Damage Mechanics in Metal Forming Advanced Modeling and Numerical Simulation

The aim of this book is to summarize the current most effective methods for modeling, simulating, and optimizing metal forming processes, and to present the main features of new, innovative methods currently being developed which will no doubt be the industrial tools of tomorrow. It discusses damage (or defect) prediction in virtual metal forming, using advanced multiphysical and multiscale fully coupled constitutive equations. Theoretical formulation, numerical aspects as well as application to various sheet and bulk metal forming are presented in detail.
Virtual metal forming is nowadays inescapable when looking to optimize numerically various metal forming processes in order to design advanced mechanical components. To do this, highly predictive constitutive equations accounting for the full coupling between various physical phenomena at various scales under large deformation including the ductile damage occurrence are required. In addition, fully 3D adaptive numerical methods related to time and space discretization are required in order to solve accurately the associated initial and boundary value problems. This book focuses on these two main and complementary aspects with application to a wide range of metal forming and machining processes.

Contents

1. Elements of Continuum Mechanics and Thermodynamics.
2. Thermomechanically-Consistent Modeling of the Metals Behavior with Ductile Damage.
3. Numerical Methods for Solving Metal Forming Problems.
4. Application to Virtual Metal Forming.

Preface xiii

Principle of Mathematical Notations xix

Chapter 1. Elements of Continuum Mechanics and Thermodynamics 1

1.1. Elements of kinematics and dynamics of materially simple continua 2

1.2. On the conservation laws for the materially simple continua. 33

1.3. Materially simple continuum thermodynamics and the necessity of constitutive equations 39

1.4. Mechanics of generalized continua. Micromorphic theory 55

Chapter 2. Thermomechanically-Consistent Modeling of the Metals Behavior with Ductile
Damage 63

2.1. On the main schemes for modeling the behavior of materially simple continuous media 64

2.2. Behavior and fracture of metals and alloys: some physical and phenomenological aspects 69

2.3. Theoretical framework of modeling and main hypotheses 91

2.4. State potential: state relations 113

2.5. Dissipation analysis: evolution equations 139

2.6. Modeling of the damage-induced volume variation 194

2.7. Modeling of the contact and friction between deformable solids 200

2.8. Nonlocal modeling of damageable behavior of micromorphic continua 215

2.9. On the micro–macro modeling of inelastic flow with ductile damage 226

Chapter 3. Numerical Methods for Solving Metal Forming Problems 243

3.1. Initial and boundary value problem associated with virtual metal forming processes 244

3.2. Temporal and spatial discretization of the IBVP 259

3.3. On some global resolution scheme of the IBVP 270

3.4. Local integration scheme: state variables computation 304

3.5. Adaptive analysis of damageable elasto-inelastic structures 337

3.6. On other spatial discretization methods 347

Chapter 4. Application to Virtual Metal Forming 355

4.1. Why use virtual metal forming? 356

4.2. Model identification methodology 359

4.3. Some applications 431

4.4. Toward the optimization of forming and machining processes 484

Appendix: Legendre–Fenchel Transformation 493

Bibliography 499

Index 515

Khemais Saanouni is Professor of applied computational mechanics, ICD/LASMIS at University of Technology, Troyes, France.