Oñate / Onate / Owen Computational Plasticity

1. Auflage 2010
ISBN: 978-1-4020-6577-4
Verlag: Springer Netherlands
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 7, 265 Seiten

Reihe: Computational Methods in Applied Sciences

This book contains 14 invited contributions written by distinguished authors who participated in the VIII International Conference on Computational Plasticity held at CIMNE/UPC (www.cimne.com) from 5-8 September 2005, in Barcelona, Spain. The chapters present recent progress and future research directions in the field of computational plasticity.

Autoren/Hrsg.

Onate, Eugenio

Owen, Roger

Oñate, Eugenio

Inhaltsverzeichnis

1;Table of Contents;6
2;Preface;8
3;Chapter 1;10
3.1;A Multi-Scale Continuum Theory for Heterogeneous Materials;10
3.1.1;1 Multi-Physics Multi-Scale Material Model;10
3.1.1.1;1.1 Kinematics and Virtual Power;10
3.1.1.2;1.2 Constitutive Relation;11
3.1.2;2 Application to Porous metals;11
3.1.2.1;2.1 Multi-Scale Model;12
3.1.2.2;2.2 Constitutive Relation;13
3.1.2.3;2.3 Numerical Results;13
3.1.3;3 Three-scale Model of High-Strength Steels;15
3.1.3.1;3.1 Multi-Scale Model;15
3.1.3.2;3.2 Constitutive Relation;16
3.1.3.3;3.3 Numerical Results;17
3.1.4;4 Conclusion;18
3.1.5;Acknowledgements;19
3.1.6;References;19
4;Chapter 2;21
4.1;Towards a Model for Large Strain Anisotropic Elasto-Plasticity;21
4.1.1;1 Introduction;21
4.1.2;2 Kinematics and Incremental Integrations;23
4.1.2.1;2.1 Kinematics of Deformation: Multiplicative Decomposition and Strain Rate Tensors;23
4.1.2.2;2.2 Integration of the Plastic Deformation Gradient;24
4.1.2.3;2.3 Rotationally-Frozen Configuration;26
4.1.3;3 Free Energy Function and Dissipation Inequality;27
4.1.3.1;3.1 Stored Energy Function: Orthotropic Hyperelasticity Based on Logarithmic Strain Measures;27
4.1.3.2;3.2 Hardening Potential;30
4.1.4;4 Mapping Tensors from Quadratic to Logarithmic Strain Space;32
4.1.5;5 Dissipation Inequality;34
4.1.6;6 Yield Functions;36
4.1.6.1;6.1 Yield Function for the Symmetric Part;37
4.1.6.2;6.2 Yield Function for the Skew Part;37
4.1.6.3;6.3 Coupling of Symmetric and Skew Parts;38
4.1.7;7 Numerical Example;38
4.1.8;8 Conclusions;39
4.1.9;References;42
5;Chapter 3;45
5.1;Localized and Diffuse Bifurcations in Porous Rocks Undergoing Shear Localization and Cataclastic Flow;45
5.1.1;1 Introduction;45
5.1.2;2 Shear Localization;48
5.1.2.1;2.1 E-mode for Shear Localization;48
5.1.2.2;2.2 Constitutive Branching for Shear Localization;50
5.1.3;3 Cataclastic Flow;54
5.1.3.1;3.1 E-mode for Cataclastic Flow;54
5.1.3.2;3.2 Constitutive Branching for Cataclastic Flow;56
5.1.4;4 Transient Plastic Flow;57
5.1.4.1;4.1 Slip Weakening;58
5.1.4.2;4.2 Cataclastic Flow;58
5.1.5;5 Closure;59
5.1.6;Acknowledgements;59
5.1.7;References;59
6;Chapter 4;62
6.1;Dispersion and Localisation in a Strain–Softening Two–Phase Medium;62
6.1.1;1 Introduction;62
6.1.2;2 Governing Equations;63
6.1.3;3 Reduction of the Governing Equations;66
6.1.4;4 Dispersion Analysis;67
6.1.5;5 Numerical Examples;69
6.1.6;6 Concluding Remarks;71
6.1.7;References;72
7;Chapter 5;74
7.1;New Developments in Surface-to-Surface Discretization Strategies for Analysis of Interface Mechanics;74
7.1.1;1 Introduction;74
7.1.2;2 Background: Mortar Projection in Contact Mechanics;75
7.1.2.1;2.1 The Mesh Tying Problem;75
7.1.2.2;2.2 Generalization to Sliding Contact;78
7.1.3;3 An Extension of the Framework: Mortar-Based Self-Contact;81
7.1.4;4 Mortar Formulation of Lubricated Contact;88
7.1.5;5 Conclusion;91
7.1.6;Acknowledgment;92
7.1.7;References;92
8;Chapter 6;94
8.1;Particle Finite Element Methods in Solid Mechanics Problems;94
8.1.1;1 Introduction;94
8.1.2;2 Fundamentals: The Particle Finite Element Method;95
8.1.2.1;2.1 Equations of Motion. Boundary Value Problem;95
8.1.2.2;2.2 Time Marching Scheme;97
8.1.3;3 Contact Strategy: Anticipating Interface Mesh;99
8.1.3.1;3.1 A Penalty Strategy at the Contact Interface;100
8.1.4;4 Representative Examples;103
8.1.4.1;4.1 Flexible Spring with Multiple Self-contacts;103
8.1.4.2;4.2 Riveting Process;105
8.1.4.3;4.3 Machining Process;107
8.1.4.4;4.4 Powder Filling Process;107
8.1.5;5 Concluding Remarks;108
8.1.6;Acknowledgements;109
8.1.7;References;109
9;Chapter 7;111
9.1;Micro-Meso-Macro Modelling of Composite Materials;111
9.1.1;1 Introduction;112
9.1.2;2 Micro-structure of Hardened Cement Paste (hcp);113
9.1.3;3 Constitutive Equations;115
9.1.4;4 Homogenization;118
9.1.5;5 Parameter Identification;120
9.1.6;6 Thermo-mechanical Coupling;122
9.1.7;7 Outlook;126
9.1.8;Acknowledgments;127
9.1.9;References;128
10;Chapter 8;129
10.1;Numerical Modeling of Transient Impact Processes with Large Deformations and Nonlinear Material Behavior;129
10.1.1;1 Introduction;129
10.1.2;2 Class of Problems;130
10.1.3;3 Adaptive Remeshing;130
10.1.3.1;3.1 Mesh Quality Check;130
10.1.3.2;3.2 Error Assessment and Mesh Density Distribution;130
10.1.3.2.1;Gradient-Based Indicators;131
10.1.3.2.2;Local Quantity Indicators;132
10.1.3.2.3;Geometric Indicator;133
10.1.3.2.4;Selection of Indicators and Final Mesh Density Distribution;133
10.1.3.3;3.3 Mesh Generation;134
10.1.3.4;3.4 Transfer of State Variables;135
10.1.4;4 Constitutive Modeling;135
10.1.4.1;4.1 Metals;135
10.1.4.2;4.2 Geomaterials;137
10.1.4.2.1;Characterization of Geomaterials Under Impact Loading;137
10.1.4.2.2;Modified Drucker-Prager-Cap Model;138
10.1.4.2.3;Powderization Under High Pressure;140
10.1.5;5 Numerical Examples;143
10.1.5.1;5.1 Adaptive Computations;143
10.1.5.1.1;Taylor Bar Impact;143
10.1.5.1.2;High-Strain Rate Compression of WHA Block;145
10.1.5.1.3;Penetration of a Steel Cylinder by WHA Long Rod;145
10.1.5.2;5.2 Geomechanical computations;146
10.1.5.2.1;Quasi-Static Tests;146
10.1.5.2.2;Triple Impact on Microconcrete;146
10.1.5.2.3;Dynamic Compaction of Powder;147
10.1.6;6 Conclusion;148
10.1.7;References;149
11;Chapter 9;151
11.1;A Computational Model For Viscoplasticity Coupled with Damage Including Unilateral Effects;151
11.1.1;1 Introduction;151
11.1.2;2 Elasto-Viscoplastic Damage Constitutive Model;153
11.1.2.1;2.1 Viscoplastic Model;153
11.1.2.2;2.2 Concept of Effective Stress;154
11.1.2.3;2.3 Elasto-Viscoplasticity Coupled with Damage;155
11.1.2.4;2.4 Damage Evolution Law;156
11.1.3;3 Integration Algorithm;158
11.1.3.1;3.1 Single-Equation Corrector;160
11.1.3.2;3.2 Consistent Tangent Operator;163
11.1.4;4 Accuracy Analysis of the Integration Algorithm;165
11.1.5;5 Concluding Remarks;169
11.1.6;References;169
12;Chapter 10;171
12.1;On Multiscale Analysis of Heterogeneous Composite Materials: Implementation of Micro-to-Macro Transitions in the Finite Element Setting;171
12.1.1;1 Introduction;171
12.1.2;2 Continuum Model at Small Strains;172
12.1.2.1;2.1 Preliminaries;172
12.1.2.2;2.2 Basic Microvariables;173
12.1.2.3;2.3 Basic Macrovariables and Averaging Theorem;173
12.1.2.3.1;The Hill-Mandel Principle;174
12.1.2.4;2.4 Definition of the Boundary Conditions for the Small Scale;174
12.1.2.4.1;Linear displacements on the boundary;175
12.1.2.4.2;Periodic deformation and antiperiodic traction on the boundary;175
12.1.3;3 Discretised Model at Small Strains;176
12.1.3.1;3.1 Introduction;176
12.1.3.2;3.2 Displacement Field Partition and Matrix Notation;177
12.1.3.3;3.3 Discretised Micro-equilibrium State and Solution Procedure;177
12.1.3.4;3.4 General Average Stress and Overall Tangent Modulus Computation;178
12.1.3.4.1;Average Stress Computation;178
12.1.3.4.2;Overall Tangent Modulus Computation;178
12.1.3.5;3.5 Linear Displacements on the Boundary Assumption;179
12.1.3.5.1;Partitioning of Algebraic Equations;179
12.1.3.5.2;Linear Displacement;180
12.1.3.5.3;Tangent Modulus of Linear Displacements on the Boundary Constraint;180
12.1.3.6;3.6 Periodic Displacements and Antiperiodic Traction on the Boundary;181
12.1.3.6.1;Partitioning of Algebraic Equations;181
12.1.3.6.2;Periodic Displacements and Antiperiodic Tractions;182
12.1.3.6.3;Tangent Modulus of Periodic Displacements and Antiperiodic Traction on the Boundary Constraints;182
12.1.4;4 Numerical Examples;183
12.1.4.1;4.1 Study of the Effect of Topology of Cavities on the Properties of the RVE;183
12.1.4.1.1;Problem Specifications;183
12.1.4.1.2;Analysis Approach;184
12.1.4.1.3;Study of the Regular Cavity Model;184
12.1.4.1.4;The RVE with Randomly Generated Voids;185
12.1.4.2;4.2 Two-scale Analysis of Stretching of an Elasto-plastic Perforated Plate;186
12.1.4.2.1;Single-scale Analysis;188
12.1.4.2.2;Two-scale Analysis;188
12.1.5;5 Conclusions;189
12.1.6;References;190
13;Chapter 11;192
13.1;Assessment of Protection Systems for Gravel-Buried Pipelines Considering Impact and Recurrent Shear Loading Caused by Thermal Deformations of the Pipe;192
13.1.1;Introduction;192
13.1.2;1 Protection Systems for Gravel-Buried Pipelines Subjected to Rockfall;192
13.1.2.1;1.1 Development of a Structural Model;193
13.1.2.1.1;Geometric Dimensions of the Considered Problem;193
13.1.2.1.2;Impact Scenario and Mode of Analysis;193
13.1.2.1.3;Estimates of the Maximum Impact Force and the Penetration Depth at Maximum Impact Force;194
13.1.2.1.4;Computation of the Distribution of Stresses Corresponding to the Maximum Impact Force;195
13.1.2.1.5;Material Modeling of Steel, Gravel and Sand;195
13.1.2.1.6;Parameter Identification;197
13.1.2.2;1.2 Validation of the Developed Structural Model;197
13.1.2.2.1;Real-scale Impact Experiment;197
13.1.2.2.2;Comparison between Model-predicted and Experimentally Determined Stress Distribution in the Steel Pipe;198
13.1.2.3;1.3 Prognoses of Structural Behavior;199
13.1.2.3.1;Prognoses Considering a Change of the Boundary Conditions;199
13.1.2.3.2;Prognoses Considering a Change of the Structural Dimensions;200
13.1.2.3.3;Prognoses Considering a Change of the Boundary Conditions and of the Structural Dimensions;200
13.1.2.4;1.4 Assessment of an Enhanced Protection System Consisting of Gravel and, Additionally, of Buried Load-Carrying Structural Elements;200
13.1.2.4.1;Buried Steel Plate Resting on Concrete Walls;201
13.1.2.4.2;Assessment of the Enhanced Protection System;202
13.1.2.5;1.5 Conclusions;202
13.1.3;2 Protection Systems Against Abrasive Shear Loading Caused by Thermal Deformation of Soil-Covered Pipelines;203
13.1.3.1;2.1 Assessment of Static Forces Exerted by Single Stone Tips onto Soil-Covered Pipelines;203
13.1.3.1.1;Loading Scenario;203
13.1.3.1.2;Structural Model;203
13.1.3.1.3;Finite Element Simulation;205
13.1.3.1.4;Relevant Forces of Tips of Single Stone Acting on Soil-covered Pipelines, as a Function of the Pipe Diameter;205
13.1.3.2;2.2 Identification of Wear Protection Strategies;205
13.1.3.2.1;Archard’s Wear Law;205
13.1.3.2.2;Protection Performance of Geosynthetics;208
13.1.3.2.3;Effective Means of Protection;209
13.1.3.3;2.3 Conclusions;209
13.1.4;References;210
14;Chapter 12;212
14.1;Enriched Free Mesh Method: An Accuracy Improvement for Node-based FEM;212
14.1.1;1 Introduction;212
14.1.2;2 Basic Concept of Free Mesh Method (FMM);213
14.1.3;3 Enriched Free Mesh Method (EFMM);215
14.1.3.1;3.1 Outline of EFMM;215
14.1.3.2;3.2 EFMM Based on the Localized Least Square Method;215
14.1.3.3;3.3 EFMM Based on Hellinger-Reissner Principle;217
14.1.4;4 Examples;218
14.1.4.1;4.1 Convergence Study: Displacement;218
14.1.4.2;4.2 Convergence Study: Error Norms;219
14.1.4.3;4.3 Patch Test;221
14.1.5;5 Concluding remarks;223
14.1.6;References;223
15;Chapter 13;225
15.1;Modelling of Metal Forming Processes and Multi-Physic Coupling;225
15.1.1;1 Introduction;225
15.1.2;2 Mechanical Approach of Metal Forming Processes;226
15.1.2.1;2.1 Constitutive Modeling;226
15.1.2.2;2.2 Finite Element Approximation;227
15.1.2.3;2.3 Numerical Issues;228
15.1.3;3 Thermal and Fluid-Solid Coupling;228
15.1.3.1;3.1 Classical Thermal and Mechanical Coupling;228
15.1.3.2;3.2 Localization;230
15.1.3.3;3.3 Fluid Solid Coupling During Heating or Heat Treatment;230
15.1.4;4 Electro Magnetic Coupling;230
15.1.4.1;4.1 The Induction Heating Process;230
15.1.4.2;4.2 The Direct Electro-Thermal Formulation;231
15.1.4.3;4.3 Finite Element Numerical Approximation;233
15.1.4.4;4.4 The Electromagnetic/Thermal Coupling Procedure;234
15.1.4.5;4.5 Results;235
15.1.5;5 Coupling with Microstructure Evolution;238
15.1.5.1;5.1 Introduction;238
15.1.5.2;5.2 Macroscopic Approach;239
15.1.5.3;5.3 Multi-Scale Coupling and the Digital Material;239
15.1.6;6 Conclusions;241
15.1.7;References;242
16;Chapter 14;243
16.1;Enhanced Rotation-Free Basic Shell Triangle. Applications to Sheet Metal Forming;243
16.1.1;1 Introduction;243
16.1.2;2 Basic Thin Shell Equations Using a Total Lagrangian Formulation;245
16.1.2.1;2.1 Shell Kinematics;245
16.1.2.2;2.2 Constitutive Models;247
16.1.3;3 Enhanced Basic Shell Triangle;249
16.1.3.1;3.1 Definition of the Element Geometry and Computation of Membrane Strains;249
16.1.3.2;3.2 Computation of Curvatures;251
16.1.3.3;3.3 The EBST1 Element;253
16.1.4;4 Boundary Conditions;254
16.1.5;5 Explicit Solution Scheme;255
16.1.6;6 Example 1. Cylindrical Panel under Impulse Loading;256
16.1.7;7 Application to Sheet Metal Forming Problems;259
16.1.7.1;7.1 S-rail Sheet Stamping;259
16.1.7.2;7.2 Stamping of Industrial Automotive Part;261
16.1.8;8 Concluding Remarks;262
16.1.9;Acknowledgements;266
16.1.10;References;267