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.

Extended multiscale finite element method for mechanical analysis of heterogeneous materials

An extended multiscale finite element method （EMsFEM） is developed for solving the mechanical problems of heterogeneous materials in elasticity.The underlying idea of the method is to construct numerically the multiscale base functions to capture the small-scale features of the coarse elements in the multiscale finite element analysis.On the basis of our existing work for periodic truss materials, the construction methods of the base functions for continuum heterogeneous materials are systematically introduced. Numerical experiments show that the choice of boundary conditions for the construction of the base functions has a big influence on the accuracy of the multiscale solutions, thus,different kinds of boundary conditions are proposed. The efficiency and accuracy of the developed method are validated and the results with different boundary conditions are verified through extensive numerical examples with both periodic and random heterogeneous micro-structures.Also, a consistency test of the method is performed numerically. The results show that the EMsFEM can effectively obtain the macro response of the heterogeneous structures as well as the response in micro-scale,especially under the periodic boundary conditions.

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.

Hydro-mechanical modeling of impermeable discontinuity in rock by extended finite element method

The extended finite element method(XFEM) is a numerical method for modeling discontinuities within the classical finite element framework. The computation mesh in XFEM is independent of the discontinuities, such that remeshing for moving discontinuities can be overcome. The extended finite element method is presented for hydro-mechanical modeling of impermeable discontinuities in rock. The governing equation of XFEM for hydraulic fracture modeling is derived by the virtual work principle of the fracture problem considering the water pressure on crack surface. The coupling relationship between water pressure gradient on crack surface and fracture opening width is obtained by semi-analytical and semi-numerical method. This method simplifies coupling analysis iteration and improves computational precision. Finally, the efficiency of the proposed method for modeling hydraulic fracture problems is verified by two examples and the advantages of the XFEM for hydraulic fracturing analysis are displayed.

Fracture properties of epoxy asphalt mixture based on extended finite element method

Crack is found to be a major distress that affects the performance of the epoxy asphalt pavement.An extended finite element method was proposed for investigating the fracture properties of the epoxy asphalt mixture.Firstly,the single-edge notched beam test was used to analyze the temperature effect and calculate the material parameters.Then,the mechanical responses were studied using numerical analysis.It is concluded that 5℃ can be selected as the critical temperature that affects the fracture properties,and numerical simulations indicate that crack propagation is found to significantly affect the stress state of the epoxy asphalt mixture.The maximum principal stress at the crack surface exhibits different trends at various temperatures.Numerical solution of stress intensity factor can well meet the theoretical solution,especially when the temperature is lower than 5℃.

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.

Treatment of discontinuous interface in liquid-solid forming with extended finite element method

Extended finite element method(XFEM) is proposed to simulate the discontinuous interface in the liquid-solid forming process.The discontinuous interface is an important phenomenon happening in the liquid-solid forming processes and it is difficult to be simulated accurately with conventional finite element method(CFEM) because it involves solid phase and liquid phase simultaneously.XFEM is becoming more and more popular with the need of solving the discontinuous problem happening in engineering field.The implementation method of XFEM is proposed on Abaqus code by using UEL(user element) with the flowchart.The key is to modify the element stiffness in the proposed method by using UEL on the platform of Abaqus code.In contrast to XFEM used in the simulation of solidification,the geometrical and physical properties of elements were modified at the same time in our method that is beneficial to getting smooth interface transition and precise analysis results.The analysis is simplified significantly with XFEM.

Simulation of three-dimensional tension-induced cracks based on cracking potential function-incorporated extended finite element method

In the finite element method,the numerical simulation of three-dimensional crack propagation is relatively rare,and it is often realized by commercial programs.In addition to the geometric complexity,the determination of the cracking direction constitutes a great challenge.In most cases,the local stress state provides the fundamental criterion to judge the presence of cracks and the direction of crack propagation.However,in the case of three-dimensional analysis,the coordination relationship between grid elements due to occurrence of cracks becomes a difficult problem for this method.In this paper,based on the extended finite element method,the stress-related function field is introduced into the calculation domain,and then the boundary value problem of the function is solved.Subsequently,the envelope surface of all propagation directions can be obtained at one time.At last,the possible surface can be selected as the direction of crack development.Based on the aforementioned procedure,such method greatly reduces the programming complexity of tracking the crack propagation.As a suitable method for simulating tension-induced failure,it can simulate multiple cracks simultaneously.

Cracking Propagation of Hardening Concrete Based on the Extended Finite Element Method

Self-deformation cracking is the cracking caused by thermal deformation, autogenous volume deformation or shrinkage deformation. In this paper, an extended finite element calculation method was deduced for concrete crack propagation under a constant hydration and hardening condition during the construction period, and a corresponding programming code was developed. The experimental investigation shows that initial crack propagation caused by self-deformation loads can be analyzed by this program. This improved algorithm was a preliminary application of the XFEM to the problem of the concrete self-deformation cracking during the hydration and hardening period. However, room for improvement exists for this algorithm in terms of matching calculation programs with mass concrete temperature fields containing cooling pipes and the influence of creep or damage on crack propagation.

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.

Using Extended Finite Element Method for Computation of the Stress Intensity Factor, Crack Growth Simulation and Predicting Fatigue Crack Growth in a Slant-Cracked Plate of 6061-T651 Aluminum

The 6061-T651 aluminium alloy is one of the most common aluminium alloys for marine components and general structures. The stress intensity factor (SIF) is an important parameter for estimating the life of the cracked structure. In this paper, the stress intensity factors of a slant-cracked plate, which is made of 6061-T651 aluminum, have been calculated using extended finite element method (XFEM) and finite element method (FEM) in ABAQUS software and the results were compared with theoretical values. Numerical values obtained from these two methods were close to the theoretical values. In simulations of crack growth at different crack angles, the crack propagation angle values were closer to the theoretical values in XFEM method. Also, the accuracy and validity of fatigue crack growth curve were much closer to the theoretical graph in XFEM than the FEM. Therefore, in this paper the capabilities of XFEM were realized in analyzing issues such as cracks.

基于XFEM的大体积结构波动传播规律及裂纹反演方法

大体积混凝土结构被广泛应用于土木、水利等领域的重大工程中,而混凝土抗拉强度低的力学特性决定了其易产生裂纹,因此,发展高效的检测方法,识别大体积混凝土结构中的裂纹信息十分必要.论文提出了一种新的方法,通过提取响应信号频谱中特定频率的幅值特征,基于BP人工神经网络建立幅值特征与裂纹信息间的映射关系,从而有效识别出裂纹信息.首先采用扩展有限元法(eXtended Finite Element Methods, XFEM)和人工吸收边界模型,分别模拟了单裂纹和双裂纹情形下,大量不同裂纹信息下特定位置传感器的响应,分析其频谱曲线并提取特征,建立频谱特征—裂尖位置数据集,以训练人工神经网络,测试集的反演效果显示,该方法具有较好的准确度,可有效识别出裂纹信息.

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。

Recent advances in the extended finite element method (XFEM) and isogeometric analysis (IGA)

The finite element method （FEM） is one of the most popular and efficient methods for computational modeling in scien- tific research and engineering . To expand its application to more complex problems, lots of new FEM-based methods have been developed in recent decades.

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.

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。

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XFEM的裂纹扩展分析

采用ABAQUS/Standard对生产线中的一个易损件进行了三维有限元分析.根据结构受力状态,将该结构简化成一个平面应力的裂纹扩展模型,并采用目前最新的有限元裂纹扩展技术(XFEM)计算结构的裂纹扩展情况.计算结果表明,有限元计算与实际结构裂纹扩展情况一致.同时,根据计算结果提出了结构改进的设计建议.

基于XFEM的平板斜裂纹动态扩展数值模拟

基于扩展有限单元法(XFEM),采用有限元软件ABAQUS研究了含斜裂纹矩形板的动态裂纹扩展过程,并讨论了裂纹初始角度、裂纹长度和冲击载荷形式等影响参数对裂纹扩展路径的影响.数值计算结果表明,拉伸冲击载荷下平板斜裂纹基本是按Ⅰ型裂纹形式沿直线扩展,改变裂纹初始角度、裂纹长度和冲击载荷形式不会对裂纹扩展路径产生显著影响,但是对裂纹扩展速度会有明显影响.