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Extended Finite Element Method

Book Description

Extended Finite Element Method provides an introduction to the extended finite element method (XFEM), a novel computational method which has been proposed to solve complex crack propagation problems. The book helps readers understand the method and make effective use of the XFEM code and software plugins now available to model and simulate these complex problems.

The book explores the governing equation behind XFEM, including level set method and enrichment shape function. The authors outline a new XFEM algorithm based on the continuum-based shell and consider numerous practical problems, including planar discontinuities, arbitrary crack propagation in shells and dynamic response in 3D composite materials.

  • Authored by an expert team from one of China's leading academic and research institutions
  • Offers complete coverage of XFEM, from fundamentals to applications, with numerous examples
  • Provides the understanding needed to effectively use the latest XFEM code and software tools to model and simulate dynamic crack problems

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