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E-raamat: Extended Finite Element Method - Theory and Applications: Theory and Applications [Wiley Online]

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Extended Finite Element Method - Theory and Applications: Theory and ApplicationsSuurem pilt
Teised raamatud teemal:
Wiley Online e-raamatudRohkem infot Wiley Online kohta
Raamatu kodulehekülg: https://onlinelibrary.wiley.com/doi/book/10.1002/9781118869673
Introduces the theory and applications of the extended finite element method (XFEM) in the linear and nonlinear problems of continua, structures and geomechanics. This title covers the theory and application of XFEM in large deformations, plasticity and contact problems.

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
Series Preface xv
Preface xvii
1 Introduction
1(30)
1.1 Introduction
1(2)
1.2 An Enriched Finite Element Method
3(2)
1.3 A Review on X-FEM: Development and Applications
5(26)
1.3.1 Coupling X-FEM with the Level-Set Method
6(1)
1.3.2 Linear Elastic Fracture Mechanics (LEFM)
7(4)
1.3.3 Cohesive Fracture Mechanics
11(3)
1.3.4 Composite Materials and Material Inhomogeneities
14(2)
1.3.5 Plasticity, Damage, and Fatigue Problems
16(3)
1.3.6 Shear Band Localization
19(1)
1.3.7 Fluid-Structure Interaction
19(1)
1.3.8 Fluid Flow in Fractured Porous Media
20(2)
1.3.9 Fluid Flow and Fluid Mechanics Problems
22(1)
1.3.10 Phase Transition and Solidification
23(1)
1.3.11 Thermal and Thermo-Mechanical Problems
24(1)
1.3.12 Plates and Shells
24(2)
1.3.13 Contact Problems
26(2)
1.3.14 Topology Optimization
28(1)
1.3.15 Piezoelectric and Magneto-Electroelastic Problems
28(1)
1.3.16 Multi-Scale Modeling
29(2)
2 Extended Finite Element Formulation
31(46)
2.1 Introduction
31(2)
2.2 The Partition of Unity Finite Element Method
33(2)
2.3 The Enrichment of Approximation Space
35(2)
2.3.1 Intrinsic Enrichment
35(1)
2.3.2 Extrinsic Enrichment
36(1)
2.4 The Basis of X-FEM Approximation
37(9)
2.4.7 The Signed Distance Function
39(4)
2.4.2 The Heaviside Function
43(3)
2.5 Blending Elements
46(3)
2.6 Governing Equation of a Body with Discontinuity
49(4)
2.6.1 The Divergence Theorem for Discontinuous Problems
50(1)
2.6.2 The Weak form of Governing Equation
51(2)
2.7 The X-FEM Discretization of Governing Equation
53(7)
2.7.1 Numerical Implementation of X-FEM Formulation
55(2)
2.7.2 Numerical Integration Algorithm
57(3)
2.8 Application of X-FEM in Weak and Strong Discontinuities
60(1)
2.8. 1 Modeling an Elastic Bar with a Strong Discontinuity
61(9)
2.8.2 Modeling an Elastic Bar with a Weak Discontinuity
63(3)
2.8.3 Modeling an Elastic Plate with a Crack Interface at its Center
66(2)
2.8.4 Modeling an Elastic Plate with a Material Interface at its Center
68(2)
2.9 Higher Order X-FEM
70(3)
2.10 Implementation of X-FEM with Higher Order Elements
73(4)
2.10.1 Higher Order X-FEM Modeling of a Plate with a Material Interface
73(2)
2.10.2 Higher Order X-FEM Modeling of a Plate with a Curved Crack Interface
75(2)
3 Enrichment Elements
77(42)
3.1 Introduction
77(1)
3.2 Tracking Moving Boundaries
78(3)
3.3 Level Set Method
81(4)
3.3.1 Numerical Implementation of LSM
82(1)
3.3.2 Coupling the LSM with X-FEM
83(2)
3.4 Fast Marching Method
85(3)
3.4.1 Coupling the FMM with X-FEM
87(1)
3.5 X-FEM Enrichment Functions
88(31)
3.5.1 Bimaterials, Voids, und Inclusions
88(3)
3.5.2 Strong Discontinuities and Crack Interfaces
91(2)
3.5.3 Brittle Cracks
93(4)
3.5.4 Cohesive Cracks
97(2)
3.5.5 Plastic Fracture Mechanics
99(2)
3.5.6 Multiple Cracks
101(1)
3.5.7 Fracture in Bimaterial Problems
102(4)
3.5.8 Polycrystalline Microstructure
106(5)
3.5.9 Dislocations
111(2)
3.5.10 Shear Band Localization
113(6)
4 Blending Elements
119(42)
4.1 Introduction
119(1)
4.2 Convergence Analysis in the X-FEM
120(4)
4.3 Ill-Conditioning in the X-FEM Method
124(4)
4.3.1 One-Dimensional Problem with Material Interface
126(2)
4.4 Blending Strategies in X-FEM
128(2)
4.5 Enhanced Strain Method
130(5)
4.5.1 An Enhanced Strain Blending Element for the Ramp Enrichment Function
132(2)
4.5.2 An Enhanced Strain Blending Element for Asymptotic Enrichment Functions
134(1)
4.6 The Hierarchical Method
135(3)
4.6.1 A Hierarchical Blending Element for Discontinuous Gradient Enrichment
135(2)
4.6.2 A Hierarchical Blending Element for Crack Tip Asymptotic Enrichments
137(1)
4.7 The Cutoff Function Method
138(5)
4.7.1 The Weighted Function Blending Method
140(2)
4.7.2 A Variant of the Cutoff Function Method
142(1)
4.8 A DG X-FEM Method
143(4)
4.9 Implementation of Some Optimal X-FEM Type Methods
147(4)
4.9.1 A Plate with a Circular Hole at Its Centre
148(1)
4.9.2 A Plate with a Horizontal Material Interface
149(2)
4.93 The Fiber Reinforced Concrete in Uniaxial Tension
151(3)
4.10 Pre-Conditioning Strategies in X-FEM
154(7)
4.10.1 Bechet's Pre-Conditioning Scheme
155(1)
4.10.2 Menk--Bordas Pre-Conditioning Scheme
156(5)
5 Large X-FEM Deformation
161(54)
5.1 Introduction
161(2)
5.2 Large FE Deformation
163(4)
5.3 The Lagrangian Large X-FEM Deformation Method
167(6)
5.3.1 The Enrichment of Displacement Field
167(3)
5.3.2 The Large X-FEM Deformation Formulation
170(2)
5.3.3 Numerical Integration Scheme
172(1)
5.4 Numerical Modeling of Large X-FEM Deformations
173(8)
5.4.1 Modeling an Axial Bar with a Weak Discontinuity
173(4)
5.4.2 Modeling a Plate with the Material Interface
177(4)
5.5 Application of X-FEM in Large Deformation Problems
181(11)
5.5.1 Die-Pressing with a Horizontal Material Interface
182(4)
5.5.2 Die-Pressing with a Rigid Central Core
186(2)
5.5.3 Closed-Die Pressing of a Shaped-Tablet Component
188(4)
5.6 The Extended Arbitrary Lagrangian--Eulerian FEM
192(16)
5.6.1 ALE Formulation
192(1)
5.6.1.1 Kinematics
193(1)
5.6.1.2 ALE Governing Equations
194(1)
5.6.2 The Weak Form of ALE Formulation
195(1)
5.6.3 The ALE FE Discretization
196(2)
5.6.4 The Uncoupled ALE Solution
198(1)
5.6.4.1 Material (Lagrangian) Phase
199(1)
5.6.4.2 Smoothing Phase
199(1)
5.6.4.3 Convection (Eulerian) Phase
200(2)
5.6.5 The X-ALE-FEM Computational Algorithm
202(1)
5.6.5.1 Level Set Update
203(1)
5.6.5.2 Stress Update with Sub-Triangular Numerical Integration
204(1)
5.6.5.3 Stress Update with Sub-Quadrilateral Numerical Integration
205(3)
5.7 Application of the X-ALE-FEM Model
208(7)
5.7.1 The Coining Test
208(1)
5.7.2 A Plate in Tension
209(6)
6 Contact Friction Modeling with X-FEM
215(52)
6.1 Introduction
215(1)
6.2 Continuum Model of Contact Friction
216(7)
6.2.7 Contact Conditions: The Kuhn--Tucker Rule
217(1)
6.2.2 Plasticity Theory of Friction
218(3)
6.2.3 Continuum Tangent Matrix of Contact Problem
221(2)
6.3 X-FEM Modeling of the Contact Problem
223(1)
6.3.1 The Gauss--Green Theorem for Discontinuous Problems
223(1)
6.12 The Weak Form of Governing Equation for a Contact Problem
224(3)
6.3.3 The Enrichment of Displacement Field
226(1)
6.4 Modeling of Contact Constraints via the Penalty Method
227(8)
6.4.1 Modeling of an Elastic Bar with a Discontinuity at Its Center
231(2)
6.4.2 Modeling of an Elastic Plate with a Discontinuity at Its Center
233(2)
6.5 Modeling of Contact Constraints via the Lagrange Multipliers Method
235(6)
6.5.7 Modeling the Discontinuity in an Elastic Bar
239(1)
6.5.2 Modeling the Discontinuity in an Elastic Plate
240(1)
6.6 Modeling of Contact Constraints via the Augmented-Lagrange Multipliers Method
241(5)
6.6.1 Modeling an Elastic Bar with a Discontinuity
244(1)
6.6.2 Modeling an Elastic Plate with a Discontinuity
245(1)
6.7 X-FEM Modeling of Large Sliding Contact Problems
246(5)
6.7.1 Large Sliding with Horizontal Material Interfaces
249(2)
6.8 Application of X-FEM Method in Frictional Contact Problems
251(16)
6.8.1 An Elastic Square Plate with Horizontal Interface
251(1)
6.8.1.1 Imposing the Unilateral Contact Constraint
252(3)
6.8.1.2 Modeling the Frictional Stick-Slip Behavior
255(1)
6.8.2 A Square Plate with an Inclined Crack
256(3)
6.8.3 A Double-Clamped Beam with a Central Crack
259(2)
6.8.4 A Rectangular Block with an S--Shaped Frictional Contact Interface
261(6)
7 Linear Fracture Mechanics with the X-FEM Technique
267(50)
7.1 Introduction
267(2)
7.2 The Basis of LEFM
269(7)
7.2.1 Energy Balance in Crack Propagation
270(1)
7.2.2 Displacement and Stress Fields at the Crack Tip Area
271(2)
7.2.3 The SIFs
273(3)
7.3 Governing Equations of a Cracked Body
276(7)
7.3.1 The Enrichment of Displacement Field
277(3)
7.3.2 Discretization of Governing Equations
280(3)
7.4 Mixed-Mode Crack Propagation Criteria
283(2)
7.4.1 The Maximum Circumferential Tensile Stress Criterion
283(1)
7.4.2 The Minimum Strain Energy Density Criterion
284(1)
7.4.3 The Maximum Energy Release Rate
284(1)
7.5 Crack Growth Simulation with X-FEM
285(5)
7.5.1 Numerical Integration Scheme
287(2)
7.5.2 Numerical Integration of Contour J---Integral
289(1)
7.6 Application of X-FEM in Linear Fracture Mechanics
290(14)
7.6.1 X-FEM Modeling of a DCB
290(4)
7.6.2 An Infinite Plate with a Finite Crack in Tension
294(4)
7.6.3 An Infinite Plate with an Inclined Crack
298(2)
7.6.4 A Plate with Two Holes and Multiple Cracks
300(4)
7.7 Curved Crack Modeling with X-FEM
304(5)
7.7.1 Modeling a Curved Center Crack in an Infinite Plate
307(2)
7.8 X-FEM Modeling of a Bimaterial Interface Crack
309(8)
7.8.1 The Interfacial Fracture Mechanics
310(1)
7.8.2 The Enrichment of the Displacement Field
311(3)
7.8.3 Modeling of a Center Crack in an Infinite Bimaterial Plate
314(3)
8 Cohesive Crack Growth with the X-FEM Technique
317(34)
8.1 Introduction
317(3)
8.2 Governing Equations of a Cracked Body
320(5)
8.2.1 The Enrichment of Displacement Field
322(1)
8.2.2 Discretization of Governing Equations
323(2)
8.3 Cohesive Crack Growth Based on the Stress Criterion
325(3)
8.3.1 Cohesive Constitutive Law
325(1)
8.3.2 Crack Growth Criterion and Crack Growth Direction
326(2)
8.3.3 Numerical Integration Scheme
328(1)
8.4 Cohesive Crack Growth Based on the SIF Criterion
328(6)
8.4.1 The Enrichment of Displacement Field
329(3)
8.4.2 The Condition for Smooth Crack Closing
332(1)
8.4.3 Crack Growth Criterion and Crack Growth Direction
332(2)
8.5 Cohesive Crack Growth Based on the Cohesive Segments Method
334(7)
8.5.1 The Enrichment of Displacement Field
334(1)
8.5.2 Cohesive Constitutive Law
335(1)
8.5.3 Crack Growth Criterion and Its Direction for Continuous Crack Propagation
336(3)
8.5.4 Crack Growth Criterion and Its Direction for Discontinuous Crack Propagation
339(2)
8.5.5 Numerical Integration Scheme
341(1)
8.6 Application of X-FEM Method in Cohesive Crack Growth
341(10)
8.6.1 A Three-Point Bending Beam with Symmetric Edge Crack
341(2)
8.6.2 A Plate with an Edge Crack under Impact Velocity
343(3)
8.6.3 A Three-Point Bending Beam with an Eccentric Crack
346(5)
9 Ductile Fracture Mechanics with a Damage-Plasticity Model in X-FEM
351(58)
9.1 Introduction
351(2)
9.2 Large FE Deformation Formulation
353(3)
9.3 Modified X-FEM Formulation
356(3)
9.4 Large X-FEM Deformation Formulation
359(5)
9.5 The Damage--Plasticity Model
364(4)
9.6 The Nonlocal Gradient Damage Plasticity
368(1)
9.7 Ductile Fracture with X-FEM Plasticity Model
369(3)
9.8 Ductile Fracture with X-FEM Non-Local Damage-Plasticity Model
372(8)
9.8.1 Crack Initiation and Crack Growth Direction
372(3)
9.8.2 Crack Growth with a Null Step Analysis
375(2)
9.8.3 Crack Growth with a Relaxation Phase Analysis
377(2)
9.8.4 Locking Issues in Crack Growth Modeling
379(1)
9.9 Application of X-FEM Damage-Plasticity Model
380(7)
9.9.1 The Necking Problem
380(3)
9.9.2 The CT Test
383(2)
9.9.3 The Double-Notched Specimen
385(2)
9.10 Dynamic Large X-FEM Deformation Formulation
387(6)
9.10.1 The Dynamic X-FEM Discretization
388(2)
9.10.2 The Large Strain Model
390(1)
9.10.3 The Contact Friction Model
391(2)
9.11 The Time Domain Discretization: The Dynamic Explicit Central Difference Method
393(3)
9.12 Implementation of Dynamic X-FEM Damage-Plasticity Model
396(13)
9.12.1 A Plate with an Inclined Crack
398(2)
9.12.2 The Low Cycle Fatigue Test
400(1)
9.12.3 The Cyclic CT Test
401(4)
9.12.4 The Double Notched Specimen in Cyclic Loading
405(4)
10 X-FEM Modeling of Saturated/Semi-Saturated Porous Media
409(52)
10.1 Introduction
409(5)
10.1.1 Governing Equations of Deformable Porous Media
411(3)
10.2 The X-FEM Formulation of Deformable Porous Media with Weak Discontinuities
414(8)
10.2.1 Approximation of Displacement and Pressure Fields
415(3)
10.2.2 The X-FEM Spatial Discretization
418(1)
10.2.3 The Time Domain Discretization and Solution Procedure
419(2)
10.2.4 Numerical Integration Scheme
421(1)
10.3 Application of the X-FEM Method in Deformable Porous Media with Arbitrary Interfaces
422(5)
10.3.1 An Elastic Soil Column
422(2)
10.3.2 An Elastic Foundation
424(3)
10.4 Modeling Hydraulic Fracture Propagation in Deformable Porous Media
427(7)
10.4.1 Governing Equations of a Fractured Porous Medium
428(2)
10.4.2 The Weak Formulation of a Fractured Porous Medium
430(4)
10.5 The X-FEM Formulation of Deformable Porous Media with Strong Discontinuities
434(8)
10.5.1 Approximation of the Displacement and Pressure Fields
434(3)
10.5.2 The X-FEM Spatial Discretization
437(1)
10.5.3 The Time Domain Discretization and Solution Procedure
438(4)
10.6 Alternative Approaches to Fluid Flow Simulation within the Fracture
442(3)
10.6.1 A Partitioned Solution Algorithm for Interfacial Pressure
442(2)
10.6.2 A Time-Dependent Constant Pressure Algorithm
444(1)
10.7 Application of the X-FEM Method in Hydraulic Fracture Propagation of Saturated Porous Media
445(10)
10.7.1 An Infinite Saturated Porous Medium with an Inclined Crack
446(3)
10.7.2 Hydraulic Fracture Propagation in an Infinite Poroelastic Medium
449(3)
10.7.3 Hydraulic Fracturing in a Concrete Gravity Dam
452(3)
10.8 X-FEM Modeling of Contact Behavior in Fractured Porous Media
455(6)
10.8.1 Contact Behavior in a Fractured Medium
455(1)
10.8.2 X-FEM Formulation of Contact along the Fracture
456(1)
10.8.3 Consolidation of a Porous Block with a Vertical Discontinuity
457(4)
11 Hydraulic Fracturing in Multi-Phase Porous Media with X-FEM
461(48)
11.1 Introduction
461(2)
11.2 The Physical Model of Multi-Phase Porous Media
463(2)
11.3 Governing Equations of Multi-Phase Porous Medium
465(2)
11.4 The X-FEM Formulation of Multi-Phase Porous Media with Weak Discontinuities
467(10)
11.4.1 Approximation of the Primary Variables
469(4)
11.4.2 Discretization of Equilibrium and Flow Continuity Equations
473(3)
11.4.3 Solution Procedure of Discretized Equilibrium Equations
476(1)
11.5 Application of X-FEM Method in Multi-Phase Porous Media with Arbitrary Interfaces
477(5)
11.6 The X-FEM Formulation for Hydraulic Fracturing in Multi-Phase Porous Media
482(5)
11.7 Discretization of Multi-Phase Governing Equations with Strong Discontinuities
487(6)
11.8 Solution Procedure for Fully Coupled Nonlinear Equations
493(4)
11.9 Computational Notes in Hydraulic Fracture Modeling
497(2)
11.10 Application of the X-FEM Method to Hydraulic Fracture Propagation of Multi-Phase Porous Media
499(10)
12 Thermo-Hydro-Mechanical Modeling of Porous Media with X-FEM
509(24)
12.1 Introduction
509(2)
12.2 THM Governing Equations of Saturated Porous Media
511(2)
12.3 Discontinuities in a THM Medium
513(1)
12.4 The X-FEM Formulation of THM Governing Equations
514(7)
12.4.1 Approximation of Displacement, Pressure, and Temperature Fields
515(2)
12.4.2 The X-FEM Spatial Discretization
517(3)
12.4.3 The Time Domain Discretization
520(1)
12.5 Application of the X-FEM Method to THM Behavior of Porous Media
521(12)
12.5.1 A Plate with an Inclined Crack in Thermal Loading
521(1)
12.5.2 A Plate with an Edge Crack in Thermal Loading
522(2)
12.5.3 An Impermeable Discontinuity in Saturated Porous Media
524(3)
12.5.4 An Inclined Fault in Porous Media
527(6)
References 533(24)
Index 557
Amir R. Khoei, Sharif University of Technology, Iran
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