基于水平集算法的扩展比例边界有限元法研究

扩展比例边界有限元法在裂纹贯穿单元采用Heaviside阶跃函数描述裂纹面两侧的不连续位移,在裂尖则采用半解析的比例边界有限元描述奇异应力场。该方法具有无需预先知道裂尖渐进场的形式,无需采用特殊的数值积分技术直接生成裂尖刚度阵,对多种应力奇异类型可根据定义直接求解广义应力强度因子的特点。该文将扩展比例边界有限元法与水平集方法相结合,进一步发展了扩展比例边界有限元法,并将其应用于解决裂纹扩展的问题。在数值算例中,通过编写完整的MATLAB分析计算程序,求解了单边缺口的三点弯曲梁和四点剪切梁的裂纹扩展问题,计算结果显示扩展比例边界有限元法能有效地预测裂纹轨迹和荷载-位移曲线。通过参数敏感性分析,还可得出该方法具有较低的网格依赖性,且对裂纹扩展步长不敏感。     

几何非线性扩展有限元法及其断裂力学应用

该文将扩展有限元方法应用到几何非线性及断裂力学问题中,并研制开发了扩展有限元Fortran程序。扩展有限元法其计算网格与不连续面相互独立,因此模拟移动的不连续面时无需对网格进行重新剖分。该文推导了几何非线性扩展有限元法的公式,在常规有限元位移模式中,基于单位分解的思想加进一个阶跃函数和二维渐近裂尖位移场,反映裂纹处位移的不连续性,并用2个水平集函数表示裂纹;采用拉格朗日描述方程建立了有限变形几何非线性扩展有限元方程;采用多点位移外推法计算裂纹应力强度因子并通过最小二乘法拟合得到更精确的结果。最后给出的大变形算例表明该文提出的几何非线性的断裂力学扩展有限元方法和相应的计算机程序是合理可行的,而且对于含裂纹及裂纹扩展的问题,扩展有限元法优于传统的有限元法。     

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。      

轮轨黏着系数对钢轨直裂纹瞬态扩展行为的影响

采用ANSYS/LS-DYNA建立了含有钢轨直裂纹的三维显式有限元模型,考虑了高速条件下轮轨间的瞬态滚动接触和裂纹面之间的滑动接触,于时域内分析了轮轨滚滑作用下裂纹面之间的瞬态法、切向接触和裂尖动态应力场强度因子。轮轨接触和裂纹面间的接触,均采用“面-面”接触算法定义,切向接触满足库伦摩擦定律。裂尖应力场强度因子采用虚拟闭合法计算,不考虑裂纹面之间的间隙,即两个裂纹面上的离散节点完全重合。牵引工况的计算结果表明,滚滑状态下的轮轨法、切向接触力不随轮轨黏着系数的增加而变化,但裂纹面间的最大法、切向接触力却随黏着系数的增加而不断减小。车轮滚到裂纹时,钢轨的弯曲变形使得两个裂纹面相互挤压闭合,即K_I值为0,而K_Ⅱ最大值约为K_Ⅲ最大值的8.1倍左右。这意味着钢轨表面的直裂纹,如果可以扩展,其在无横移牵引工况下的扩展应该以Ⅱ型撕裂为主导。随着粘着系数由0.1增至0.5时,无横移牵引工况下K_Ⅱ最大值仅增大3.98%,而K_Ⅲ最大值反而降低20.8%。     

扩展有限元法在裂纹扩展问题中的应用

扩展有限元法(Extended finite element method,XFEM)是近几年发展起来的数值方法,属于传统有限元法的扩展,具有区别于传统有限元法的优点,在求解不连续断裂问题上具有更高的精度及效率。本文针对影响裂纹扩展的主要因素进行探讨,继而介绍扩展有限元的基本原理,并对其在裂纹扩展中的应用进行综述,同时对该方法的下一步研究进行了展望。     

基于MLS-NMM的摩擦接触问题研究

摩擦接触问题的求解是将基于移动最小二乘插值的数值流形法（MLS-NMM）应用到裂纹扩展的必经之路。该文通过结合罚-线性互补方式的施加接触边界条件,并使用拉格朗日乘子法施加本质边界条件,得出一套基于MLS_NMM的摩擦接触问题的求解体系。该方法无需节点与边界重合,则可域外布点和均匀布点,来提高插值精度和降低布点难度,尤其是接触边界处。采用罚-线性互补的方式施加接触条件,使计算格式统一而简洁,利于编程实现。通过算例表明,该方法能准确地模拟接触面的张开、黏结和滑动状态,证明该方法对求解接触摩擦问题是可行的、有效的。     

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。     

模拟三维裂纹问题的自适应多尺度扩展有限元法

为了在大型结构分析中考虑小裂纹或以小的代价提高裂纹附近求解精度,该文建立了分析三维裂纹问题的自适应多尺度扩展有限元法。基于恢复法评估三维扩展有限元后验误差,大于给定误差值的单元进行细化。所有尺度单元采用八结点六面体单元,采用六面体任意结点单元连接不同尺度单元。采用互作用积分法计算三维应力强度因子。三维I 型裂纹和I-II 复合型裂纹算例分析表明了该方法的正确性和有效性。     

混凝土裂纹扩展过程模拟的扩展有限元法研究

扩展有限元法(theextendedFiniteElementMethod,XFEM)为数值模拟结构裂纹扩展过程提供了一条有效途径。该文介绍了用扩展有限元法对混凝土结构裂纹扩展过程进行数值模拟的实现方法。采用虚拟裂缝模型模拟混凝土非线性断裂行为,针对二维四边形单元推导了详细的有限元列式。采用3种方案对非线性方程系统进行求解,分析了其求解思路并概括了其求解步骤。通过对带初始边缘裂纹的单向拉伸混凝土板的数值模拟,对3种求解方案的计算结果进行了分析和讨论。     

基于扩展有限元法的钢筋混凝土梁复合断裂过程模拟研究

针对钢筋混凝土梁裂纹扩展问题,基于扩展有限元法,建立了预置裂纹的简支混凝土梁三维模型,用粘聚裂纹模型描述裂纹面间的力学行为,采用线性的软化曲线表示裂纹尖端断裂过程区的应变软化行为,分别对素混凝土梁和钢筋混凝土梁的复合断裂过程进行模拟,分析了纵向钢筋对裂纹扩展路径、荷载-挠度和荷载 -CMOD (裂缝开口处张开位移)曲线的影响,并与文献中的试验结果进行对比,计算结果与试验结果吻合良好,展示了扩展有限元法在结构断裂破坏分析方面的独特优势。     

A contact algorithm for frictional crack propagation with the extended finite element method

We present an incremental quasi‐static contact algorithm for path‐dependent frictional crack propagation in the framework of the extended finite element (FE) method. The discrete formulation allows for the modeling of frictional contact independent of the FE mesh. Standard Coulomb plasticity model is introduced to model the frictional contact on the surface of discontinuity. The contact constraint is borrowed from non‐linear contact mechanics and embedded within a localized element by penalty method. Newton–Raphson iteration with consistent linearization is used to advance the solution. We show the superior convergence performance of the proposed iterative method compared with a previously published algorithm called ‘LATIN’ for frictional crack propagation. Numerical examples include simulation of crack initiation and propagation in 2D plane strain with and without bulk plasticity. In the presence of bulk plasticity, the problem is also solved using an augmented Lagrangian procedure to demonstrate the efficacy and adequacy of the standard penalty solution. Copyright © 2008 John Wiley & Sons, Ltd.     

Parametric quadratic programming method for elastic contact fracture analysis

A solution procedure for elastic contact fracture mechanics has been proposed in this paper. The procedure is based on the quadratic programming and finite element method (FEM). In this paper, parametric quadratic programming method for two-dimensional contact mechanics analysis is applied to the crack problems involving the crack surfaces in frictional contact. Based on a linear complementary contact condition, the parametric variational principle and FEM, a linear complementary method is extended to analyze contact fracture mechanics. The near-tip fields are properly modeled in the analysis using special crack tip elements with quarter-point nodes. Stress intensity factor solutions are presented for some frictional contact fracture problems and are compared with known results where available.     

XFEM simulation of stable crack growth using J–R curve under finite strain plasticity

In the present work, extended finite element method (XFEM) has been extended to simulate stable crack growth problems using J–R criterion under finite strain plasticity. In XFEM, a physical representation of crack is not required, and a crack is completely modeled by enrichment functions. The modeling of large deformation is performed using updated Lagrangian approach. The nonlinear equations obtained as a result of large deformation are solved by Newton–Raphson iterative method. Von-Mises yield criterion is used with isotropic hardening to model the finite strain plasticity. The elastic-predictor and plastic-corrector algorithm is employed for stress computation. Three problems i.e. crack growth in compact tension specimen; crack growth in triple point bend specimen and crack growth in bi-metallic triple point bend specimen are solved using J–R curve under plane stress condition to demonstrate the capability of XFEM in crack growth problems.     

The improvement of crack propagation modelling in triangular 2D structures using the extended finite element method

In this paper, a novel geometric method combined with the piecewise linear function method is introduced into the extended finite element method (XFEM) to determine the crack tip element and crack surface element. Then, by combining with the advanced mesh technique, a novel method is proposed to improve the modelling of crack propagation in triangular 2D structure with the XFEM. The numerical tests show that the accuracy, the convergence, and the stability of the XFEM can be improved using the proposed method. Moreover, the applicability of the conventional multiple enrichment scheme is discussed. Compared with the proposed method, the conventional multiple enrichment scheme has deficiency in mixed mode I and II crack. Finally, a comparative study shows that the performance of the XFEM by using the proposed method to model the crack propagation can be greatly improved.     

二维摩擦接触问题迭代法与非线性互补算法的等价性

本文证明了二维摩擦接触问题一种迭代法与非线性互补算法的等价性,为迭代法的收敛性找到了理论依据,并由此提出了这种迭代法的修正方法,使迭代法也能保证收敛。     

An iterative algorithm for modeling crack closure and sliding

In this paper, a simple and efficient iterative algorithm is adopted to model crack closure and sliding with the displacement discontinuity method (DDM). The problem of a subsurface crack in a half-plane under indentation loading considered by Elvin and Leung (Elvin N, Leung C. A fast iterative boundary element method for solving closed crack problems. Engng Fract Mech 1999;63:631-48) and DeBremaecker and Ferris (DeBremaecker J-Cl, Ferris MC. A comparison of two algorithm for solving closed crack problems. Engng Fract Mech 2000;66:601-05) is reexamined using the iterative DDM. The cases of a partially closed crack with both frictionless and frictional contacts are considered. Benchmark results for the stress intensity factors and the interfacial crack mechanisms for a subsurface crack are presented and compared with the results obtained from the fast iterative algorithm of Elvin and Leung and those from the PATH algorithm of DeBremaecker and Ferris.     

基于扩展有限元方法的界面接触算法

该文构建了适用于扩展有限元法(XFEM)的界面接触算法,该算法具备模拟界面上粘连、滑动和分离状态的能力.对平面摩擦问题的计算结果表明,该方法对于界面接触行为的描述能力与常规接触面单元十分接近.对平面应变压剪试样中剪切带问题的模拟分析表明,该算法合理地反映了摩擦接触的耗散机制,从而避免了零能耗散现象,能够较准确地描述平面...     

A solution method for frictional contact problems of a crack in FGMs under mechanical and thermal loads

This article provides a numerical treatment of a finite crack in an interfacial layer with spatially varying elastic properties under in-plane mechanical and thermal loading conditions. The variation of stress intensity factors and energy release rates with the functions which are governing the material properties of the interfacial layer is studied. Transient and steady-state response of a central crack in FGMs subjected to the mechanical and thermal loads are investigated. Unlike earlier studies which consider the cracks encountered as open, the current investigation studies cracks in an essentially compressive environment in which the crack faces are in contact and frictional effects play an important role. To solve this contact problem, a simple and efficient, iterative finite element method developed by authors is used. Numerical examples are provided to verify the technique and the results are compared with those of the published papers. This revised version was published online in July 2006 with corrections to the Cover Date.     

Analysis of three‐dimensional crack initiation and propagation using the extended finite element method

An Erratum has been published for this article in International Journal for Numerical Methods in Engineering 2005, 63(8): 1228. We present a new formulation and a numerical procedure for the quasi‐static analysis of three‐dimensional crack propagation in brittle and quasi‐brittle solids. The extended finite element method (XFEM) is combined with linear tetrahedral elements. A viscosity‐regularized continuum damage constitutive model is used and coupled with the XFEM formulation resulting in a regularized ‘crack‐band’ version of XFEM. The evolving discontinuity surface is discretized through a C⁰ surface formed by the union of the triangles and quadrilaterals that separate each cracked element in two. The element's properties allow a closed form integration and a particularly efficient implementation allowing large‐scale 3D problems to be studied. Several examples of crack propagation are shown, illustrating the good results that can be achieved. Copyright © 2005 John Wiley & Sons, Ltd.     

Dual boundary element analysis of closed cracks

A two-dimensional boundary element method for analysis of closed or partially closed cracks under normal and frictional forces is developed. The single domain dual formulation is used. As a contact problem is non-linear due to the friction phenomena at the crack interface and also because of the boundary conditions which may change during the loading, it is formulated in an incremental and iterative fashion. The stress intensity factors are calculated with the J-integral method. Also crack growth is considered. Several benchmark cases have been analysed to verify the results given by the method. The stress intensity factors and crack paths calculated are similar to those given in the literature. © 1997 John Wiley & Sons, Ltd.