect to the direction of fibers. Each case is characterized by very simple closed-form expressions for the effective coefficients, which were obtained using the asymptotic homogenization method. Local problems defined on a periodic square unit cell are solved using Weierstrassian and Natanzon’s functions and perturbation theory relative to small anisotropy. In the isotropic limit, comparison with rigorous bounds and some well-known mixing rules are made. Also, comparisons with finite element calculations show that the derived closed-form formulae provide excellent results even for large anisotropy.