粘聚裂纹扩展的强化有限元h型网格自适应模拟

非连续变形分析和非规则节点处理是基于单元细划的粘聚裂纹扩展网格自适应模拟的关键。首先,利用强化有限单元法中数学单元和物理单元分离的特点,通过引入过渡单元,将适用于非连续变形描述的数学模式覆盖法和方便处理非规则节点的物理模式重构法结合,提出了强化有限单元法的统一关联法则,并导出了相应的单元列式。其次,基于数学裂纹尖端影响域和裂尖单元尺寸,提出了基于强化有限单元法的粘聚裂纹扩展过程模拟的h型网格自适应策略。最后,通过两个算例验证了本文方法的合理性和有效性。     

数学网格和物理网格分离的有限单元法(II):粘聚裂纹扩展问题中的应用

强化有限单元法将物理网格与数学网格分离开来,可以方便地描述非连续变形;粘聚区域模型是模拟断裂过程区作用最简单有效的方法,且可以避免裂纹尖端的应力奇异性.本文以平面问题为例,将强化有限单元法与粘聚区域模型相结合,利用富集数学节点描述任意粘聚裂纹扩展过程中的非连续变形问题,提出了裂纹扩展过程中数学节点富集和数学单元定义的方法.本文还导出了与平面4～8节点平面等参单元对应的8～16节点粘聚裂纹单元列武.最后,通过三点弯梁的裂纹扩展过程模拟验证了本文提出的粘聚裂纹扩展模拟方法的有效性.     

基于单位分解法的无网格数值流形方法

在数值流形方法和单位分解法的基础上，提出了无网格数值流形方法. 无网格数值流形 方法在分析时采用了双重覆盖系统，即数学覆盖和物理覆盖. 数学覆盖提供的节点形成求解 域的有限覆盖和单位分解函数；而物理覆盖描述问题的几何区域及其域内不连续性. 与原有 的数值流形方法相比，无网格数值流形方法的数学覆盖形状更加灵活，可以用一系列节点的 影响域来建立数学覆盖和单位分解函数，具有无网格方法的特性，从而摆脱了传统的数值流 形方法中网格所带来的困难. 与无网格方法相比，由于采用了有限覆盖技术，试函数的构造 不受域内不连续的影响，克服了原有的无网格方法在处理不连续问题时所遇到的困难. 详细推导了无网格数值流形方法的试函数和求解方程，最后给出了算例，验证了该方法的正 确性.     

固定网格的数值流形方法研究

针对单纯几何非线性的材料大变形问题, 提出一种新的研究思路------固定数学网格的数值流形方法, 简称固定网格流形法, 可以看作是采用了固定网格的拉格朗日方法. 它充分利用数值流形方法的数学网格与材料物理边界分离的特性, 具备拉格朗日法和欧拉法各自的优势, 避免了原始拉格朗日法的网格扭曲问题以及欧拉法对移动边界难以精确描述和迁移项较难处理的问题. 采用数值流形方法的大变形分步计算格式, 使得固定网格流形法实现起来并不复杂, 仅需要每步切割网格形成新的流形单元, 以及对初应力载荷进行适当的处理, 而后者是固定网格流形法的关键. 针对固定的矩形数学网格开展研究, 采用一阶多项式覆盖函数的高阶流形法, 给出了两种初应力计算方法, 并用悬臂梁大变形算例验证了固定网格流形法的可行性, 将来需要进一步解决初应力载荷所带来的计算稳定问题.      

弹性力学中的一种非协调数值流形方法

通过引入数学和物理双重网格，将插值域与 积分域分别定义在不同的覆盖上，即在数学网格上进行插值函数的构造，物理网格上完成 系统能量泛函积分运算，最后通过覆盖权函数将二者联结在一起. 它的优点是单元网格划 分随意，不受复杂边界形状和二相材料界面的限制，单元可以是任意形状，是较之于有限 元方法更一般的数值模拟方法. 在4节点四边形数值流形方法中，由于单元总体位移函数 包含的完全多项式不完全，使得计算精度不够精确，为此，在单元总体位移函数上附 加非协调位移基本项，使之趋于完全，提出了弹性力学问题的一种改进的数值流形 方法------非协调数值流形方法. 通过内部自由度静力凝聚处理，导出了消除内参后的单元应变矩阵 和单元刚度矩阵，使得在不增加广义节点自由度的前提下，大大提高了数值流形方法的计 算精度和计算效率. 同时对非协调项进行了显式处理，可以对工程实践起到更切实的帮助. 数值试验表明，它们能够保证收敛，有较高的精度，对畸变不敏感，从而证明了该方法的 可行性.     

数值流形方法及其在岩石力学中的应用

数值流形方法是目前岩石力学分析的主要方法之一.该方法起源于不连续变形分析,主要用于统一求解连续和非连续问题,其核心技术是在分析时采用了双重网格:数学网格提供的节点形成求解域的有限覆盖和权函数;而物理网格为求解的积分域.数学网格被用来建立数学覆盖,数学覆盖与物理网格的交集定义为物理覆盖,由物理覆盖的交集形成流形单元.流形方法的优点在于它使用了独立的数学和物理网格,具有和有限元明显不同的定义形式,且数学网格对于同一问题不同的求解精度的需求可以很方便地细化.由于该方法考虑了块体运动学,可以模拟节理岩体裂隙的开裂和闭合过程,因而在岩石力学中得到了广泛应用,近年来许多学者对该方法进行了研究.本文简要叙述了节理岩体的数值方法从连续到非连续的发展过程,详细地介绍了数值流形方法的组成和数值流形方法在岩石力学及其相关领域的研究和发展概况,最后就作者所关心的一些问题,如三维问题的数值流形方法、数值流形方法在物理非线性问题和裂纹扩展问题中的应用、相关的耦合方法等进行了探讨.      

数值流形单元法数学网格自适应

基于数值流形方法和有限覆盖技术,将有限元法的后验误差估计理论及h型网格自适应技术推广应用到数值流形单元法中,提出了数值流形单元法的后验误差估计方法和数学网格自适应技术,并编制了相应的程序。数值算例表明,经过网格自适应,可以在粗糙的初始网格基础上得到质量比较理想的网格,计算结果可达到用户要求的精度。     

三维连续与非连续变形分析

将石根华博士所提出的二维非连续变形分析——Discontinuous Deformation Analysis（DDA）方法扩展到三维情况,并对三维不连续块体进行有限元网格剖分,即块体之间的接触采用DDA描述,块体内部的位移场和应力场则采用有限单元法描述,从而将三维DDA与有限元方法结合起来,增强了DDA方法与有限元方法解决实际工程问题的能力,实现了三维连续与非连续变形分析.给出了基本公式的推导过程和各子矩阵的形式.典型接触、碰撞算例证明了所提出方法的有效性和正确性.     

基于三角网格的四阶Hermite型对流守恒格式

提出一种基于三角网格的求解双曲对流方程的高阶守恒型格式.该格式首先在每个三角单元上重构二元三次Hermite插值多项式,以当前时刻单元节点处解的函数值、一阶空间导数值和该单元的积分平均值为插值条件.然后,利用Semi-Lagrange方法得到单元节点处的下一时刻解的函数值及导数值,而下一时刻的解的单元积分平均值由有限体积方法得到.本文所提出的格式将原始CIP方法从结构网格推广到非结构网格上,使得CIP方法能灵活地用于处理复杂边界问题.该格式为显式紧致格式,计算简单且易于实现.数值实验表明,该格式对于光滑解问题能达到四阶空间精度,而对于非光滑解问题能准确地捕捉激波的位置,改进了原始CIP格式的不守恒性.     

网格自适应技术在复杂外形流场模拟中的应用

建立了一套适用于非结构混合网格自适应方法,针对激波和涡的不同特征采用不同加密探测器,各向异性加密棱柱单元并沿物面法向方向剖分所有棱柱层,各向异性剖分四面体单元,并保证四面体与棱柱交界面上网格协调。构造Hermit插值近似投影物面新加网格点和基于Laplacian光滑方法对空间网格进行优化。通过网格自适应加密,使用Roe格式计算高超声速球头绕流的红玉现象得到明显减轻。F16飞机含激波和脱体涡的流场自适应计算表明,网格加密集中在激波面和涡核附近区域,激波和涡计算更准确。     

内聚力模型裂纹问题分析的解析奇异单元

内聚力模型已经被广泛应用于需要考虑断裂过程区的裂纹问题当中,然而常用的数值方法应用于分析内聚力模型裂纹问题时还存在着一些不足,比如不能准确的给出断裂过程区的长度、需要网格加密等。为了克服这些缺点,论文构造了一个新型的解析奇异单元,并将之应用于基于内聚力模型的裂纹分析当中。首先将虚拟裂纹表面处的内聚力用拉格拉日插值的方法近似表示为多项式的形式,而多项式表示的内聚力所对应的特解可以被解析地给出。然后利用一个简单的迭代分析,基于内聚力模型的裂纹问题就可以被模拟出来了。最后,给出二个数值算例来证明本文方法的有效性。     

Analysis of crack growth and crack-tip plasticity in ductile materials using cohesive zone models

Crack initiation and crack growth resistance in elastic plastic materials, dominated by crack-tip plasticity are analyzed with the crack modeled as a cohesive zone. Two different types (exponential and bilinear) of cohesive zone models (CZMs) have been used to represent the mechanical behavior of the cohesive zones. In this work, it is suggested that different forms of CZMs (e.g., exponential, bilinear) are the manifestations of different micromechanisms-based inelastic processes that participate in dissipating energy during the fracture process and each form is specific to each material system. It is postulated that the total energy release rate comprises the plastic dissipation rate in the bounding material and the separation energy rate within the fracture process zone, the latter is determined by CZMs. The total energy release rate then becomes a function of the material properties (e.g., yield strength, strain hardening exponent) and cohesive properties of the fracture process zone (e.g., cohesive strength and cohesive energy), and the form of cohesive zone model (CZM) that determines the rate of energy dissipation in the forward and wake regions of the crack. The effects of material parameters, cohesive zone parameters as well as the form/shape of CZMs in predicting the crack growth resistance and the size of plastic zone (SPZ) surrounding the crack tip are systematically examined. It is found that in addition to the cohesive strength and cohesive energy, the form (shape) of the traction–separation law of CZM plays a very critical role in determining the crack growth resistance (R-curve) of a given material. It is further observed that the shape of the CZM corresponds to inelastic processes active in the forward and wake regions of the crack, and has a profound influence on the R-curve and SPZ.     

A thermomechanical cohesive zone model for bridged delamination cracks

The coupled thermomechanical numerical analysis of composite laminates with bridged delamination cracks loaded by a temperature gradient is described. The numerical approach presented is based on the framework of a cohesive zone model. A traction-separation law is presented which accounts for breakdown of the micromechanisms responsible for load transfer across bridged delamination cracks. The load transfer behavior is coupled to heat conduction across the bridged delamination crack. The coupled crack-bridging model is implemented into a finite element framework as a thermomechanical cohesive zone model (CZM). The fundamental response of the thermomechanical CZM is described. Subsequently, bridged delamination cracks of fixed lengths are studied. Values of the crack tip energy release rate and of the crack heat flux are computed to characterize the loading of the structure. Specimen geometries are considered that lead to crack opening through bending deformation and buckling delamination. The influence of critical mechanical and thermal parameters of the bridging zone on the thermomechanical delamination behavior is discussed. Bridging fibers not only contribute to crack conductance, but by keeping the crack opening small they allow heat flux across the delamination crack to be sustained longer, and thereby contribute to reduced levels of thermal stresses. The micro-mechanism based cohesive zone model allows the assessment of the effectiveness of the individual mechanisms contributing to the thermomechanical crack bridging embedded into the structural analysis.     

Direct Extraction of Cohesive Fracture Properties from Digital Image Correlation: A Hybrid Inverse Technique

The accuracy of an adopted cohesive zone model (CZM) can affect the simulated fracture response significantly. The CZM has been usually obtained using global experimental response, e.g., load versus either crack opening displacement or load-line displacement. Apparently, deduction of a local material property from a global response does not provide full confidence of the adopted model. The difficulties are: (1) fundamentally, stress cannot be measured directly and the cohesive stress distribution is non-uniform; (2) accurate measurement of the full crack profile (crack opening displacement at every point) is experimentally difficult to obtain. An attractive feature of digital image correlation (DIC) is that it allows relatively accurate measurement of the whole displacement field on a flat surface. It has been utilized to measure the mode I traction-separation relation. A hybrid inverse method based on combined use of DIC and finite element method is used in this study to compute the cohesive properties of a ductile adhesive, Devcon Plastic Welder II, and a quasi-brittle plastic, G-10/FR4 Garolite. Fracture tests were conducted on single edge-notched beam specimens (SENB) under four-point bending. A full-field DIC algorithm was employed to compute the smooth and continuous displacement field, which is then used as input to a finite element model for inverse analysis through an optimization procedure. The unknown CZM is constructed using a flexible B-spline without any “a priori” assumption on the shape. The inversely computed CZMs for both materials yield consistent results. Finally, the computed CZMs are verified through fracture simulation, which shows good experimental agreement.     

Separation work analysis of cohesive law and consistently coupled cohesive law

An appropriate coupled cohesive law for predicting the mixed mode failure is established by combining normal separation and tangential separation of surfaces in the cohesive zone model(CZM) and the cohesive element method.The Xu-Needleman exponential cohesive law with the fully shear failure mechanism is one of the most popular models.Based on the proposed consistently coupled rule/principle,the Xu-Needleman law with the fully shear failure mechanism is proved to be a non-consistently coupled cohesive la...     

压电复合材料粘接界面断裂有限元模拟

根据数字化FRMM(Fix-Ratio Mix-Mode)断裂试验,得到了压电复合材料试件的断裂韧性和位移及应变场。本文在试验的基础上,通过非线性有限元软件ABAQUS及用户子程序UMAT进行了模拟分析,采用基于损伤力学的粘聚区模型(CZM)对压电复合材料界面的起裂和脱胶扩展进行了分析,并与VCCT方法进行了比较。计算得到的荷载位移曲线更接近于试验结果,但在裂纹扩展路径上的吻合需要对粘聚区法则进一步修正。通过进一步对CZM参数进行分析,表明界面粘结强度和界面刚度对计算结果的影响很大。研究结果表明,粘聚区模型可以很好地表征压电复合材料弱粘接界面脱胶断裂问题。     

Crack growth resistance of shape memory alloys by means of a cohesive zone model

Crack growth resistance of shape memory alloys (SMAs) is dominated by the transformation zone in the vicinity of the crack tip. In this study, the transformation toughening behavior of a slowly propagating crack in an SMA under plane strain conditions and mode I deformation is numerically investigated. A small-scale transformation zone is assumed. A cohesive zone model is implemented to simulate crack growth within a finite element scheme. Resistance curves are obtained for a range of parameters that specify the cohesive traction-separation constitutive law. It is found that the choice of the cohesive strength t₀ has a great influence on the toughening behavior of the material. Moreover, the reversibility of the transformation can significantly reduce the toughening of the alloy. The shape of the initial transformation zone, as well as that of a growing crack is determined. The effect of the Young's moduli ratio of the martensite and austenite phases is examined.