Extended Finite Element Method: for Fracture Analysis of Structures
Extended Finite Element Method: for Fracture Analysis of Structures
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发表时间：
2008-03
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通讯作者：
S. Mohammadi
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作者：
S. Mohammadi
奉献精神。前言。命名法。第一章绪论。1.1结构分析。1.2不连续点分析。1.3断裂力学。1.4裂缝建模。1.4.1本地和非本地模型。1.4.2涂抹裂纹模型。1.4.3离散元间裂缝。1.4.4离散裂纹元件。1.4.5奇异元素。1.4.6富集元素。1.5替代技术。1.6 xfem应用回顾。1.6.1 XFEM的一般方面。1.6.2定位与断裂。1.6.3复合材料。1.6.4接触。1.6.5动力学。1.6.6大变形/壳体。1.6.7多尺度。1.6.8多相/凝固。1.7本书的范围。第二章断裂力学综述。2.2弹性基础。2.2.1应力应变关系。2.2.2 Airy应力函数。2.2.3复应力函数。2.3 left的基本知识。2.3.1断裂力学。2.3.2圆孔。2.3.3椭圆孔。2.3.4尖锐裂纹的Westergaard分析。2.4应力强度因子，k。2.4.1应力强度因子的定义。2.4.2 LEFM应力强度因子举例。2.4.3格里菲斯的力量和能量理论。2.4.4脆性材料。2.4.5准脆性材料。2.4.6裂纹稳定性。2.4.7固定握把与固定负载。2.4.8混合模式裂纹扩展。2.5 k和g的求解过程。2.5.1位移外推/相关法。2.5.2模式一能量释放速率。2.5.3 I型刚度导数/虚裂纹模型。2.5.4混合模式情况下的两个虚拟裂纹扩展。2.5.5基于位移分解的单虚拟裂纹扩展。2.5.6四分之一点奇异元素。2.6弹塑性断裂力学。2.6.1塑性区。2.6.2裂纹尖端张开位移（CTOD）。2.6.3 J积分。2.6.4塑性裂纹尖端场。2.6.5 J。2.7基于j积分的数值方法。2.7.1节点解决方案。2.7.2一般有限元解。2.7.3等效域积分（EDI）法。2.7.4交互积分法。第三章各向同性问题的扩展有限元法。3.2 xfem发展回顾。3.3有限元基础。3.3.1等参数有限元，简单回顾。3.3.2断裂力学的有限元解。3.4分割统一。3.5浓缩。3.5.1内在富集。3.5.2外在富集。3.5.3单元有限元划分法。3.5.4广义有限元法。3.5.5扩展有限元法。3.5.6 hp云富集。3.5.7 PU富集的概括。3.5.8从标准近似过渡到充实近似。3.6各向同性xfem。3.6.1基本XFEM近似。3.6.2带符号距离函数。3.6.3强不连续场建模。3.6.4弱不连续场建模。3.6.5塑性富集。3.6.6不连续富集节点的选择。3.6.7裂缝建模。3.7离散化与积分。3.7.1控制方程。3.7.2 XFEM离散化。3.7.3元素划分和数值积分。3.7.4裂缝相交。3.8跟踪移动边界。3.8.1级别设置方法。3.8.2快速进步法。3.8.3有序逆风法。3.9数值模拟。3.9.1有中心裂缝的拉伸板。3.9.2双面裂纹。3.9.3双内共线裂纹。3.9.4无限大板的中心裂纹。3.9.5有限板的边缘裂纹。第4章正交各向异性问题的XFEM。4.2各向异性弹性。4.2.1弹性解决方案。4.2.2各向异性应力函数。4.2.3正交各向异性混合模问题。4.2.4各向异性能量释放率和应力强度因子。材料。4.2.5各向异性奇异元素。4.3近裂纹尖端解析解。4.3.1裂纹尖端近位移场（I类）。4.3.2裂纹尖端近位移场（II类）。4.3.3统一的裂纹尖端近位移场（两类）。4.4各向异性。4.4.1控制方程。4.4.2 XFEM离散化。4.4.3 SIF计算。4.5数值模拟。4.5.1裂纹平行于材料正交异性轴线的板材。4.5.2具有正交异性轴线多个方向的边裂纹。4.5.3带裂纹倾角的单棱缺口拉伸试样。4.5.4中心斜裂。4.5.5受点荷载作用的圆盘的倾斜中心裂缝。4.5.6各向同性和各向同性材料之间的裂纹。拉伸牵引。第5章内聚裂纹的XFEM。5.2粘性裂缝。5.2.1内聚裂纹模型。5.2.2黏性裂纹数值模型。5.2.3裂纹扩展准则。5.2.4快速回跳行为。5.2.5内聚裂纹Griffith准则。5.2.6内聚裂纹模型。5.3 xfem为粘性裂缝。5.3.1富集函数。5.3.2控制方程。5.3.3 XFEM离散化。5.4数值模拟。5.4.1混合模弯曲梁。5.4.2四点弯梁。5.4.3双悬臂梁。第六章新领域。6.1引言。6.2界面裂缝。6.2.1各向同性双材料界面弹性解。6.2.2界面裂缝的稳定性。6.2.3界面裂缝的XFEM近似。6.3接触。6.3.1接触问题的数值模型。6.3.2接触问题的XFEM建模。6.4动态断裂。6.4.1 XFEM动态裂纹扩展。6.4.2动态LEFM。6.4.3动态正交各向异性LEFM。6.4.4动态XFEM的基本公式。6.4.5 XFEM离散化。6.4.6时间集成。6.4.7时间有限元法。6.4.8时间扩展有限元法。6.5多尺度xfem。6.5.1基本配方。6.5.2变焦技术。6.5.3均质化技术。6.5.4 XFEM离散化。6.6多相xfem。6.6.1基本配方。6.6.2 XFEM近似。6.6.3两相流体流动。6.6.4 XFEM近似。第7章XFEM流程。7.2可用的开源xfem。7.3. 有限元分析。7.3.1定义模型。7.3.2创建有限元网格。7.3.3线弹性分析。7.3.4变形大。7.3.5非线性（弹塑性）分析。7.3.6材料本构矩阵。7.4 XFEM。7.4.1前端跟踪。7.4.2富集检测。7.4.3浓缩函数。7.4.4 Ramp（过渡）函数。7.4.5 B矩阵的求值。7.5数值积分。7.5.1 Sub-quads。7.5.2 Sub-triangles。7.6解决者。7.6.1 XFEM自由度。7.6.2时间集成。7.6.3联立方程求解器。7.6.4裂缝长度控制。7.7后处理。7.7.1应力强度因子。7.7.2裂纹扩展。7.7.3其他应用。7.8配置更新。引用。指数
Dedication. Preface . Nomenclature . Chapter 1 Introduction. 1.1 ANALYSIS OF STRUCTURES. 1.2 ANALYSIS OF DISCONTINUITIES. 1.3 FRACTURE MECHANICS. 1.4 CRACK MODELLING. 1.4.1 Local and non-local models. 1.4.2 Smeared crack model. 1.4.3 Discrete inter-element crack. 1.4.4 Discrete cracked element. 1.4.5 Singular elements. 1.4.6 Enriched elements. 1.5 ALTERNATIVE TECHNIQUES. 1.6 A REVIEW OF XFEM APPLICATIONS. 1.6.1 General aspects of XFEM. 1.6.2 Localisation and fracture. 1.6.3 Composites. 1.6.4 Contact. 1.6.5 Dynamics. 1.6.6 Large deformation/shells. 1.6.7 Multiscale. 1.6.8 Multiphase/solidification. 1.7 SCOPE OF THE BOOK. Chapter 2 Fracture Mechanics, a Review. 2.1 INTRODUCTION. 2.2 BASICS OF ELASTICITY. 2.2.1 Stress-strain relations. 2.2.2 Airy stress function. 2.2.3 Complex stress functions. 2.3 BASICS OF LEFM. 2.3.1 Fracture mechanics. 2.3.2 Circular hole. 2.3.3 Elliptical hole. 2.3.4 Westergaard analysis of a sharp crack. 2.4 STRESS INTENSITY FACTOR, K . 2.4.1 Definition of the stress intensity factor. 2.4.2 Examples of stress intensity factors for LEFM. 2.4.3 Griffith theories of strength and energy. 2.4.4 Brittle material. 2.4.5 Quasi-brittle material. 2.4.6 Crack stability. 2.4.7 Fixed grip versus fixed load. 2.4.8 Mixed mode crack propagation. 2.5 SOLUTION PROCEDURES FOR K AND G . 2.5.1 Displacement extrapolation/correlation method. 2.5.2 Mode I energy release rate. 2.5.3 Mode I stiffness derivative/virtual crack model. 2.5.4 Two virtual crack extensions for mixed mode cases. 2.5.5 Single virtual crack extension based on displacement decomposition. 2.5.6 Quarter point singular elements. 2.6 ELASTOPLASTIC FRACTURE MECHANICS (EPFM). 2.6.1 Plastic zone. 2.6.2 Crack tip opening displacements (CTOD). 2.6.3 J integral. 2.6.4 Plastic crack tip fields. 2.6.5 Generalisation of J . 2.7 NUMERICAL METHODS BASED ON THE J INTEGRAL. 2.7.1 Nodal solution. 2.7.2 General finite element solution. 2.7.3 Equivalent domain integral (EDI) method. 2.7.4 Interaction integral method. Chapter 3 Extended Finite Element Method for Isotropic Problems. 3.1 INTRODUCTION. 3.2 A REVIEW OF XFEM DEVELOPMENT. 3.3 BASICS OF FEM. 3.3.1 Isoparametric finite elements, a short review. 3.3.2 Finite element solutions for fracture mechanics. 3.4 PARTITION OF UNITY. 3.5 ENRICHMENT. 3.5.1 Intrinsic enrichment. 3.5.2 Extrinsic enrichment. 3.5.3 Partition of unity finite element method. 3.5.4 Generalised finite element method. 3.5.5 Extended finite element method. 3.5.6 Hp-clouds enrichment. 3.5.7 Generalisation of the PU enrichment. 3.5.8 Transition from standard to enriched approximation. 3.6 ISOTROPIC XFEM. 3.6.1 Basic XFEM approximation. 3.6.2 Signed distance function. 3.6.3 Modelling strong discontinuous fields. 3.6.4 Modelling weak discontinuous fields. 3.6.5 Plastic enrichment. 3.6.6 Selection of nodes for discontinuity enrichment. 3.6.7 Modelling the crack. 3.7 DISCRETIZATION AND INTEGRATION. 3.7.1 Governing equation. 3.7.2 XFEM discretization. 3.7.3 Element partitioning and numerical integration. 3.7.4 Crack intersection. 3.8 TRACKING MOVING BOUNDARIES. 3.8.1 Level set method. 3.8.2 Fast marching method. 3.8.3 Ordered upwind method. 3.9 NUMERICAL SIMULATIONS. 3.9.1 A tensile plate with a central crack. 3.9.2 Double edge cracks. 3.9.3 Double internal collinear cracks. 3.9.4 A central crack in an infinite plate. 3.9.5 An edge crack in a finite plate. Chapter 4 XFEM for Orthotropic Problems. 4.1 INTRODUCTION. 4.2 ANISOTROPIC ELASTICITY. 4.2.1 Elasticity solution. 4.2.2 Anisotropic stress functions. 4.2.3 Orthotropic mixed mode problems. 4.2.4 Energy release rate and stress intensity factor for anisotropic. materials. 4.2.5 Anisotropic singular elements. 4.3 ANALYTICAL SOLUTIONS FOR NEAR CRACK TIP. 4.3.1 Near crack tip displacement field (class I). 4.3.2 Near crack tip displacement field (class II). 4.3.3 Unified near crack tip displacement field (both classes). 4.4 ANISOTROPIC XFEM. 4.4.1 Governing equation. 4.4.2 XFEM discretization. 4.4.3 SIF calculations. 4.5 NUMERICAL SIMULATIONS. 4.5.1 Plate with a crack parallel to material axis of orthotropy. 4.5.2 Edge crack with several orientations of the axes of orthotropy. 4.5.3 Single edge notched tensile specimen with crack inclination. 4.5.4 Central slanted crack. 4.5.5 An inclined centre crack in a disk subjected to point loads. 4.5.6 A crack between orthotropic and isotropic materials subjected to. tensile tractions. Chapter 5 XFEM for Cohesive Cracks. 5.1 INTRODUCTION. 5.2 COHESIVE CRACKS. 5.2.1 Cohesive crack models. 5.2.2 Numerical models for cohesive cracks. 5.2.3 Crack propagation criteria. 5.2.4 Snap-back behaviour. 5.2.5 Griffith criterion for cohesive crack. 5.2.6 Cohesive crack model. 5.3 XFEM FOR COHESIVE CRACKS. 5.3.1 Enrichment functions. 5.3.2 Governing equations. 5.3.3 XFEM discretization. 5.4 NUMERICAL SIMULATIONS. 5.4.1 Mixed mode bending beam. 5.4.2 Four point bending beam. 5.4.3 Double cantilever beam. Chapter 6 New Frontiers. 6.1 INTRODUCTION. 6.2 INTERFACE CRACKS. 6.2.1 Elasticity solution for isotropic bimaterial interface. 6.2.2 Stability of interface cracks. 6.2.3 XFEM approximation for interface cracks. 6.3 CONTACT. 6.3.1 Numerical models for a contact problem. 6.3.2 XFEM modelling of a contact problem. 6.4 DYNAMIC FRACTURE. 6.4.1 Dynamic crack propagation by XFEM. 6.4.2 Dynamic LEFM. 6.4.3 Dynamic orthotropic LEFM. 6.4.4 Basic formulation of dynamic XFEM. 6.4.5 XFEM discretization. 6.4.6 Time integration. 6.4.7 Time finite element method. 6.4.8 Time extended finite element method. 6.5 MULTISCALE XFEM. 6.5.1 Basic formulation. 6.5.2 The zoom technique. 6.5.3 Homogenisation based techniques. 6.5.4 XFEM discretization. 6.6 MULTIPHASE XFEM. 6.6.1 Basic formulation. 6.6.2 XFEM approximation. 6.6.3 Two-phase fluid flow. 6.6.4 XFEM approximation. Chapter 7 XFEM Flow. 7.1 INTRODUCTION. 7.2 AVAILABLE OPEN-SOURCE XFEM. 7.3. FINITE ELEMENT ANALYSIS. 7.3.1 Defining the model. 7.3.2 Creating the finite element mesh. 7.3.3 Linear elastic analysis. 7.3.4 Large deformation. 7.3.5 Nonlinear (elastoplastic) analysis. 7.3.6 Material constitutive matrix. 7.4 XFEM. 7.4.1 Front tracking. 7.4.2 Enrichment detection. 7.4.3 Enrichment functions. 7.4.4 Ramp (transition) functions. 7.4.5 Evaluation of the B matrix. 7.5 NUMERICAL INTEGRATION. 7.5.1 Sub-quads. 7.5.2 Sub-triangles. 7.6 SOLVER. 7.6.1 XFEM degrees of freedom. 7.6.2 Time integration. 7.6.3 Simultaneous equations solver. 7.6.4 Crack length control. 7.7 POST-PROCESSING. 7.7.1 Stress intensity factor. 7.7.2 Crack growth. 7.7.3 Other applications. 7.8 CONFIGURATION UPDATE. References . Index