考虑温度影响的混凝土微观断裂模型

该文以各组分体积不变为准则建立了考虑温度影响的混凝土三相微观断裂球体模型。将混凝土组成简化为骨料,水及水泥浆体,并以模型中各层模拟;认为高温下混凝土的断裂为模型中间层水汽蒸发逸出的结果。通过气体状态方程分析了模型内部气压随温度的变化,并研究了骨料和水泥浆体层的应力状态。分析了含圆盘形裂纹的混凝土的可释放弹性能和表面能,并根据Griffith断裂准则给出了混凝土断裂韧性随温度的变化规律。对该文模型进行数值模拟,并与相关试验结果对比,结果证明了该文模型能够有效地计算高温下和高温后混凝土的断裂韧性。同时分析发现:随着温度的升高,混凝土可释放弹性能增大而开裂时的裂纹初始长度将减小。     

用扩展有限元方法模拟混凝土的复合型开裂过程

用扩展有限元法对混凝土梁复合型开裂过程进行了数值模拟。裂纹面间的力学行为采用粘聚裂纹模型来描述,通过引入切向保留刚度考虑剪力分量的影响。开裂方向的计算采用了一种简化的最大切向应力准则。对Arrea和Ingraffea的混凝土梁复合开裂实验进行了数值模拟。计算给出了裂纹萌生、扩展的过程及破坏形态,并获得了与实验结果对比良好的荷载-裂纹开口滑移曲线。结果表明,扩展有限元法通过附加特定的位移模式,使裂纹两侧不连位移场的表达独立于网格划分,是一种能够模拟准脆性材料复合开裂问题的有效方法。     

几类典型网格下三维弹性问题的代数多层网格法

有限元方法是数值求解三维弹性问题的一类重要的离散化方法.在有限元分析中,网格的几何形状及网格质量会对有限元离散代数系统的求解产生很大影响.该文系统研究了几类典型网格对几种常用AMG法计算效率的影响,并进行了详细的性能测试与比较.利用容易获知的部分几何与分析信息(如方程类型,节点自由度信息),再结合经典AMG法中的网格粗...     

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。     

基于多边形比例边界有限元的复合材料裂纹扩展模拟

该文采用近年提出的多边形比例边界有限元(Polygon Scaled Boundary Finite Elements,PSBFE),结合基于拓扑的局部网格重剖分方法,首次模拟了层状复合材料交界面、不同弹性模量的圆形夹杂对复合材料裂纹扩展的影响。结果表明,该文方法可以有效模拟复合材料的裂纹扩展,算例的结果同现有文献的实验数据和数值模拟结果吻合良好,采用不同网格密度和不同裂纹扩展步长对计算结果影响不大。基于SBFEM的PSBFE可以半解析求解裂纹尖端应力奇异性,具有比FEM更高的精度。另一方面,同现有基于SBFEM的裂纹扩展方法相比,基于拓扑的局部网格重剖分的PSBFE可以处理任意复杂的二维模型,具有更好的通用性。     

基于拓展虚内键本构模型的多裂纹混凝土结构破坏分析

拓展虚内键(Augmented virtual internal bond, AVIB)是基于虚内键理论的一种多尺度本构模型,它同时考虑了微观虚内键的法向和切向变形,应用Xu-Needleman势函数描述虚内键,并在微观势函数基础上直接导出了宏观本构方程。由于脆性材料的抗压强度与微元体的应力状态有关,为了反映这种微元应力效应,依据混凝土三轴抗压强度准则定义了应力效应系数,并将其反映到AVIB本构模型中。对于已有裂纹,采用无厚度单元劈裂法进行建模,避免了网格重划分问题和单独设置接触单元问题。结合AVIB模型与无厚度单元劈裂法,对多裂纹混凝土结构的破坏进行了模拟分析。结果表明,预制裂纹的长度不同,导致结构的主裂纹扩展方式不同。模拟所得的结构破坏模式及荷载-主裂纹口张开位移曲线与相关文献报道结果基本一致,表明了该方法的有效性。由于该文所采用的AVIB本构方程中已蕴涵了混凝土断裂能及三轴强度准则,因而在整个断裂模拟过程中,既避免了外部的断裂准则问题,同时又不需要网格重构及附加自由度,提高了计算效率,为大体积混凝土结构的破坏分析提供了一种简单的可行方法。     

青藏高原环境下混凝土结构密实性超声无损检测研究

青藏高原的环境条件限制常导致混凝土出现密实性缺陷问题，如何对混凝土的密实性缺陷进行精确的无损检测，是保障结构承载力及耐久性的关键。该文结合此前在西藏雅鲁藏布江藏木大桥与广西南宁实地开展的混凝土超声试验结果，基于不同气压下混凝土实体的超声波速计算模型，建立了以气压、水胶比为参数的混凝土实体部分超声波速计算模型；进一步对混凝土在不同孔隙率、缺陷条件、骨料分布情况条件下的超声波速进行了计算分析。揭示了孔隙率及缺陷条件对混凝土超声波速的影响规律及机理。研究了骨料分布占比对混凝土超声检测结果的影响规律，建立了混凝土整体超声波速的多因素计算模型，并提出了基于超声波速的混凝土密实性统计分析方法，可以为实际工程中混凝土结构密实性的超声无损检测结果分析提供理论依据。     

无网格伽辽金法求解轴对称问题

将无网格技术用于求解轴对称问题,通过加权余量法导出了无网格伽辽金法计算公式,考虑了不同介质的影响,编制了相应的计算程序,并对钢筋对混凝土管性能的影响进行了弹性和粘弹性的计算分析,与其它解相比,得到令人满意的数值结果。在粘弹性问题求解过程中,采用一种时间域自适应精细算法,给出了的径向位移与环向应力误差收敛速率曲线。     

基于徐变损伤理论的早龄期大体积混凝土化学-热-力多场耦合模型研究

受水化放热的影响,大体积混凝土在早龄期阶段涉及多个物理场作用,极易发生损伤、开裂等不利行为,会对结构服役期内的耐久性和安全性产生严重的影响。针对此问题,该文基于经典损伤理论框架,发展了一类适用于早龄期大体积混凝土的化学-热-力多场耦合模型,综合地反映了早龄期混凝土的开裂、徐变、温度变形、自收缩变形和龄期效应。通过将水化反应方程与热传导方程联立建立了化学-热场耦合作用模型。进而,基于弹塑性损伤理论框架搭建本构关系,引入考虑损伤影响的微观应力-固化理论以刻画混凝土的线性徐变和非线性徐变,根据温度和水化度的变化求解热膨胀变形和自收缩变形,并考虑了随龄期变化的混凝土力学性能的影响。结合相应的显式求解算法,将上述多场耦合模型应用于Maridal涵洞早龄期力学行为的模拟分析,并探究了混凝土徐变变形的影响。计算结果表明：该文模型可以实现对早龄期大体积混凝土开裂过程的准确模拟,对早龄期混凝土受力性能和开裂行为的研究具有一定的参考意义。     

考虑材料组成特性的混凝土轴拉破坏过程细观数值模拟

为反映骨料、砂浆及其之间的界面过渡区的组合特点和材料性能,基于材料细观非均匀性和有限元方法的混凝土破坏过程细观数值模拟需进行复杂、细致的网格剖分,导致了繁重的前处理工作和可观的计算量。该文对混凝土材料细观单元材质组成的单一化假定进行改进,将内嵌界面过渡区材料的规则化单元视为一种广义复合材料单元,建立了复合型界面损伤模型。采用等效方法确定单元的复合弹性关系,通过有限元法计算单元的局部应力;用细观层次上弹性力学性能的弱化描述单元组成材料的损伤,混凝土材料的破坏过程通过单元各组分的损伤模拟。应用该复合型界面损伤模型研究了混凝土试件的单轴拉伸破坏过程,细观数值模拟结果符合混凝土试件的宏观破坏特征,表明该模型可作为分析混凝土材料破坏过程的一种有效途径。     

含裂纹混凝土的三维渗透性分析

该文假设含裂纹的混凝土材料是由孔隙基体和裂纹组成的二相复合材料,基于相互作用直推法（IDD）给出了三维周期裂纹渗透性的表达式。基于单元嵌入技术和弹性比拟的数值模拟新方法,解决了三维细观连续有限元实体模型的建模和网格划分问题,实现了含混凝土裂纹的三维渗透模拟。假设裂纹为圆盘状,引入周期性的概念并提出三维周期裂纹结构模型,分析裂纹直径、裂纹周期、裂纹倾角和裂纹间距等因素对整体等效渗透性能的影响。将得到的数值解和IDD理论解进行对比分析,结果表明:在裂纹密度较低时,数值解和理论解吻合得很好,但随着裂纹密度的增大,二者之间的误差逐渐增大;当裂纹趋于连通时,IDD解低估了裂纹之间的近场相互作用而偏离数值解;裂纹接近连通时,整体等效渗透率与裂纹密度呈对数关系,可用渐进对数表达式准确描述。     

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.     

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。     

Numerical modelling for scattering of waves in three-dimensional cracked material

In this paper, a mathematical model is proposed for the problem of the scattering of plane waves in a three-dimensional cracked materials. Instead of obtaining closed-form solutions as in conventional theoretical analysis methods, this approach, called the Equivalent Nodal Force (ENF) method formulates the mechanical effects of cracks as an equivalent nodal force in a numerical procedure, and physically translates cracked material into an equivalent continuous one. Several mechanical relations between waves and cracks are evident from this method. Also the results of several numerical calculations are presented and these are compared with those obtained by the conventional methods.     

A Novel Hexahedral Interface Element for Nonlinear Crack Analysis

Existence of a crack in structures would lead to a sudden failure and damage. Establishing a precise analytical model for the cracked element would be a powerful tool to achieve the right answers in the analysis of the structure. The main aim of this article is to formulate a hexahedral interface element for use in nonlinear crack analysis. In this investigation, the kinematics of the discontinuous displacement field along with the virtual work principle, for a body with an internal discontinuity, is utilized. Based on the suggested interpolation functions for the discrete segments, and also the element displacement field, the element stiffness matrix is calculated. The proposed element can be used for modeling of the discrete cracks in three-dimensional problems, such as a concrete dam. Several numerical examples are analyzed for the accuracy test and a few of them are presented here. The results indicated that utilizing sufficient elements yields suitable answers.     

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。     

Longitudinal vibration of a continuous cracked bar

A continuous cracked bar vibration theory is developed for longitudinal vibration of rods with an edge crack. The Hu–Washizu–Barr variational formulation was used to develop the differential equation and the boundary conditions of the cracked bar as a one-dimensional continuum. The crack was modelled as a continuous flexibility using the displacement field in the vicinity of the crack found with fracture mechanics methods.

The results of three independent evaluations of the lowest natural frequency of longitudinal vibrations of a bar with a single edge crack are presented: the continuous cracked bar vibration theory, the lumped crack bar vibration analysis, and experimental results obtained on aluminum bars with fatigue cracks. Experimental results fall between the values predicted by the two analytical methods. Moreover, the continuous bar theory agrees better with the experimental results than the lumped crack flexibility theory for small cracks. For larger cracks, a/h>0.4, experimentation was difficult due to the co-existence of several coupled modes and no reliable results could be obtained.     

Ritz analysis of discontinuous beams using local trigonometric functions

The objective of the current paper is to present a Ritz-type analytical model for predicting the behavior of discontinuous beams such as thin-walled beams with cracks and multiply-stepped beams. The beam is discretized in the cracked as well as the un-cracked domains for a cracked thin-walled beam and in uniform beams for a multiple-stepped beam. A set of local trigonometric trial functions is used to define the twist angle for the cracked domain and the un-cracked domains, as well as to define the displacement field for uniform domains. A global equation system of unknown Ritz coefficients is derived by minimizing the Lagrangian functional or the total potential energy. In the present Ritz model, the interface continuity conditions between sub-domains are investigated and enforced into the global equation system using the condensation procedure or the Lagrange multipliers. Examples are presented to illustrate the effectiveness of the current model for free vibration and torsional analysis. Results obtained from the current model are found to agree well with those obtained using a detailed finite element method or with existing results in literature. The proposed model offers an efficient approach to reduce the modeling efforts and computational time required to analyze complex beams with cracks or multiple steps.     

Computation of stress intensity factors of interface cracks based on interaction energy release rates and BEM sensitivity analysis

Stress intensity factors of bimaterial interface cracks are evaluated based on the interaction energy release rates. The interaction energy release rate is defined based on the energy release rates of a cracked body, corresponding to two independent loading conditions, actual field and an auxiliary field, and is related to the sensitivities of the potential energies for crack extensions. The potential energy of a cracked body is expressed with a domain integral, which is converted to a boundary integral expression by applying the divergence theorem. By differentiating this expression with the crack length, a boundary integral expression for the interaction energy release rate is obtained. The boundary integral representation for the interaction energy release rate involves the displacement, the traction, and their sensitivity coefficients with respect to the crack length. The boundary element sensitivity analyses are used to calculate these quantities accurately. A regularized boundary integral equation relating the boundary displacement and traction is differentiated with respect to an arbitrary shape parameter to derive the regularized boundary integral equation for the sensitivity coefficients of the boundary displacement and traction. The proposed approach is applied to several cracks in dissimilar media and the results are compared with those obtained by the conventional approach based on the extrapolation method. The analytical displacement and stress solutions for an interface crack between two infinite dissimilar media subjected to uniform stresses at infinity are used to give the auxiliary field, in which the values of the stress intensity factors are known. It is demonstrated that the present method can give accurate results for the stress intensity factors of various bimaterial interface cracks under coarse mesh discretizations.     

Analysis of surface cracks using the line-spring boundary element method and the virtual crack extension technique

The authors have developed a new line-spring boundary element method which couples the line-spring model with the boundary element method to deal with the problem of a surface cracked plate. However, the drawback of the line-spring model is that a reliable stress intensity factor could not be directly obtained near the free surface intersection. Therefore, the virtual crack extension technique is employed in a post-processor of the line-spring boundary element method to obtain the stress intensity factor at the crack front-free surface intersection. Theoretical analysis is described. Stress intensity factors for surface cracks are calculated to verify the proposed method. The interaction of two surface cracks is also investigated. The solutions obtained by the line-spring boundary element method show that the method proposed is efficient and reasonably accurate.