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.      

基于自洽法的电化学沉积修复饱和混凝土细观描述

针对当前电化学沉积修复混凝土缺乏细观层次上的理论描述,首先,以饱和混凝土的细观结构和电化学沉积修复的主要机理为基础, 提出了含电化学沉积产物、水和混凝土基体在内的三相复合材料细观力学模型. 其次,为了从细观层次定量描述电化学沉积修复对混凝土宏观性能的影响,基于自洽法对上述细观力学模型进行多层次均匀化处理,获取电化学沉积修复饱和混凝土的有效性能,其中,第一层均匀化是采用广义自洽模型获取等效夹杂的有效性能,第二层均匀化是采用自洽方法和沃伊特(Voigt) 上限相结合的方式获取修复混凝土的有效性能. 最后,为了验证该文所提出模型和方法的有效性,对比了该文的预测结果、试验数据和已有模型,结果表明了该文模型和方法是合理的.     

基于近场动力学理论的层压板损伤分析方法

提出了一种基于近场动力学理论 的纤维增强复合材料层压板的渐进损伤分析方法.在弹性力学和复合材料力学的基础上, 推导了适用于近场动力学建模的微模量和临界伸长率等基本参量, 结合经典层压板理论中的偏轴模量, 构建了适用于各向异性材料的对点力函数, 可分析3种形式的损伤:纤维断裂, 基体开裂和分层破坏.分析了含圆孔层压板在拉伸载荷作用下的破坏过程, 预测结果与试验结果吻合良好.     

A multi-phase micromechanical model for unsaturated concrete repaired using the electrochemical deposition method

Most concrete structures repaired using the electrochemical deposition method (EDM) are not fully saturated in reality. To theoretically illustrate the deposition healing process by micromechanics and quantitatively describe the effective properties of unsaturated concrete during the EDM healing process, a multi-phase multi-level micromechanical framework is proposed based on the microstructure of unsaturated concrete and the EDM’s healing mechanism. In the proposed model, the volume fractions of water and deposition products, the water effect (including further hydration and viscosity in pores) and the shapes of pores in the concrete are comprehensively considered. Moreover, multi-level homogenization procedures are employed to predict the effective properties of unsaturated concrete repaired using the EDM. For the first-level homogenization of this model, a modified function is presented to correct the Mori–Tanaka (M–T) method, which is used to predict the effective properties of equivalent inclusions composed of deposition products and water. To demonstrate the feasibility of the proposed micromechanical model, predictions obtained via the proposed multi-phase micromechanical model are compared with the experimental data, including results from extreme states during the EDM healing process. Finally, the influences of equivalent aspect ratios and deposition product properties on the healing effectiveness of EDM are discussed based on the proposed micromechanical model.     

复合材料应力分析的均匀化方法

建立了基于均匀化理论的确定复合材料结构应力场的方法．其实质是用均质的宏观结构和非均质的具有周期性分布的细观结构描述原结构;将力学量表示成关于宏观坐标和细观坐标的函数,并用细观和宏观两种尺度之比为小参数展开,用摄动技术将原问题化为一细观均匀化问题和一宏观均匀化问题．这两个问题的解确定了包含等效位移和一阶近似位移的位移场,由此获得应力场．利用该方法给出了圆柱形孔隙材料和单向纤维复合材料在单向拉伸时的应力场以及空隙材料简支梁的局部应力场,说明了该方法的有效性     

基于迭代法的非线性弹性均质化研究

微观结构对复合材料的宏观力学性能具有至关重要的影响, 通过合理设计复合材料微观结构可以得到期望的宏观性能. 均质化方法作为一种有效的设计方法, 它从微观结构的角度出发, 利用均匀化的概念, 实现了对复合材料宏观力学性能的预测和设计. 而当考虑非线性因素, 均质化的实现就非常困难. 本文利用双渐近展开方法, 将位移按照宏观位移和微观位移展开, 推导了非线性弹性均质化方程. 通过直接迭代法, 对非线性弹性均质化方程进行了求解, 并给出了具体的迭代方法和实现步骤. 本文基于迭代步骤和非线性弹性均质化方程编写MATLAB 程序, 对3种典型本构关系的周期性多孔材料平面问题进行了计算, 对比细致模型的应变能、最大位移和等效泊松比, 对程序及迭代方法的准确性进行了验证. 之后对一种三元橡胶基复合材料进行多尺度均质化, 将其分为芯丝尺度和层间尺度. 用线弹性的均质化方法得到了芯丝尺度的等效弹性参数, 并将其作为层间尺度的材料参数. 在层间尺度应用非线性弹性均质化方法对结构进行计算, 得到材料的宏观等效性能, 并以实验结果为基准进行评价.      

Strength homogenization of matrix-inclusion composites using the linear comparison composite approach

A homogenization procedure to estimate the macroscopic strength of nonlinear matrix-inclusion composites with different strength characteristics of the matrix and inclusions, respectively, is presented in this paper. The strength up-scaling is formulated within the framework of the yield design theory and the linear comparison composite (LCC) approach, introduced by Ponte Castaneda (2002) and extended to frictional models by Ortega et al. (2011), which estimates the macroscopic strength of composite materials in terms of an optimally chosen linear thermo–elastic comparison composite with a similar underlying microstructure. In the paper various combinations for the underlying material behavior for the individual phases of the composite are considered: The matrix phase can be a quasi frictional material characterized either by a Drucker–Prager-type (hyperbolic) or an elliptical strength criterion, which predicts a strength limit also in hydrostatic compression, while the inclusion phase either may represent empty pores, pore voids filled with a pore fluid, rigid inclusions, or solid inclusions, whose strength characteristics also maybe described by a Drucker–Prager-type or an elliptical strength criterion. For generating the homogenized strength criterion efficiently in such general cases of matrix-inclusion composites, a novel algorithm is proposed in the paper. The validation of the proposed strength homogenization procedure for selected combinations of strength characteristics of the matrix material and the inclusions is conducted by comparisons with experimental results and alternative existing strength homogenization models.     

材料弹塑性性能数值模拟的多尺度方法

将均匀化方法和渐近分析(Asymptotic Analysis)与参变量变分原理相结合提出了一种模拟复合材料非线性性能的多尺度数值方法.该方法用渐近分析建立宏-细观变量之间的联系,利用参变量变分原理计算非线性响应,求解过程采用迭代算法.为提高计算精度,针对Von-Mises准则和Tsai-Hill准则,提出了一个基于参变量变分原理的改进算法,算例表明该方法可以显著消除传统方法采用线性展开式构造线性互补条件所带来的误差.     

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.     

Z-pin复合材料细观模型固化残余应力研究

针对植入Z-pin后碳纤维增强复合材料的微观结构,通过施加Z-pin周期性边界约束条件,建立了Z-pin复合材料单层板单胞细观模型．考虑固化过程中树脂体积收缩、弹性模量随固化度变化和纤维因Z-pin进入偏转因素,运用有限单元法计算了单胞结构在固化成型工艺过程中树脂和纤维应力发展和分布,并研究了Z-pin直径和分布密度对单层板面内残余应力的影响．结果表明：凝胶点之前,树脂模量和残余应力很小,凝胶点之后,树脂模量和残余应力增加较快;残余应力分布与纤维偏转有关;Z-pin直径和分布密度增加会使固化残余应力增大．     

Gravitational forces in dual-porosity systems: I. Model derivation by homogenization

We consider the problem of modeling flow through naturally fractured porous media. In this type of media, various physical phenomena occur on disparate length scales, so it is difficult to properly average their effects. In particular, gravitational forces pose special problems. In this paper we develop a general understanding of how to incorporate gravitational forces into the dual-porosity concept. We accomplish this through the mathematical technique of formal two-scale homogenization. This technique enables us to average the single-porosity, Darcy equations that govern the flow on the finest (fracture thickness) scale. The resulting homogenized equations are of dual-porosity type. We consider three flow situations, the flow of a single component in a single phase, the flow of two fluid components in two completely immiscible phases, and the completely miscible flow of two components.This work was supported in part by the National Science Foundation and by the State of Texas Governor's Energy Office.     

复合材料周期性线弹性微结构的拓扑优化设计

提出复合材料周期性线弹性微结构拓扑优化设计的模型.模型1设计具有极值弹性特性的复合材料,模型2设计多工况最刚微结构单胞.通过该模型和均匀化技术可以获得优化的微结构单胞,进而改善或者得到最优宏观特性的复合材料.为了便于制造和应用,用胞体材料而不是多相材料来得到复合材料的极值弹性特性和最大刚度.优化结果表明,该模型与数值方法相结合可以有效地实现微结构的拓扑优化设计.     

纤维加强复合材料的总体粘弹性响应

在某些纤维增强复合材料(FRC)中使用金属或高分子聚合物作为基体材料.在高温等情况下,这类材料具有明显的粘弹性特性.本文采用Riemann-Liouville形式的分数阶导数模型描述基体的粘弹性特性.通过渐近均匀化方法给出了预测FRC整体三维本构关系的解析表达式.给出了应用于基体具有Makris粘弹性关系的具体形式.以圆截面纤维正方形排列的情形为例,给出了等效模量随纤维体积比的变化曲线.结果说明,这类复合材料仍具有粘弹性特性,其整体粘弹性本构关系的弹性部分综合了纤维弹性和基体弹性的贡献,粘性部分来自基体粘性的贡献,复合材料具有和基体相同的粘性系数和分数阶.为分析微结构特征对整体特性的贡献,须求解两类局部问题.可以看出,在整体的等效模量中包含了局部变形的贡献,局部变形增加了复合材料的耦合刚度.     

单向纤维复合材料粘弹性性能预测

建立了基于均匀化理论的单向纤维复合材料粘弹性性能预测方法。对单向纤维增强复合材料粘弹性问题的控制方程进行Laplace变换,在像空间中利用均匀化理论建立宏观松弛模量的Laplace变换与微结构描述参数以及变换参数间的关系。用Prony级数模拟松弛模量随变换参数的变化形式,并根据像空间中一系列变换参数对应的松弛模量的数值,采用函数拟合技术确定Prony级数的形式,从而确定用显示形式表示的松弛模量的Laplace变换随变换参数的变化规律。对显式表达式的逆变换获得时间域内的松弛模量。该方法利用拟合函数的逆变换避开了复杂的数值Laplace逆变换,使单向纤维增强复合材料的粘弹性性能的确定变得容易。文中给出了单向纤维复合材料松弛模量的数值预测结果并同有限元法模拟试验的结果对比,验证了预测结果的准确性以及本文方法的有效性。     

复合材料组分性能随机性识别的克里金随机分析方法

建立非均匀材料宏观力学性能与微结构参数之间的定量关系一直是人们所关心的问题,利用材料微结构参数和组分性能预报复合材料宏观力学性能,已经取得了很大的进展,然而已知复合材料宏观性能,如何开展组分性能的随机识别,目前的研究工作还不多见.论文考虑了复合材料的随机性,在已知复合材料宏观有效性能的随机性条件下,采用克里金随机分析方法,对复合材料组分性能的随机性进行识别,通过单向纤维复合材料的宏观有效性能的随机性,计算得到了纤维弹性模量的均值与方差,证明了该方法的有效性.     

金属基纳米复合材料等效弹性模量的均匀化方法数值模拟

均匀化理论利用位移场双尺度渐近展开建立有限元列式,本文将其与有限元通用程序相结合,应用于金属基复合材料的弹性本构数值模拟。通过对不同尺度增强相金属基复合材料等效模量的数值模拟,考察了均匀化方法的适用情况。数值计算结果表明,对常规尺度增强相金属基复合材料,均匀化方法可以较准确地预测其等效弹性模量;对纳米增强相金属基复合材料,该方法仍可给出较好的预测,但存在某种程度的系统偏差。通过对纳米尺度增强机理的分析讨论,认为纳米增强相与基体材料问的界面效应可能有别于连续介质假设,指出可以考虑采用离散原子-连续介质耦合模型改进数值模拟结果。     

Gravitational forces in dual-porosity systems: II. Computational validation of the homogenized model

Three models are considered for single component, single phase flow in naturally fractured porous media. The microscopic model holds on the Darcy scale, and it is considered to govern the system. The macroscopic, dual-porosity model was derived in Part I of this work from the microscopic model by two-scale mathematical homogenization. In this paper, we show that the dual-porosity model predicts well the behavior of the microscopic model by comparing their computed solutions in certain reasonable test cases. Homogenization gives a complex formula for a key parameter in the dual-porosity model; herein a simple approximation to this formula is presented. The third model considered is a single-porosity model with averaged parameters. It is shown that this type of model cannot predict the behavior of the microscopic flow.This work was supported in part by the National Science Foundation and by the State of Texas Governor's Energy Office.     

层状纤维圆柱壳轴向压缩破损实验研究

通过对端部引发缺陷层状纤维复合材料圆柱壳在轴向准静态和冲击压缩下的实验研究,分析其渐进压缩破损模式和破坏模式的形成机理．研究此类结构的缓冲性能．实验研究表明随着纤维铺设角度的改变其破损模式的主导形式与分层扩展强度、环向断裂强度和纤维与基体脱胶裂纹相关．它们的断裂韧度的高低决定结构的能量吸收能力