Discontinuum Mechanics: Using Finite and Discrete Elements

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Designed mainly for postgraduate students and researchers, this volume introduces the mathematical and computational concepts of contact mechanics which are increasingly used in this sometimes difficult field and highlights the main problems encountered when dealing with the highly complex phenomena of discontinuum mechanics.
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Product Details

  • ISBN-13: 9781853129599
  • Publisher: WIT Press
  • Publication date: 1/1/2003
  • Edition description: with CD-ROM
  • Pages: 328
  • Product dimensions: 6.10 (w) x 9.10 (h) x 1.00 (d)

Table of Contents

Ch. 1 Introduction 1
1.1 Discontinuum Mechanics, Why? 1
1.2 Alternative Approaches 6
1.3 Scope of the Book 8
1.4 Notations 9
Ch. 2 Discontinuum Mechanics - A Review 11
2.1 Geomechanical Applications 12
2.2 Granular Materials 20
2.3 Impact Analysis (Progressive Fracturing) 21
2.4 Particulate Flow 32
2.5 Other Applications 34
Ch. 3 Constraint Enforcing Methods 35
3.1 Introduction 35
3.2 Definition of a Constraint 35
3.3 Constraint Enforcement 40
3.4 Variational Forms 56
3.5 The Penalty Method 58
Ch. 4 Nonlinear FE Discretization 69
4.1 Introduction 69
4.2 Large Deformation Kinematics 69
4.3 Initial/Boundary Value Problem 80
4.4 Finite Element Discretization 85
4.5 Explicit Time Integration 87
Ch. 5 Normal Contact 93
5.1 Introduction 93
5.2 Hydrocode Formulation 94
5.3 DYNA Penalty Formulation 104
5.4 2D Node to Edge Penalty Contact 108
5.5 Edge to Edge Contact 118
Ch. 6 Frictional Contact 121
6.1 Introduction 121
6.2 Frictional Contact - The Basics 121
6.3 2D Frictional Contact Models Without Hardening 135
6.4 3D Frictional Contact Models Without Hardening 147
6.5 3D Frictional Contact Models With Frictional Hardening 155
6.6 Node to Face Frictional Contact Models 166
Ch. 7 Discontinuum Contact Mechanics 181
7.1 Introduction 181
7.2 Contact Detection 185
7.3 Object Representation 221
Ch. 8 Remeshing Techniques 245
8.1 Introduction 245
8.2 Mesh Dependency 246
8.3 Fracture Mechanics 247
8.4 Strain Softening Models 249
8.5 Damage Mechanics 253
8.6 Anisotropic Material Models 258
8.7 Localization and Crack Direction 267
8.8 Remeshing Algorithm 276
App. A UTDem code 279
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