Extended Finite Element Method Theory and Applications [Hardcover]

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

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