Extended finite element-based cohesive zone method for modeling simultaneous hydraulic fracture height growth in layered reservoirs

In this study,a fully coupled hydromechanical model within the extended finite element method(XFEM)-based cohesive zone method(CZM)is employed to investigate the simultaneous height growth behavior of multi-cluster hydraulic fractures in layered porous reservoirs with modulus contrast.The coupled hydromechanical model is first verified against an analytical solution and a laboratory experiment.Then,the fracture geometry(e.g.height,aperture,and area)and fluid pressure evolutions of multiple hydraulic fractures placed in a porous reservoir interbedded with alternating stiff and soft layers are investigated using the model.The stress and pore pressure distributions within the layered reservoir during fluid injection are also presented.The simulation results reveal that stress umbrellas are easily to form among multiple hydraulic fractures’tips when propagating in soft layers,which impedes the simultaneous height growth.It is also observed that the impediment effect of soft layer is much more significant in the fractures suppressed by the preferential growth of adjoining fractures.After that,the combined effect of in situ stress ratio and fracturing spacing on the multi-fracture height growth is presented,and the results elucidate the influence of in situ stress ratio on the height growth behavior depending on the fracture spacing.Finally,it is found that the inclusion of soft layers changes the aperture distribution of outmost and interior hydraulic fractures.The results obtained from this study may provide some insights on the understanding of hydraulic fracture height containment observed in filed.

Mesoscopic characterization and modeling of microcracking in cementitious materials by the extended finite element method

This study develops a mesoscopic framework and methodology for the modeling of microcracks in concrete. A new algorithm is first proposed for the generation of random concrete meso-structure including microcracks and then coupled with the extended finite element method to simulate the heterogeneities and discontinuities present in the meso-structure of concrete. The proposed procedure is verified and exemplified by a series of numerical simulations. The simulation results show that microcracks can exert considerable impact on the fracture performance of concrete. More broadly, this work provides valuable insight into the initiation and propagation mechanism of microcracks in concrete and helps to foster a better understanding of the micro-mechanical behavior of cementitious materials.

基于XFEM的汽车铝合金断裂行为表征

车用铝薄壁合金5052H32和6061T6以其优异的成形性被广泛用于轻量化车身的冲压钣金件和结构件中。为建立反映材料实际力学特性的表征模型,针对其非线性本构响应中的弹塑性变形、损伤演化及韧性断裂不同发展阶段,分别开发出J-C弹塑性模型、损伤控制模型,以及与应力集中状态相关的J-C失效模型、GTN细观损伤模型和MMC断裂模型,并以参数反演、遗传算法寻优等手段标定了各模型的有效参量,形成力学演变全过程表征。利用上述模型结合扩展有限元法精确模拟了薄壁试件拉伸断裂的过程,通过与实验一致的内部裂纹动态生长行为、应变场和断口形貌,验证了所提取本构性能参数的准确性,且采用经验MMC准则的预测精度最高,形变误差仅为4.7%。

Numerical analysis of rock fracturing by gas pressure using the extended finite element method

High energy gas fracturing is a simple approach of applying high pressure gas to stimulate wells by gen- erating several radial cracks without creating any other damages to the wells. In this paper, a numerical algorithm is proposed to quantitatively simulate propagation of these fractures around a pressurized hole as a quasi-static phenomenon. The gas flow through the cracks is assumed as a one-dimensional transient flow, governed by equations of conservation of mass and momentum. The fractured medium is modeled with the extended finite element method, and the stress intensity factor is calculated by the simple, though sufficiently accurate, displacement ex- trapolation method. To evaluate the proposed algorithm, two field tests are simulated and the unknown parameters are determined through calibration. Sensitivity analyses are performed on the main effective parameters. Considering that the level of uncertainty is very high in these types of engineering problems, the results show a good agreement with the experimental data. They are also consistent with the theory that the final crack length is mainly determined by the gas pressure rather than the initial crack length produced by the stress waves.

Thermoelastic analysis of multiple defects with the extended finite element method

In this paper, the extended finite element method (XFEM) is adopted to analyze the interaction between a single macroscopic inclusion and a single macroscopic crack as well as that between multiple macroscopic or microscopic defects under thermal/mechanical load. The effects of different shapes of multiple inclusions on the material thermomechanical response are investigated, and the level set method is coupled with XFEM to analyze the interaction of multiple defects. Further, the discretized extended finite element approximations in relation to thermoelastic problems of multiple defects under displacement or temperature field are given. Also, the interfaces of cracks or materials are represented by level set functions, which allow the mesh assignment not to conform to crack or material interfaces. Moreover, stress intensity factors of cracks are obtained by the interaction integral method or the M-integral method, and the stress/strain/stiffness fields are simulated in the case of multiple cracks or multiple inclusions. Finally, some numerical examples are provided to demonstrate the accuracy of our proposed method.

Evaluation of mixed-mode stress intensity factors by extended finite element method

Extended finite element method （XFEM） implementation of the interaction integral methodology for evaluating the stress intensity factors （SIF） of the mixed-mode crack problem is presented. A discontinuous function and the near-tip asymptotic function are added to the classic finite element approximation to model the crack behavior. Two-state integral by the superposition of actual and auxiliary fields is derived to calculate the SIFs. Applications of the proposed technique to the inclined centre crack plate with inclined angle from 0° to 90° and slant edge crack plate with slant angle 45°, 67.5° and 90° are presented, and comparisons are made with closed form solutions. The results show that the proposed method is convenient, accurate and computationallv efficient.

XFEM和修正剑桥模型模拟高聚物劈裂注浆方法研究

针对自膨胀高聚物材料在土体中劈裂扩散仿真手段尚不完备的现状,初步建立了一种模拟高聚物对土体劈裂压密作用的仿真方法。该方法采用扩展有限元离散求解区域土体介质,用修正剑桥模型描述土体力学特性,利用高聚物密度-围压关系迭代计算作用于裂缝面的浆液膨胀压力,实现了对土体劈裂缝扩展过程的数值模拟,通过与试验结果的对比验证了该方法的适用性。算例分析表明,应用该方法能够模拟膨胀力作用下土体裂缝启裂过程、扩展走向和浆脉厚度变化,获得裂缝周围土体变形模量、孔隙比、应力场和密度场分布特征,为深入研究膨胀性高聚物注浆材料对土体劈裂压密机制奠定了基础。

基于XFEM钢桥面板-U肋焊缝疲劳裂纹扩展规律及其影响因素分析

目的研究正交异性钢桥面板与U肋焊缝在循环荷载作用下萌生于焊趾、焊跟处的疲劳裂纹扩展规律及影响因素。方法基于扩展有限单元法(XFEM),利用ABAQUS有限元软件建立了3U肋正交异性板数值分析模型,通过引入初始裂纹长度、面板厚度、应力比三个变量参数,分析评价这些参数变化对焊趾、焊跟处的疲劳裂纹扩展规律及疲劳寿命影响程度。结果初始裂纹长度由0.5 mm增加至1.5 mm、面板厚度由14 mm增加至20 mm、应力比由0.1增加至0.8时,焊趾处裂纹疲劳寿命分别减少46.6%、提高797%、提高364%,焊跟处裂纹疲劳寿命分别减少51.2%、提高425%、提高351%。结论XFEM能准确预测面板与U肋焊缝疲劳细节的疲劳裂纹扩展路径及其疲劳寿命;初始裂纹长度越长、面板厚度和应力比越小,疲劳裂纹的扩展速率愈快、相应的疲劳寿命越小。

3D Nonlinear XFEM Simulation of Delamination in Unidirectional Composite Laminates: A Sensitivity Analysis of Modeling Parameters

This article presents a three-dimensional extended finite element (XFEM) approach for numerical simulation of delamination in unidirectional composites under fracture mode I. A cohesive zone model in front of the crack tip is used to include interface material nonlinearities. To avoid instability during simulations, a critical cohesive zone length is defined such that user-defined XFEM elements are only activated along the crack tip inside this zone. To demonstrate the accuracy of the new approach, XFEM results are compared to a set of benchmark experimental data from the literature as well as conventional FEM, mesh free, and interface element approaches. To evaluate the effect of modeling parameters, a set of sensitivity analyses have also been performed on the penalty stiffness factor, critical cohesive zone length, and mesh size. It has been discussed how the same model can be used for other fracture modes when both opening and contact mechanisms are active.

隧道衬砌裂缝特征对承载力的影响分析

为明确松动荷载作用下,衬砌裂缝特征对结构承载性能的影响,通过1∶10模型试验和数值分析研究了带裂缝结构的受力变形特征、破坏模式和极限承载能力。结果表明:对于预制裂缝长度不超过L/3(试件纵向长度)、深度不超过0.7 H(试件厚度)的试件,裂缝发展存在阶段性特征,试件破坏由拱腰失效引起,属于延性破坏。对于预制裂缝长度不低于2 L/3或深度不低于0.9 H的试件,裂缝发展过程不存在阶段性特征,试件破坏由拱顶失效引起,属于脆性破坏;随裂缝长度和深度增加,结构极限承载力降低。当预制裂缝长度为L/3且深度为0.3 H、0.7 H、0.9 H,以及长度为2 L/3且深度为0.3 H、0.7 H时,试件极限承载力依次为完整试件的86.96%、78.26%、73.91%、69.57%、60.87%。相比于裂缝深度,纵向长度对结构承载性能影响更明显,可作为裂缝评价的重要指标;提出了基于裂缝特征的衬砌承载力预测公式,可明确带裂衬砌的极限承载力,为结构性能评估、加固时机及加固参数的选取提供依据。

考虑化学反应的高聚物压密劈裂注浆仿真研究

考虑浆液化学反应原理,综合运用扩展有限元理论、修正剑桥模型和高聚物浆液膨胀力计算模型,建立了模拟高聚物在土体中压密劈裂注浆动态过程的二维仿真分析方法。通过模型试验验证了所提出方法的适用性,进而分析了浆液膨胀力、浆脉形态、土体孔隙比随时间变化规律及注浆孔埋深、土体断裂韧度对浆脉扩展过程的影响。结果表明:受高聚物化学反应进程驱动,在浆液与土体耦合作用下,浆液膨胀力初期随时间近似呈线性增长,达到峰值后快速下降并趋于稳定;浆脉长度和宽度发展速度不同步,裂缝启裂至二次扩展阶段,浆脉长度基本保持不变,宽度线性增大,裂缝二次扩展后,浆脉长度近似线性增大,而宽度增长速率趋缓;受浆液挤密作用影响,裂缝两侧一定范围内土体孔隙比显著降低,沿垂直于裂缝面方向,距注浆孔中心越近,孔隙比越小;孔隙比随时间整体呈下降趋势,随着裂缝的扩展和后期膨胀压力的下降,紧邻裂缝面两侧土体孔隙比有一定恢复,随后趋于稳定;随着注浆孔埋深和土体断裂韧度的增加,浆脉长度逐渐减小,宽度不断增大,两者变化速率基本保持不变;浆脉扩展稳定时间随埋深的增大而提前,随断裂韧度的增大而延后。

水中高压电脉冲作用下径向预制裂纹扩展规律

为研究水中高压电脉冲作用下页岩多条预制裂纹同步扩展应力干扰作用对裂纹扩展影响,通过裂纹扩展轨迹、扩展长度、平均宽度、偏转角度和裂纹间等效应力分布的变化规律,综合考虑裂纹夹角、裂纹数量、水平地应力差等因素对裂纹起裂、扩展的影响。采用真三轴高压脉冲水力压裂试验平台进行实验室压裂试验和扩展有限元法(extended finite element method, XFEM)数值模拟计算,利用PCAS(pore and cracks analysis system)裂隙分析软件分析裂纹几何形态特征。结果表明:水中高压电脉冲作用下,预制裂纹可沿径向及轴向起裂、扩展;径向双裂纹间夹角越大,缝间干扰作用越弱,裂纹扩展曲折程度越好,扩展效果越好;等夹角径向三裂纹扩展,中间裂纹受应力干扰、受抑制作用最大,不等夹角径向三裂纹扩展,远离中间裂纹的右侧裂纹受干扰最小,扩展效果最好;随着水平地应力差增加,裂纹间应力干扰作用增强,裂纹扩展效果逐渐减弱。研究成果可为分析水中高压电脉冲作用下页岩多预制裂纹扩展过程和规律提供一定的参考。

径向井辅助前置液酸压裂缝扩展数值模拟

基于扩展有限元及双尺度连续模型理论建立径向井辅助前置液酸压裂缝扩展模型,引入偏离系数作为量化评价指标,分析各因素对裂缝形态的影响,并利用灰色关联分析方法明确主控因素。结果表明:径向井对前置液酸压裂缝扩展具有显著引导作用,裂缝优先沿径向井方向起裂并扩展一定距离,而后逐渐偏向最大水平主应力方向;径向井方位角、水平地应力差和地层弹性模量越小,径向井长度越长,偏离系数越小,径向井引导效果越好,其中水平地应力差为主控因素;当径向井方位角为15°时,前置液酸压裂缝沿着径向井方向扩展14.32 m后偏向最大水平主应力方向,径向井的引导效果最好,偏离系数为0.005。

基于XFEM与Cohesive模型分析PBX裂纹产生与扩展

利用扩展有限元法(XFEM)分析PBX-9502带孔板状试件在整体压缩下由局部裂纹萌生到裂纹扩展全过程的开裂破坏机理。采用应力状态相关的强度面、非关联流动法则及Cohesive模型,描述了材料在复杂应力状态下的非线性本构行为以及材料的破坏行为。进行了数值模拟结果与美国洛斯阿拉莫斯国家实验室(LANL)试验结果的对比。结果表明,含孔洞的平板在整体压应力环境下孔洞周围产生局部拉伸应力,这种拉伸条件导致局部裂纹萌生。数值模拟的裂纹发展趋势与试验结果相吻合,包括裂纹时程的整体走势和拐点、启裂时刻、裂纹初期扩展速度等。基于扩展有限元方法和内聚模型法,可模拟高聚物粘结炸药(PBX)含能材料的裂纹萌生、扩展。

基于有限元技术的疲劳裂纹扩展方法研究进展

疲劳裂纹是引起工程结构断裂失效的重要因素之一.目前疲劳裂纹扩展的有限元仿真商业软件有ANSYS、ABAQUS、FRANC3D、ZENCRACK等,这些软件为疲劳裂纹扩展过程的研究提供了有力支撑.本文对目前疲劳裂纹扩展的有限元仿真方法进行了综述.阐明了疲劳裂纹的定义以及研究疲劳裂纹扩展行为的必要性;介绍了三种用于模拟疲劳裂纹扩展的有限元方法:扩展有限元法(XFEM)、内聚力模型(CZM)和虚拟裂纹闭合技术(VCCT);分别总结了三种方法的基本理论和核心思想,对三种方法的应用与发展进行了分类归纳;最后对三种有限元方法进行分析,指出每种方法各自的优势及目前存在的局限性,并对疲劳裂纹扩展有限元仿真技术的未来改进方向给出了建议.

基于XFEM的强震区砼重力坝开裂与配筋抗震措施研究

已有震害表明,混凝土坝遭遇强烈地震将不可避免地产生开裂。扩展有限元法(XFEM)通过在相关节点的影响域上富集非连续位移模式,使得对非连续位移场的表征独立于单元边界,可以有效描述混凝土中的裂纹扩展。基于扩展有限元模型,采用合理的地震波动模型对国内某混凝土重力坝强震下的动力破坏过程进行了分析;针对大坝破坏情况,应用嵌入式滑移模型模拟了混凝土重力坝配筋前后的地震响应和破坏状况,据此评价局部配筋的抗震效果。研究表明,局部配置抗震钢筋虽无法防止裂缝的发生,但可有效限制坝体裂缝的开裂扩展范围及深度,减少裂缝的开度,有效改善坝体的抗震性能。

扩展有限元法(XFEM)及其应用

扩展有限元法(extendedfiniteelementmethod,XFEM)是1999年提出的一种求解不连续力学问题的数值方法,它继承了常规有限元法(CFEM)的所有优点,在模拟界面、裂纹生长、复杂流体等不连续问题时特别有效,短短几年间得到了快速发展与应用.XFEM与CFEM的最根本区别在于,它所使用的网格与结构内部的几何或物理界面无关,从而克服了在诸如裂纹尖端等高应力和变形集中区进行高密度网格剖分所带来的困难,模拟裂纹生长时也无需对网格进行重新剖分.重点介绍XFEM的基本原理、实施步骤及应用实例等,并进行必要的评述.单位分解概念保证了XFEM的收敛,基于此,XFEM通过改进单元的形状函数使之包含问题不连续性的基本成分,从而放松对网格密度的过分要求.水平集法是XFEM中常用的确定内部界面位置和跟踪其生长的数值技术,任何内部界面可用它的零水平集函数表示.第2和第3节分别简要介绍单位分解法和水平集法;第4节和第5节介绍XFEM的基本思想、详细实施步骤和若干应用实例,同时修正了以往文献中的一些不妥之处;最后,初步展望了该领域尚需进一步研究的课题.

XFEM及其在正交异性钢桥面板疲劳裂纹扩展中的应用

为了研究某大桥扁平钢箱梁正交异性钢桥面板模型试验中出现裂纹的原因,根据试验模型创建了三维扩展有限元(XFEM)模型进行整节段数值计算,利用不连续伽辽金扩展有限元(DG-XFEM)对裂纹扩展进行了模拟。结果表明:弧形开孔与U肋连接附近为高应力区,该高应力与几何不连续、焊接缺陷引起的应力集中及残余应力等不利因素叠加,使得弧形开孔与U肋连接附近成为疲劳最敏感的部位,即疲劳裂纹产生地;裂纹扩展的初始阶段与主应力等值线垂直,沿最大主应力方向扩展;裂纹出现的位置、扩展路径和长度与试验结果符合很好,与实际桥梁裂纹出现的位置和形态基本一致,也与裂纹扩展的基本理论一致。

基于XFEM的混凝土开裂数值模拟研究

扩展有限元法(XFEM)是近年来发展起来的分析不连续问题(特别是断裂问题)的一种有效方法。介绍了扩展有限元法的基本原理,给出了采用扩展有限元法进行混凝土开裂、裂纹扩展分析的方法,最后采用扩展有限元法模拟了含初始裂纹的混凝土试件和重力坝的开裂扩展过程,分析了其位移、应力场分布规律。算例表明扩展有限元法在进行断裂分析时克服了常规有限元法的缺点,避免了常规有限元法在分析断裂问题时繁琐的前处理过程,不需要裂纹面与有限元网格一致,不需要在裂缝周围布置高密度网格,模拟裂纹扩展过程时不需要不断地重新划分网格,展示了扩展有限元法在裂纹扩展分析中的独特优势。

基于扩展有限元方法的自愈微胶囊和基体力学性能适配的研究

微胶囊自修复树脂矿物复合材料作为一种自愈合智能材料得到了广泛的应用。微胶囊及时开裂,释放愈合剂从而修复基体中产生的微裂纹,是确保其自愈性能的关键。本工作基于扩展有限元方法结合内聚力模型,分析在不同偏置裂纹下微胶囊和环氧树脂基体之间的力学性能配比以及界面性能对裂纹扩展路径和微胶囊可裂性的影响。研究结果表明:(1)裂纹的扩展路径主要取决于微胶囊与基体的断裂性能配比,而弹性性能配比起次要作用。(2)当界面具有足够的粘结强度时,相对于断裂韧性配比,微胶囊与基体的断裂强度配比是影响微胶囊开裂的主要因素。(3)裂纹的偏置距离越大,裂纹越容易发生偏转,微胶囊越不容易开裂。(4)界面缺陷的存在有利于界面裂纹的产生,不利于微胶囊的开裂。研究结果可为自修复材料在工程中的应用提供理论依据。