Stéphane Bordas, Alexander Menk

Partition of Unity Methods

• Gebundenes Buch

Produktbeschreibung

First book to offer a guide to the foundations of the XFEM and its implementation
A revolution similar to that initiated by the FEM is taking place through the XFEM, which is already implemented in leading commercial packages (ABAQUS, ANSYS, etc.) that are taught at undergraduate and post-graduate levels and to industrial end-users.

XFEM provides a detailed overview of the basics around the newly introduced extended finite element method for applications in solving moving boundary problems. XFEM is introduced naturally as an extension of FEM, through simple one dimensional examples which then allow the introduction of higher-dimensional problems. Throughout the book, each key concept is highlighted by the corresponding piece of MATLAB code which is provided via an accompanying web portal. Uniquely, this portal allows readers to obtain real-time feedback and help from an existing community of more than 130 researchers and industrialists.

Demystifies the theory behind XFEM and makes it accessible to all with previous knowledge of the FEM
Provides a simple introduction to XFEM but also provides a range of tools which the reader can build upon to take on a large breadth of more complex problems.
Presents each key theoretical concept in parallel with its implementational aspects in the form of simple MATLAB routines provided along with the book via an interactive companion website and portal
Provides a detailed account of applications of XFEM to fracture mechanics, including techniques absent from current literature

Produktdetails

• Verlag: Wiley & Sons
• 1. Auflage
• Seitenzahl: 368
• Erscheinungstermin: 16. Oktober 2023
• Englisch
• Abmessung: 260mm x 208mm x 24mm
• Gewicht: 1009g
• ISBN-13: 9780470667088
• ISBN-10: 0470667087
• Artikelnr.: 39373332

Autorenporträt

Stéphane P. A. Bordas is a Professor in Computational Mechanics and earned his PhD from Northwestern University, USA, in 2004. He has published over 200 papers in unfitted simulation of free boundary problems and data driven modelling of complex systems. He has supervised over 30 PhD students and is Editor- in-Chief of Advances in Applied Mechanics. Alexander Menk is employed by Bosch GmbH. He is a PhD graduate from Glasgow University, UK, supervised by Prof. Bordas. His contributions range from automatic numerically determined enrichment to preconditioners for extended finite element methods for fracture. Sundararajan Natarajan has been a Professor of Computational Mechanics since 2014 and earned his PhD from Cardiff University, UK, supervised by Prof. Bordas and Prof. Kerfriden. He has made strong contributions to a number of methods on unfitted methods for free boundary problems, in particular on numerical integration and strain smoothing.

Inhaltsangabe

List of Contributors xi Preface xiii Acknowledgments xv 1 Introduction 1
1.1 The Finite Element Method 2 1.2 Suitability of the Finite Element
Method 9 1.3 Some Limitations of the FEM 11 1.4 The Idea of Enrichment 16
1.5 Conclusions 19 2 A Step-by-Step Introduction to Enrichment 23 2.1
History of Enrichment for Singularities and Localized Gradients 25 2.2 Weak
Discontinuities for One-dimensional Problems 38 2.3 Strong Discontinuities
for One-dimensional Problem 58 2.4 Conclusions 61 3 Partition of Unity
Revisited 67 3.1 Completeness, Consistency, and Reproducing Conditions 67
3.2 Partition of Unity 68 3.3 Enrichment 69 3.4 Numerical Examples 86 3.5
Conclusions 95 4 Advanced Topics 99 4.1 Size of the Enrichment Zone 99 4.2
Numerical Integration 100 4.3 Blending Elements and Corrections 108 4.4
Preconditioning Techniques 116 5 Applications 125 5.1 Linear Elastic
Fracture in Two Dimensions with XFEM 125 5.2 Numerical Enrichment for
Anisotropic Linear Elastic Fracture Mechanics 130 5.3 Creep and Crack
Growth in Polycrystals 133 5.4 Fatigue Crack Growth Simulations 138 5.5
Rectangular Plate with an Inclined Crack Subjected to Thermo-Mechanical
Loading 140 6 Recovery-Based Error Estimation and Bounding in XFEM 145 6.1
Introduction 145 6.2 Error Estimation in the Energy Norm. The ZZ Error
Estimator 147 6.3 Recovery-based Error Estimation in XFEM 151 6.4 Recovery
Techniques in Error Bounding. Practical Error Bounds. 174 6.5 Error
Estimation in Quantities of Interest 179 7 Phi-FEM: An Efficient Simulation
Tool Using Simple Meshes for Problems in Structure Mechanics and Heat
Transfer 191 7.1 Introduction 191 7.2 Linear Elasticity 194 7.3 Linear
Elasticity with Multiple Materials 204 7.4 Linear Elasticity with Cracks
208 7.5 Heat Equation 212 7.6 Conclusions and Perspectives 214 8 eXtended
Boundary Element Method (XBEM) for Fracture Mechanics and Wave Problems 217
8.1 Introduction 217 8.2 Conventional BEM Formulation 218 8.3 Shortcomings
of the Conventional Formulations 226 8.4 Partition of Unity BEM Formulation
228 8.5 XBEM for Accurate Fracture Analysis 228 8.6 XBEM for ShortWave
Simulation 235 8.7 Conditioning and its Control 243 8.8 Conclusions 245 9
Combined Extended Finite Element and Level Set Method (XFE-LSM) for Free
Boundary Problems 249 9.1 Motivation 249 9.2 The Level Set Method 250 9.3
Biofilm Evolution 256 9.4 Conclusion 269 10 XFEM for 3D Fracture Simulation
273 10.1 Introduction 273 10.2 Governing Equations 274 10.3 XFEM Enrichment
Approximation 275 10.4 Vector Level Set 280 10.5 Computation of Stress
Intensity Factor 282 10.6 Numerical Simulations 288 10.7 Summary 300 11
XFEM Modeling of Cracked Elastic-Plastic Solids 303 11.1 Introduction 303
11.2 Conventional von Mises Plasticity 303 11.3 Strain Gradient Plasticity
312 11.4 Conclusions 323 12 An Introduction to Multiscale analysis with
XFEM 329 12.1 Introduction 329 12.2 Molecular Statics 330 12.3 Hierarchical
Multiscale Models of Elastic Behavior -- The Cauchy-Born Rule 336 12.4
Current Multiscale Analysis -- The Bridging Domain Method 338 12.5 The
eXtended Bridging Domain Method 340 References 344 Index 345