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Introduces the theory and applications of the extended finite element method (XFEM) in the linear and nonlinear problems of continua, structures and geomechanics
* Explores the concept of partition of unity, various enrichment functions, and fundamentals of XFEM formulation.
* Covers numerous applications of XFEM including fracture mechanics, large deformation, plasticity, multiphase flow, hydraulic fracturing and contact problems
* Accompanied by a website hosting source code and examples
List of contents
Series Preface xv
Preface xvii
1 Introduction 1
1.1 Introduction 1
1.2 An Enriched Finite Element Method 3
1.3 A Review on X-FEM: Development and Applications 5
1.3.1 Coupling X-FEM with the Level-Set Method 6
1.3.2 Linear Elastic Fracture Mechanics (LEFM) 7
1.3.3 Cohesive Fracture Mechanics 11
1.3.4 Composite Materials and Material Inhomogeneities 14
1.3.5 Plasticity, Damage, and Fatigue Problems 16
1.3.6 Shear Band Localization 19
1.3.7 Fluid-Structure Interaction 19
1.3.8 Fluid Flow in Fractured Porous Media 20
1.3.9 Fluid Flow and Fluid Mechanics Problems 22
1.3.10 Phase Transition and Solidification 23
1.3.11 Thermal and Thermo-Mechanical Problems 24
1.3.12 Plates and Shells 24
1.3.13 Contact Problems 26
1.3.14 Topology Optimization 28
1.3.15 Piezoelectric and Magneto-Electroelastic Problems 28
1.3.16 Multi-Scale Modeling 29
2 Extended Finite Element Formulation 31
2.1 Introduction 31
2.2 The Partition of Unity Finite Element Method 33
2.3 The Enrichment of Approximation Space 35
2.3.1 Intrinsic Enrichment 35
2.3.2 Extrinsic Enrichment 36
2.4 The Basis of X-FEM Approximation 37
2.4.1 The Signed Distance Function 39
2.4.2 The Heaviside Function 43
2.5 Blending Elements 46
2.6 Governing Equation of a Body with Discontinuity 49
2.6.1 The Divergence Theorem for Discontinuous Problems 50
2.6.2 The Weak form of Governing Equation 51
2.7 The X-FEM Discretization of Governing Equation 53
2.7.1 Numerical Implementation of X-FEM Formulation 55
2.7.2 Numerical Integration Algorithm 57
2.8 Application of X-FEM in Weak and Strong Discontinuities 60
2.8.1 Modeling an Elastic Bar with a Strong Discontinuity 61
2.8.2 Modeling an Elastic Bar with a Weak Discontinuity 63
2.8.3 Modeling an Elastic Plate with a Crack Interface at its Center 66
2.8.4 Modeling an Elastic Plate with a Material Interface at its Center 68
2.9 Higher Order X-FEM 70
2.10 Implementation of X-FEM with Higher Order Elements 73
2.10.1 Higher Order X-FEM Modeling of a Plate with a Material Interface 73
2.10.2 Higher Order X-FEM Modeling of a Plate with a Curved Crack Interface 75
3 Enrichment Elements 77
3.1 Introduction 77
3.2 Tracking Moving Boundaries 78
3.3 Level Set Method 81
3.3.1 Numerical Implementation of LSM 82
3.3.2 Coupling the LSM with X-FEM 83
3.4 Fast Marching Method 85
3.4.1 Coupling the FMM with X-FEM 87
3.5 X-FEM Enrichment Functions 88
3.5.1 Bimaterials, Voids, and Inclusions 88
3.5.2 Strong Discontinuities and Crack Interfaces 91
3.5.3 Brittle Cracks 93
3.5.4 Cohesive Cracks 97
3.5.5 Plastic Fracture Mechanics 99
3.5.6 Multiple Cracks 101
3.5.7 Fracture in Bimaterial Problems 102
3.5.8 Polycrystalline Microstructure 106
3.5.9 Dislocations 111
3.5.10 Shear Band Localization 113
4 Blending Elements 119
4.1 Introduction 119
4.2 Convergence Analysis in the X-FEM 120
4.3 Ill-Conditioning in the X-FEM Method 124
4.3.1 One-Dimensional Problem with Material Interface 126
4.4 Blending Strategies in X-FEM 128
4.5 Enhanced Strain Method 130
4.5.1 An Enhanced Strain Blending Element for the Ramp Enrichment Function 132
About the author
Amir R. Khoei, Sharif University of Technology, Iran
Summary
Introduces the theory and applications of the extended finite element method (XFEM) in the linear and nonlinear problems of continua, structures and geomechanics * Explores the concept of partition of unity, various enrichment functions, and fundamentals of XFEM formulation.
