含裂纹夹杂多孔材料的渗透性理论与数值分析

多孔材料的裂纹网络对宏观渗透性的影响显著,正确描述裂纹网络对材料渗透率的影响具有重要的工程意义。该文将开裂多孔材料视作由多孔基体和裂纹夹杂二相组成的复合材料,基于细观力学理论模型中的相互作用直推法(IDD)给出了渗透率张量的IDD理论解。为分析裂纹长度、密度、取向、间距和连通度等裂纹网络细观形貌参数对宏观渗透率的影响,该文使用具有周期结构的重复单元模型建立了二维数值分析模型,采用有限单元法进行数值求解并与IDD理论解进行了对比验证。理论研究表明,IDD理论模型采用单一的开裂密度指标来表征多孔介质的裂纹网络,在开裂密度不大时能够统一地描述裂纹长度、取向、平均横向间距和纵向间距等多个细观形貌指标对材料整体渗透性能的影响,具有良好的适用性和精度;数值分析表明,在裂纹网络的密度不断增大、裂纹相互趋近并最终连通的过程中,IDD理论解逐渐偏离数值解并低估裂纹间相互作用,此时材料渗透率与裂纹密度呈对数关系;网络裂纹一旦连通,整体渗透率则发生突变,此时渗透率的确定需要特别考虑连通裂纹之间的强烈近场相互作用。     

不同裂纹分布的孔隙材料渗透系数

含裂纹孔隙材料渗透性由裂纹的微观结构决定,其研究对工程实践意义重大。该文假设含裂纹孔隙材料是由孔隙基体和裂纹组成的二相复合材料,基于细观均匀化理论给出了四种不同裂纹分布的渗透张量稀疏解、相互作用直推（IDD）解和修正的IDD解。基于单元嵌入技术和弹性比拟的数值模拟方法,采用不连通的离散裂纹模型,研究了裂纹数目对有效渗透系数数值解收敛性的影响及不同裂纹分布的孔隙材料渗透性,并将得到的数值解和理论解对比分析,结果表明:随着裂纹数目的增加,有效渗透系数的变化范围逐渐减小,并最终趋于稳定,而且选择合适的裂纹数目,能同时保证计算的随机收敛性和合理的计算效率;对于所研究的四种分布的裂纹,相比稀疏解,IDD解更接近数值解,但随着裂纹密度的增加,裂纹间的相互作用增强,IDD解会逐渐偏离数值解;修正的IDD解充分考虑了裂纹间的相互作用和边界效应,能更好地估计含裂纹孔隙材料的渗透性。     

含孔洞和裂隙混合缺陷的干燥水泥砂浆导热系数相互作用直推预测模型

水泥砂浆在浇筑、养护和受荷载后易出现缺陷,会显著改变其热传导性能.将水泥砂浆中缺陷分为孔洞和裂隙两种基本类型,基于细观力学理论中的相互作用直推(IDD)估计法,建立了孔洞和裂隙单独存在或同时存在时干燥水泥砂浆等效导热系数预测模型;基于数值模拟结果反推法,提出裂隙随机分布影响函数,改进了IDD模型预测精度;与数值模拟结果...     

基于细观单元等效化方法的混凝土动态破坏行为分析

混凝土材料具有明显的应变率效应,对其力学性质增强机理的认识还不统一。在细观随机骨料模型基础上,采用特征单元尺度划分试件网格,推导了考虑材料拉/压强度应变率效应的细观单元等效本构关系,建立了非均质混凝土材料的细观单元等效化数值模型。基于二维模型对Dilger等混凝土动态压缩试验进行了数值模拟,获得的数值结果与试验数据及随机骨料模型结果吻合良好,证明了细观单元等效化方法的准确性;进而对三维混凝土试件动态单轴拉伸和压缩破坏模式及宏观力学性质的加载速率效应进行了研究。数值结果表明:随着加载速率的增加,混凝土裂纹(损伤)数量增大,混凝土破坏将耗散更多的能量,是混凝土动态强度提高的主要原因。     

墙体材料理论湿渗透模型与应用分析

在室内外环境的影响下,墙体内存在热湿传递。建立了单层墙体材料(或调湿材料)理论湿渗透模型并对模型进行了求解。计算出了常用不同建筑材料在不同湿周期作用下的理论湿渗透厚度。计算结果表明理论湿渗透厚度随环境湿变化周期增大而增大,同时不同建筑材料的理论湿渗透厚度也差异很大。在计算墙体与室内湿交换的模型中,等效湿渗透模型应用较广泛。但该模型基于材料不被穿透的假设获得的,理论湿渗透厚度可用来检查等效湿渗透模型的有效性。该理论厚度也可作为调湿材料厚度设计时的参考。     

混凝土拉伸损伤演变的细观力学研究

对二维平面应力问题,根据能量耗散等价假设,即当产生微裂纹所需能量等于形成损伤所需的能量时,细观损伤状态等价于宏观损伤状态,建立了单轴拉伸与双轴拉伸情况下混凝土宏观损伤变量与细观损伤参数(微裂纹密度)的关系。微裂纹扩展准则采用复合型准则。计算结果表明,混凝土双轴受拉发生破坏时的损伤值随横向拉应力的增大而增大。本文求得的有效弹性模量与细观力学的SCM结果吻合较好,与忽略相互作用的Taylor方法结果也基本吻合。     

裂纹面动摩擦作用对脆性材料动力破坏的影响EI北大核心CSCD

基于岩石类材料的I型裂纹模型,提出了一种考虑裂纹密度、裂纹相互作用以及裂纹面动摩擦作用的脆性材料动力模型。以正方形阵列分布的裂纹为例,定量分析了不同裂纹密度及不同摩擦行为对试件的裂纹扩展过程、试件受力和破坏的影响。数值计算结果表明:随着裂纹密度增大,裂纹间的相互作用增强,试件破坏时的加载应力降低,惯性效应引起试件轴向附加应力增大。裂纹面的滑动会降低裂纹面的动摩擦系数,促进裂纹发展,并降低试件的强度。相对于常数摩擦系数,考虑速度及状态依赖型摩擦模型对裂纹面的滑动过程更为合理。动强度因子对比结果显示出试件明显的应变率效应和尺寸效应。     

磁电弹性材料中含有带四条裂纹的正方形孔的反平面断裂问题

针对反平面剪切力作用下,磁电弹性材料中含有带四条裂纹的正方形孔口的断裂问题进行了深入地探索。基于线弹性断裂理论和Riemann-Schwarz解析延拓定理,利用复变函数方法和留数定理,通过构造合适的数值保角映射函数,将解析函数边值问题转化为柯西积分方程组进行解答,获得了磁电非渗透边界条件下裂纹尖端断裂力学参数的显式表达式。通过与已有结果的对比,验证了方法的有效性。利用数值算例描述了孔洞尺寸、四条裂纹长度和机–电–磁载荷等因素对裂纹扩展参数的影响规律。结果表明：水平右裂纹对孔口裂纹扩展影响更显著;垂直裂纹影响水平裂纹的扩展趋势;在磁电非渗透边界条件下,随着机械载荷的增大,裂纹尖端的应力强度因子变大,而电载荷和磁载荷对裂纹的扩展与机械载荷的大小和方向密切相关。该分析方法为求解复杂多连通域的智能复合材料问题提供了一条有效途径,研究成果为含裂纹的复合材料或结构的优化设计提供了科学依据。     

均匀热流下导热裂纹Ⅱ型温度应力强度因子的解析解

研究含中心裂纹无限大板受远场均匀热流作用,热流密度方向与裂纹有一夹角的情况。当垂直于裂纹面方向有定量热流穿过裂纹时,采用复变函数理论,得出了温度、应力与位移场解析解。利用位移单值条件,确定出温度应力强度因子的解析表达式。针对铝合金LY12材料进行了数值计算,研究了裂纹导热情况与热流方向对温度场及温度应力强度因子的影响。研究表明:该文给定的温度边界条件下,只产生Ⅱ型温度应力强度因子,不产生Ⅰ型温度应力强度因子。热荷载可等效为一个远场均匀作用的剪应力。Ⅱ型温度应力场取决于热流密度沿垂直裂纹面方向的分量,平行于裂纹方向的热流分量对温度应力场没有影响。     

混凝土中多点同步爆炸能量聚集效应分析

根据混凝土中C-J爆轰理论,用AUTODYN软件分别对1、2、4、5点装药在混凝土中的同步爆炸进行了数值模拟。通过数值仿真所得数据,分别从爆炸应力波和爆炸能量角度研究了多点爆炸能量聚集效应。结果表明:在相同装药当量条件下,多点爆炸应力波在装药对称位置发生相互作用压力叠加,造成混凝土变形能密度及内能密度较单点爆炸时显著下降,提高了装药的能量利用率,从而导致多点起爆毁伤区域较单点爆炸时增大。另外,由无量纲分析建立了较合理的能量耦合系数模型,为混凝土中多点爆炸毁伤效果提供理论依据。     

Effect of crack density and connectivity on the permeability of microcracked solids

In composite theory microcracks in solid are usually treated as degenerated inclusions separately embedded in matrix. For heterogeneous engineering composites like concrete and rock, the real cracking patterns are more complicate and quite different from this assumption due to the natural clustering and inter-connection of microcracks. This paper investigates the permeability of solids containing a crack network with finite connectivity following both theoretical and numerical approaches. Firstly, no connectivity is assumed for cracks and the interaction direct derivative (IDD) method is employed to obtain the crack-altered permeability of solids. Then the amplification of permeability by crack connectivity is quantified for parallel crack cases and for general crack patterns. This amplification effect is modeled by a crack length augmentation factor. In this way the IDD method is extended to evaluate the permeability of cracked solids for a finite crack connectivity before total percolation of cracks. Afterwards, by a carefully designed Monte-Carlo algorithm, the representative volume element (RVE) is built numerically for cracked solids with cracks having random spatial locations and random lengths. The permeability of 2D cracked solids is solved by finite element method (FEM). Through this numerical tool, the effect of both crack density and connectivity on the permeability is solved, and especially the relation between crack connectivity and the geometrical coefficient of crack clustering is put into evidence. From this study it is showed that the extended IDD method can be adapted to a microcracked solid with finite connectivity and can provide good estimates for the permeability.     

基于X-SBFEM的裂纹体非网格重剖分耦合模型研究

扩展有限元法利用了非网格重剖分技术,但需要基于裂尖解析解构造复杂的插值基函数,计算精度受网格疏密和插值基函数等因素影响。比例边界有限元法则在求解无限域和裂尖奇异性问题优势明显,两者衔接于有限元法理论内,可建立一种结合二者优势的断裂耦合数值模型。该文从虚功原理出发,利用位移协调与力平衡机制,提出了一种断裂计算的新方法X-SBFEM,达到了扩展有限元模拟裂纹主体、比例边界有限元模拟裂尖的目的。在数值算例中,通过边裂纹和混合型裂纹的应力强度因子计算,并与理论解对比,验证了该方法的准确性和有效性。     

含裂纹压电材料的Cell-Based光滑扩展有限元法

为精确而有效地求解机电耦合作用下含裂纹压电材料的断裂参数,首先,通过将复势函数法、扩展有限元法和光滑梯度技术引入到含裂纹压电材料的断裂机理问题中,提出了含裂纹压电材料的Cell-Based光滑扩展有限元法;然后,对含中心裂纹的压电材料强度因子进行了模拟,并将模拟结果与扩展有限元法和有限元法的计算结果进行了对比。数值算例结果表明:Cell-Based光滑扩展有限元法兼具扩展有限元法和光滑有限元法的特点,不仅单元网格与裂纹面相互独立,且裂尖处单元不需精密划分,与此同时,Cell-Based光滑扩展有限元法还具有形函数简单且不需求导、对网格质量要求低且求解精度高等优点。所得结论表明Cell-Based光滑扩展有限元法是压电材料断裂分析的有效数值方法。      

轮轨摩擦接触下钢轨多裂纹相互作用研究

利用热机耦合有限元法,建立了轮轨摩擦接触时钢轨表面多裂纹的热弹性平面应变有限元模型。数值模型中,考虑轮轨摩擦温升对轮轨材料参数的影响,通过移动载荷和热源来模拟运动车轮对钢轨的作用。分析了轮轨滑动接触时多裂纹相互作用和表面裂纹数量对钢轨疲劳裂纹扩展特性的影响。计算结果表明:与单个裂纹相比,多裂纹有降低钢轨疲劳裂纹扩展的作用;钢轨裂纹尖端应力强度因子K1和应力强度因子范围?K2均随裂纹数的增多而减小;钢轨表面裂纹数为5条时可以反映更多裂纹时的裂纹扩展特性。     

EVOLUTION OF TRANSVERSE MATRIX CRACKING IN CROSS-PLY LAMINATES

The objective of this paper is to develop a micromechanics model for the onset and subsequent multiplication of transverse cracks in the 90° layers of a cross-ply laminate under uniaxial tension. The micromechanics study of transverse matrix cracking is performed by a combination of finite element and analytical analyses. Based on the Griffith fracture criterion, the evolution of transverse matrix crack density is predicted. The prediction compares well with existing experimental data in the literature. Analytical expressions of the non-linear effective stress–strain curves are also obtained for a wide range of material systems. In addition, an analytical expression of the effective stiffness is derived based on the differential self-consistent method. The analytical results agree very well with the finite element calculations.     

SIF statistics in micro cracked solid: Effect of crack density, orientation and clustering

The paper addresses the problem of stress intensity factors (SIFs) statistics in a randomly cracked solid. For this aim, the representative unit cell approach has been used. The geometry of a microcracked solid is modeled by a periodic structure with a unit cell containing a number of cracks sufficient to account for the micro structure statistics. The method developed recently by Kushch et al. [V.I. Kushch, I. Sevostianov, L. Mishnaevsky Jr., Stress concentration and effective stiffness of aligned fiber reinforced composite with anisotropic constituents. International Journal of Solids and Structures 45 (2008) 5103-5117] is applied to obtain the exact series solution for the local stress field and SIFs for each separate crack. The method combines the superposition principle, the technique of complex potentials and new results in the theory of special functions. An appropriate choice of potentials provides reduction of the boundary-value problem to a set of linear algebraic equations and thus high numerical efficiency of the method. A wide series of computational experiments has been performed and the statistically meaningful results have been obtained discovering the way and extent to which the SIF statistics is affected by the micro structure parameters, namely, the crack density, their angular scattering and cluster formation. It is found that SIF distribution follows the Gnedenko-Gumbel asymptotic rule. An analytical expression is suggested for the SIF statistics in a microcracked material and a simple meso mechanical model of the cluster of cracks is proposed.     

基于单元嵌入技术和弹性比拟的含裂纹混凝土三维渗流模拟方法

混凝土结构在服役过程中受到力学荷载和环境因素的影响会产生裂纹,裂纹的产生、扩展和连通会显著影响混凝土的渗透性。该文将混凝土看作由基体和裂纹夹杂二相组成的复合材料,采用单元嵌入技术,有效地解决了基于连续网格的实体裂纹模型存在的网格协调问题。考虑到弹性问题与渗流问题在数学上的相似性,通过对含裂纹混凝土位移场和应力场的弹性比拟,得到相应的渗流场。在计算过程中,分别研究了渗透系数、网格尺寸及裂纹张开度对渗流场的影响,以及该文方法对多裂纹体的适用性。计算结果表明:该文的方法与实体裂纹模型的渗流场计算结果吻合,保证了结果的正确性。同时也降低了三维裂纹建模的难度,提高了计算的效率。     

The numerical solution of crack problems in plane elasticity in the case of loading discontinuities

The direct quadrature method of numerical solution of Cauchy type singular integral equations encountered in plane elasticity crack problems is applied to the case where the loading distribution along the crack edges presents jump discontinuities. This is made by using a well-known modification of the quadrature method which is free of undesirable errors due to the loading discontinuities. Hence, the method is ideal to treat the aforementioned class of crack problems and, particularly, crack problems where the Dugdale-Barenblatt elastic-perfectly plastic model is adopted. Finally, a numerical application of the method to the problem of a periodic array of cracks with a loading distribution presenting a jump discontinuity is made. The numerical results obtained in this problem compare favorably with the corresponding theoretical results available in this special problem.