Extended Finite Element Method

Table of contents

1. Cover image
2. Title page
3. Table of Contents
4. Copyright
5. Preface
6. Chapter 1. Overview of Extended Finite Element Method
   1. 1.1. Significance of Studying Computational Fracture Mechanics
   2. 1.2. Introduction to X-FEM
   3. 1.3. Research Status and Development of X-FEM
   4. 1.4. Organization of this Book
7. Chapter 2. Fundamental Linear Elastic Fracture Mechanics
   1. 2.1. Introduction
   2. 2.2. Two-Dimensional Linear Elastic Fracture Mechanics
   3. 2.3. Material Fracture Toughness
   4. 2.4. Fracture Criterion of Linear Elastic Material
   5. 2.5. Complex Fracture Criterion
   6. 2.6. Interaction Integral
   7. 2.7. Summary
8. Chapter 3. Dynamic Crack Propagation
   1. 3.1. Introduction to Dynamic Fracture Mechanics
   2. 3.2. Linear Elastic Dynamic Fracture Theory
   3. 3.3. Crack Driving Force Computation
   4. 3.4. Crack Propagation in Steady State
   5. 3.5. Engineering Applications of Dynamic Fracture Mechanics
   6. 3.6. Summary
9. Chapter 4. Fundamental Concept and Formula of X-FEM
   1. 4.1. X-FEM Based on the Partition of Unity
   2. 4.2. Level Set Method
   3. 4.3. Enriched Shape Function
   4. 4.4. Governing Equation and Weak Form
   5. 4.5. Integration on Spatial Discontinuity Field
   6. 4.6. Time Integration and Lumped Mass Matrix
   7. 4.7. Postprocessing Demonstration
   8. 4.8. One-Dimensional X-FEM
   9. 4.9. Summary
10. Chapter 5. Numerical Study of Two-Dimensional Fracture Problems with X-FEM
    1. 5.1. Numerical Study and Precision Analysis of X-FEM
    2. 5.2. Two-Dimensional High-Order X-FEM
    3. 5.3. Crack Branching Simulation
    4. 5.4. Summary
11. Chapter 6. X-FEM on Continuum-Based Shell Elements
    1. 6.1. Introduction
    2. 6.2. Overview of Plate and Shell Fracture Mechanics
    3. 6.3. Plate and Shell Theory Applied In Finite Element Analysis
    4. 6.4. Brief Introduction to General Shell Elements
    5. 6.5. X-FEM on CB Shell Elements
    6. 6.6. Crack Propagation Criterion
    7. 6.7. Numerical Examples
    8. 6.8. Summary
12. Chapter 7. Subinterfacial Crack Growth in Bimaterials
    1. 7.1. Introduction
    2. 7.2. Theoretical Solutions of Subinterfacial Fracture
    3. 7.3. Simulation of Subinterfacial Cracks Based On X-FEM
    4. 7.4. Equilibrium State of Subinterfacial Mode I Cracks
    5. 7.5. Effect on Subinterfacial Crack Growth from a Tilted Interface
    6. 7.6. Summary
13. Chapter 8. X-FEM Modeling of Polymer Matrix Particulate/Fibrous Composites
    1. 8.1. Introduction
    2. 8.2. Level Set Method for Composite Materials
    3. 8.3. Microstructure Generation
    4. 8.4. Material Constitutive Model
    5. 8.5. Numerical Examples
    6. 8.6. Summary
14. Chapter 9. X-FEM Simulation of Two-Phase Flows
    1. 9.1. Governing Equations and Interfacial Conditions
    2. 9.2. Interfacial Description of Two-Phase Flows
    3. 9.3. X-FEM and Unknown Parameters Discretization
    4. 9.4. Discretization of Governing Equations
    5. 9.5. Numerical Integral Method
    6. 9.6. Examples and Analyses
    7. 9.7. Summary
15. Chapter 10. Research Progress and Challenges of X-FEM
    1. 10.1. Research on Micro-Scale Crystal Plasticity
    2. 10.2. Application of Multi-Scale Simulation
    3. 10.3. Modeling of Deformation Localization
    4. 10.4. Summary
16. Appendix A: Westergaard Stress Function Method
17. Appendix B: J Integration
18. References
19. Index