Computational Plasticity

Cover......Page 1
Computational Plasticity (Springer, 2007)......Page 4
ISBN 978-1-4020-6576-7......Page 5
Table of Contents......Page 6
Preface......Page 8
1.1 Kinematics and Virtual Power......Page 10
2 Application to Porous metals......Page 11
2.1 Multi-Scale Model......Page 12
2.3 Numerical Results......Page 13
3.1 Multi-Scale Model......Page 15
3.2 Constitutive Relation......Page 16
3.3 Numerical Results......Page 17
4 Conclusion......Page 18
References......Page 19
1 Introduction......Page 21
2.1 Kinematics of Deformation: Multiplicative Decomposition and Strain Rate Tensors......Page 23
2.2 Integration of the Plastic Deformation Gradient......Page 24
2.3 Rotationally-Frozen Configuration......Page 26
3.1 Stored Energy Function: Orthotropic Hyperelasticity Based on Logarithmic Strain Measures......Page 27
3.2 Hardening Potential......Page 30
4 Mapping Tensors from Quadratic to Logarithmic Strain Space......Page 32
5 Dissipation Inequality......Page 34
6 Yield Functions......Page 36
6.2 Yield Function for the Skew Part......Page 37
7 Numerical Example......Page 38
8 Conclusions......Page 39
References......Page 42
1 Introduction......Page 45
2.1 E-mode for Shear Localization......Page 48
2.2 Constitutive Branching for Shear Localization......Page 50
3.1 E-mode for Cataclastic Flow......Page 54
3.2 Constitutive Branching for Cataclastic Flow......Page 56
4 Transient Plastic Flow......Page 57
4.2 Cataclastic Flow......Page 58
References......Page 59
1 Introduction......Page 62
2 Governing Equations......Page 63
3 Reduction of the Governing Equations......Page 66
4 Dispersion Analysis......Page 67
5 Numerical Examples......Page 69
6 Concluding Remarks......Page 71
References......Page 72
1 Introduction......Page 74
2.1 The Mesh Tying Problem......Page 75
2.2 Generalization to Sliding Contact......Page 78
3 An Extension of the Framework: Mortar-Based Self-Contact......Page 81
4 Mortar Formulation of Lubricated Contact......Page 88
5 Conclusion......Page 91
References......Page 92
1 Introduction......Page 94
2.1 Equations of Motion. Boundary Value Problem......Page 95
2.2 Time Marching Scheme......Page 97
3 Contact Strategy: Anticipating Interface Mesh......Page 99
3.1 A Penalty Strategy at the Contact Interface......Page 100
4.1 Flexible Spring with Multiple Self-contacts......Page 103
4.2 Riveting Process......Page 105
4.4 Powder Filling Process......Page 107
5 Concluding Remarks......Page 108
References......Page 109
Micro-Meso-Macro Modelling of Composite Materials......Page 111
1 Introduction......Page 112
2 Micro-structure of Hardened Cement Paste (hcp)......Page 113
3 Constitutive Equations......Page 115
4 Homogenization......Page 118
5 Parameter Identification......Page 120
6 Thermo-mechanical Coupling......Page 122
7 Outlook......Page 126
Acknowledgments......Page 127
References......Page 128
1 Introduction......Page 129
3.2 Error Assessment and Mesh Density Distribution......Page 130
Gradient-Based Indicators......Page 131
Local Quantity Indicators......Page 132
Selection of Indicators and Final Mesh Density Distribution......Page 133
3.3 Mesh Generation......Page 134
4.1 Metals......Page 135
Characterization of Geomaterials Under Impact Loading......Page 137
Modified Drucker-Prager-Cap Model......Page 138
Powderization Under High Pressure......Page 140
Taylor Bar Impact......Page 143
Penetration of a Steel Cylinder by WHA Long Rod......Page 145
Triple Impact on Microconcrete......Page 146
Dynamic Compaction of Powder......Page 147
6 Conclusion......Page 148
References......Page 149
1 Introduction......Page 151
2.1 Viscoplastic Model......Page 153
2.2 Concept of Effective Stress......Page 154
2.3 Elasto-Viscoplasticity Coupled with Damage......Page 155
2.4 Damage Evolution Law......Page 156
3 Integration Algorithm......Page 158
3.1 Single-Equation Corrector......Page 160
3.2 Consistent Tangent Operator......Page 163
4 Accuracy Analysis of the Integration Algorithm......Page 165
References......Page 169
1 Introduction......Page 171
2.1 Preliminaries......Page 172
2.3 Basic Macrovariables and Averaging Theorem......Page 173
2.4 Definition of the Boundary Conditions for the Small Scale......Page 174
Periodic deformation and antiperiodic traction on the boundary......Page 175
3.1 Introduction......Page 176
3.3 Discretised Micro-equilibrium State and Solution Procedure......Page 177
Overall Tangent Modulus Computation......Page 178
Partitioning of Algebraic Equations......Page 179
Tangent Modulus of Linear Displacements on the Boundary Constraint......Page 180
Partitioning of Algebraic Equations......Page 181
Tangent Modulus of Periodic Displacements and Antiperiodic Traction on the Boundary Constraints......Page 182
Problem Specifications......Page 183
Study of the Regular Cavity Model......Page 184
The RVE with Randomly Generated Voids......Page 185
4.2 Two-scale Analysis of Stretching of an Elasto-plastic Perforated Plate......Page 186
Two-scale Analysis......Page 188
5 Conclusions......Page 189
References......Page 190
1 Protection Systems for Gravel-Buried Pipelines Subjected to Rockfall......Page 192
Impact Scenario and Mode of Analysis......Page 193
Estimates of the Maximum Impact Force and the Penetration Depth at Maximum Impact Force......Page 194
Material Modeling of Steel, Gravel and Sand......Page 195
Real-scale Impact Experiment......Page 197
Comparison between Model-predicted and Experimentally Determined Stress Distribution in the Steel Pipe......Page 198
Prognoses Considering a Change of the Boundary Conditions......Page 199
1.4 Assessment of an Enhanced Protection System Consisting of Gravel and, Additionally, of Buried Load-Carrying Structural Elements......Page 200
Buried Steel Plate Resting on Concrete Walls......Page 201
1.5 Conclusions......Page 202
Structural Model......Page 203
Archard’s Wear Law......Page 205
Protection Performance of Geosynthetics......Page 208
2.3 Conclusions......Page 209
References......Page 210
1 Introduction......Page 212
2 Basic Concept of Free Mesh Method (FMM)......Page 213
3.2 EFMM Based on the Localized Least Square Method......Page 215
3.3 EFMM Based on Hellinger-Reissner Principle......Page 217
4.1 Convergence Study: Displacement......Page 218
4.2 Convergence Study: Error Norms......Page 219
4.3 Patch Test......Page 221
References......Page 223
1 Introduction......Page 225
2.1 Constitutive Modeling......Page 226
2.2 Finite Element Approximation......Page 227
3.1 Classical Thermal and Mechanical Coupling......Page 228
4.1 The Induction Heating Process......Page 230
4.2 The Direct Electro-Thermal Formulation......Page 231
4.3 Finite Element Numerical Approximation......Page 233
4.4 The Electromagnetic/Thermal Coupling Procedure......Page 234
4.5 Results......Page 235
5.1 Introduction......Page 238
5.3 Multi-Scale Coupling and the Digital Material......Page 239
6 Conclusions......Page 241
References......Page 242
1 Introduction......Page 243
2.1 Shell Kinematics......Page 245
2.2 Constitutive Models......Page 247
3.1 Definition of the Element Geometry and Computation of Membrane Strains......Page 249
3.2 Computation of Curvatures......Page 251
3.3 The EBST1 Element......Page 253
4 Boundary Conditions......Page 254
5 Explicit Solution Scheme......Page 255
6 Example 1. Cylindrical Panel under Impulse Loading......Page 256
7.1 S-rail Sheet Stamping......Page 259
7.2 Stamping of Industrial Automotive Part......Page 261
8 Concluding Remarks......Page 262
Acknowledgements......Page 266
References......Page 267
Series: Computational Methods in Applied Sciences......Page 270