Computational Plasticity (eBook)

Table of Contents 6
Preface 8
Chapter 1 10
A Multi-Scale Continuum Theory for Heterogeneous Materials 10
1 Multi-Physics Multi-Scale Material Model 10
1.1 Kinematics and Virtual Power 10
1.2 Constitutive Relation 11
2 Application to Porous metals 11
2.1 Multi-Scale Model 12
2.2 Constitutive Relation 13
2.3 Numerical Results 13
3 Three-scale Model of High-Strength Steels 15
3.1 Multi-Scale Model 15
3.2 Constitutive Relation 16
3.3 Numerical Results 17
4 Conclusion 18
Acknowledgements 19
References 19
Chapter 2 21
Towards a Model for Large Strain Anisotropic Elasto-Plasticity 21
1 Introduction 21
2 Kinematics and Incremental Integrations 23
2.1 Kinematics of Deformation: Multiplicative Decomposition and Strain Rate Tensors 23
2.2 Integration of the Plastic Deformation Gradient 24
2.3 Rotationally-Frozen Configuration 26
3 Free Energy Function and Dissipation Inequality 27
3.1 Stored Energy Function: Orthotropic Hyperelasticity Based on Logarithmic Strain Measures 27
3.2 Hardening Potential 30
4 Mapping Tensors from Quadratic to Logarithmic Strain Space 32
5 Dissipation Inequality 34
6 Yield Functions 36
6.1 Yield Function for the Symmetric Part 37
6.2 Yield Function for the Skew Part 37
6.3 Coupling of Symmetric and Skew Parts 38
7 Numerical Example 38
8 Conclusions 39
References 42
Chapter 3 45
Localized and Diffuse Bifurcations in Porous Rocks Undergoing Shear Localization and Cataclastic Flow 45
1 Introduction 45
2 Shear Localization 48
2.1 E-mode for Shear Localization 48
2.2 Constitutive Branching for Shear Localization 50
3 Cataclastic Flow 54
3.1 E-mode for Cataclastic Flow 54
3.2 Constitutive Branching for Cataclastic Flow 56
4 Transient Plastic Flow 57
4.1 Slip Weakening 58
4.2 Cataclastic Flow 58
5 Closure 59
Acknowledgements 59
References 59
Chapter 4 62
Dispersion and Localisation in a Strain–Softening Two–Phase Medium 62
1 Introduction 62
2 Governing Equations 63
3 Reduction of the Governing Equations 66
4 Dispersion Analysis 67
5 Numerical Examples 69
6 Concluding Remarks 71
References 72
Chapter 5 74
New Developments in Surface-to-Surface Discretization Strategies for Analysis of Interface Mechanics 74
1 Introduction 74
2 Background: Mortar Projection in Contact Mechanics 75
2.1 The Mesh Tying Problem 75
2.2 Generalization to Sliding Contact 78
3 An Extension of the Framework: Mortar-Based Self-Contact 81
4 Mortar Formulation of Lubricated Contact 88
5 Conclusion 91
Acknowledgment 92
References 92
Chapter 6 94
Particle Finite Element Methods in Solid Mechanics Problems 94
1 Introduction 94
2 Fundamentals: The Particle Finite Element Method 95
2.1 Equations of Motion. Boundary Value Problem 95
2.2 Time Marching Scheme 97
3 Contact Strategy: Anticipating Interface Mesh 99
3.1 A Penalty Strategy at the Contact Interface 100
4 Representative Examples 103
4.1 Flexible Spring with Multiple Self-contacts 103
4.2 Riveting Process 105
4.3 Machining Process 107
4.4 Powder Filling Process 107
5 Concluding Remarks 108
Acknowledgements 109
References 109
Chapter 7 111
Micro-Meso-Macro Modelling of Composite Materials 111
1 Introduction 112
2 Micro-structure of Hardened Cement Paste (hcp) 113
3 Constitutive Equations 115
4 Homogenization 118
5 Parameter Identification 120
6 Thermo-mechanical Coupling 122
7 Outlook 126
Acknowledgments 127
References 128
Chapter 8 129
Numerical Modeling of Transient Impact Processes with Large Deformations and Nonlinear Material Behavior 129
1 Introduction 129
2 Class of Problems 130
3 Adaptive Remeshing 130
3.1 Mesh Quality Check 130
3.2 Error Assessment and Mesh Density Distribution 130
Gradient-Based Indicators 131
Local Quantity Indicators 132
Geometric Indicator 133
Selection of Indicators and Final Mesh Density Distribution 133
3.3 Mesh Generation 134
3.4 Transfer of State Variables 135
4 Constitutive Modeling 135
4.1 Metals 135
4.2 Geomaterials 137
Characterization of Geomaterials Under Impact Loading 137
Modified Drucker-Prager-Cap Model 138
Powderization Under High Pressure 140
5 Numerical Examples 143
5.1 Adaptive Computations 143
Taylor Bar Impact 143
High-Strain Rate Compression of WHA Block 145
Penetration of a Steel Cylinder by WHA Long Rod 145
5.2 Geomechanical computations 146
Quasi-Static Tests 146
Triple Impact on Microconcrete 146
Dynamic Compaction of Powder 147
6 Conclusion 148
References 149
Chapter 9 151
A Computational Model For Viscoplasticity Coupled with Damage Including Unilateral Effects 151
1 Introduction 151
2 Elasto-Viscoplastic Damage Constitutive Model 153
2.1 Viscoplastic Model 153
2.2 Concept of Effective Stress 154
2.3 Elasto-Viscoplasticity Coupled with Damage 155
2.4 Damage Evolution Law 156
3 Integration Algorithm 158
3.1 Single-Equation Corrector 160
3.2 Consistent Tangent Operator 163
4 Accuracy Analysis of the Integration Algorithm 165
5 Concluding Remarks 169
References 169
Chapter 10 171
On Multiscale Analysis of Heterogeneous Composite Materials: Implementation of Micro-to-Macro Transitions in the Finite Element Setting 171
1 Introduction 171
2 Continuum Model at Small Strains 172
2.1 Preliminaries 172
2.2 Basic Microvariables 173
2.3 Basic Macrovariables and Averaging Theorem 173
The Hill-Mandel Principle 174
2.4 Definition of the Boundary Conditions for the Small Scale 174
Linear displacements on the boundary 175
Periodic deformation and antiperiodic traction on the boundary 175
3 Discretised Model at Small Strains 176
3.1 Introduction 176
3.2 Displacement Field Partition and Matrix Notation 177
3.3 Discretised Micro-equilibrium State and Solution Procedure 177
3.4 General Average Stress and Overall Tangent Modulus Computation 178
Average Stress Computation 178
Overall Tangent Modulus Computation 178
3.5 Linear Displacements on the Boundary Assumption 179
Partitioning of Algebraic Equations 179
Linear Displacement 180
Tangent Modulus of Linear Displacements on the Boundary Constraint 180
3.6 Periodic Displacements and Antiperiodic Traction on the Boundary 181
Partitioning of Algebraic Equations 181
Periodic Displacements and Antiperiodic Tractions 182
Tangent Modulus of Periodic Displacements and Antiperiodic Traction on the Boundary Constraints 182
4 Numerical Examples 183
4.1 Study of the Effect of Topology of Cavities on the Properties of the RVE 183
Problem Specifications 183
Analysis Approach 184
Study of the Regular Cavity Model 184
The RVE with Randomly Generated Voids 185
4.2 Two-scale Analysis of Stretching of an Elasto-plastic Perforated Plate 186
Single-scale Analysis 188
Two-scale Analysis 188
5 Conclusions 189
References 190
Chapter 11 192
Assessment of Protection Systems for Gravel-Buried Pipelines Considering Impact and Recurrent Shear Loading Caused by Thermal Deformations of the Pipe 192
Introduction 192
1 Protection Systems for Gravel-Buried Pipelines Subjected to Rockfall 192
1.1 Development of a Structural Model 193
Geometric Dimensions of the Considered Problem 193
Impact Scenario and Mode of Analysis 193
Estimates of the Maximum Impact Force and the Penetration Depth at Maximum Impact Force 194
Computation of the Distribution of Stresses Corresponding to the Maximum Impact Force 195
Material Modeling of Steel, Gravel and Sand 195
Parameter Identification 197
1.2 Validation of the Developed Structural Model 197
Real-scale Impact Experiment 197
Comparison between Model-predicted and Experimentally Determined Stress Distribution in the Steel Pipe 198
1.3 Prognoses of Structural Behavior 199
Prognoses Considering a Change of the Boundary Conditions 199
Prognoses Considering a Change of the Structural Dimensions 200
Prognoses Considering a Change of the Boundary Conditions and of the Structural Dimensions 200
1.4 Assessment of an Enhanced Protection System Consisting of Gravel and, Additionally, of Buried Load-Carrying Structural Elements 200
Buried Steel Plate Resting on Concrete Walls 201
Assessment of the Enhanced Protection System 202
1.5 Conclusions 202
2 Protection Systems Against Abrasive Shear Loading Caused by Thermal Deformation of Soil-Covered Pipelines 203
2.1 Assessment of Static Forces Exerted by Single Stone Tips onto Soil-Covered Pipelines 203
Loading Scenario 203
Structural Model 203
Finite Element Simulation 205
Relevant Forces of Tips of Single Stone Acting on Soil-covered Pipelines, as a Function of the Pipe Diameter 205
2.2 Identification of Wear Protection Strategies 205
Archard’s Wear Law 205
Protection Performance of Geosynthetics 208
Effective Means of Protection 209
2.3 Conclusions 209
References 210
Chapter 12 212
Enriched Free Mesh Method: An Accuracy Improvement for Node-based FEM 212
1 Introduction 212
2 Basic Concept of Free Mesh Method (FMM) 213
3 Enriched Free Mesh Method (EFMM) 215
3.1 Outline of EFMM 215
3.2 EFMM Based on the Localized Least Square Method 215
3.3 EFMM Based on Hellinger-Reissner Principle 217
4 Examples 218
4.1 Convergence Study: Displacement 218
4.2 Convergence Study: Error Norms 219
4.3 Patch Test 221
5 Concluding remarks 223
References 223
Chapter 13 225
Modelling of Metal Forming Processes and Multi-Physic Coupling 225
1 Introduction 225
2 Mechanical Approach of Metal Forming Processes 226
2.1 Constitutive Modeling 226
2.2 Finite Element Approximation 227
2.3 Numerical Issues 228
3 Thermal and Fluid-Solid Coupling 228
3.1 Classical Thermal and Mechanical Coupling 228
3.2 Localization 230
3.3 Fluid Solid Coupling During Heating or Heat Treatment 230
4 Electro Magnetic Coupling 230
4.1 The Induction Heating Process 230
4.2 The Direct Electro-Thermal Formulation 231
4.3 Finite Element Numerical Approximation 233
4.4 The Electromagnetic/Thermal Coupling Procedure 234
4.5 Results 235
5 Coupling with Microstructure Evolution 238
5.1 Introduction 238
5.2 Macroscopic Approach 239
5.3 Multi-Scale Coupling and the Digital Material 239
6 Conclusions 241
References 242
Chapter 14 243
Enhanced Rotation-Free Basic Shell Triangle. Applications to Sheet Metal Forming 243
1 Introduction 243
2 Basic Thin Shell Equations Using a Total Lagrangian Formulation 245
2.1 Shell Kinematics 245
2.2 Constitutive Models 247
3 Enhanced Basic Shell Triangle 249
3.1 Definition of the Element Geometry and Computation of Membrane Strains 249
3.2 Computation of Curvatures 251
3.3 The EBST1 Element 253
4 Boundary Conditions 254
5 Explicit Solution Scheme 255
6 Example 1. Cylindrical Panel under Impulse Loading 256
7 Application to Sheet Metal Forming Problems 259
7.1 S-rail Sheet Stamping 259
7.2 Stamping of Industrial Automotive Part 261
8 Concluding Remarks 262
Acknowledgements 266
References 267