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
Chapter
1.2 INTRODUCTION TO X-FEM
1.3 RESEARCH STATUS AND DEVELOPMENT OF X-FEM
1.4 ORGANIZATION OF THIS BOOK
Chapter 2 - Fundamental Linear Elastic Fracture Mechanics
2.2 TWO-DIMENSIONAL LINEAR ELASTIC FRACTURE MECHANICS
2.3 MATERIAL FRACTURE TOUGHNESS
2.4 FRACTURE CRITERION OF LINEAR ELASTIC MATERIAL
2.5 COMPLEX FRACTURE CRITERION
Chapter 3 - Dynamic Crack Propagation
3.1 INTRODUCTION TO DYNAMIC FRACTURE MECHANICS
3.2 LINEAR ELASTIC DYNAMIC FRACTURE THEORY
3.3 CRACK DRIVING FORCE COMPUTATION
3.4 CRACK PROPAGATION IN STEADY STATE
3.5 ENGINEERING APPLICATIONS OF DYNAMIC FRACTURE MECHANICS
Chapter 4 - Fundamental Concept and Formula of X-FEM
4.1 X-FEM BASED ON THE PARTITION OF UNITY
4.3 ENRICHED SHAPE FUNCTION
4.4 GOVERNING EQUATION AND WEAK FORM
4.5 INTEGRATION ON SPATIAL DISCONTINUITY FIELD
4.6 TIME INTEGRATION AND LUMPED MASS MATRIX
4.7 POSTPROCESSING DEMONSTRATION
4.8 ONE-DIMENSIONAL X-FEM
Chapter 5 - Numerical Study of Two-Dimensional Fracture Problems with X-FEM
5.1 NUMERICAL STUDY AND PRECISION ANALYSIS OF X-FEM
5.2 TWO-DIMENSIONAL HIGH-ORDER X-FEM
5.3 CRACK BRANCHING SIMULATION
Chapter 6 - X-FEM on Continuum-Based Shell Elements
6.2 OVERVIEW OF PLATE AND SHELL FRACTURE MECHANICS
6.3 PLATE AND SHELL THEORY APPLIED IN FINITE ELEMENT ANALYSIS
6.4 BRIEF INTRODUCTION TO GENERAL SHELL ELEMENTS
6.5 X-FEM ON CB SHELL ELEMENTS
6.6 CRACK PROPAGATION CRITERION
Chapter 7 - Subinterfacial Crack Growth in Bimaterials
7.2 THEORETICAL SOLUTIONS OF SUBINTERFACIAL FRACTURE
7.3 SIMULATION OF SUBINTERFACIAL CRACKS BASED ON X-FEM
7.4 EQUILIBRIUM STATE OF SUBINTERFACIAL MODE I CRACKS
7.5 EFFECT ON SUBINTERFACIAL CRACK GROWTH FROM A TILTED INTERFACE
Chapter 8 - X-FEM Modeling of Polymer Matrix Particulate/Fibrous Composites
8.2 LEVEL SET METHOD FOR COMPOSITE MATERIALS
8.3 MICROSTRUCTURE GENERATION
8.4 MATERIAL CONSTITUTIVE MODEL
Chapter 9 - X-FEM Simulation of Two-Phase Flows
9.1 GOVERNING EQUATIONS AND INTERFACIAL CONDITIONS
9.2 INTERFACIAL DESCRIPTION OF TWO-PHASE FLOWS
9.3 X-FEM AND UNKNOWN PARAMETERS DISCRETIZATION
9.4 DISCRETIZATION OF GOVERNING EQUATIONS
9.5 NUMERICAL INTEGRAL METHOD
9.6 EXAMPLES AND ANALYSES
Chapter 10 - Research Progress and Challenges of X-FEM
10.1 RESEARCH ON MICRO-SCALE CRYSTAL PLASTICITY
10.2 APPLICATION OF MULTI-SCALE SIMULATION
10.3 MODELING OF DEFORMATION LOCALIZATION
Appendix A - Westergaard Stress Function Method
A.1. PLANE PROBLEM AND ANTIPLANE SHEAR PROBLEM IN LINEAR ELASTIC MECHANICS
A.2. COMPLEX VARIABLE STRESS FUNCTION
A.3. WESTERGAARD STRESS FUNCTION
A.4. ESSENTIAL FRACTURE PROBLEMS
Appendix B - J Integration
B.1 PHYSICAL SIGNIFICANCE OF THE J INTEGRAL
B.2 ROUTE INDEPENDENCE OF THE J INTEGRAL
B.3 ENERGY EXPLANATION OF THE J INTEGRAL
B.4 CRACK INITIATION CRITERION OF THE J INTEGRAL
Extended Finite Element Method
：Tsinghua University Press Computational Mechanics Series
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