Damage Mechanics in Metal Forming

Preface xiii
Principle of Mathematical Notations xix
Chapter 1. Elements of Continuum Mechanics and Thermodynamics1
1.1. Elements of kinematics and dynamics of materially simplecontinua 2
1.2. On the conservation laws for the materially simplecontinua. 33
1.3. Materially simple continuum thermodynamics and thenecessity of constitutive equations 39
1.4. Mechanics of generalized continua. Micromorphic theory55
Chapter 2. Thermomechanically-Consistent Modeling of theMetals Behavior with Ductile
Damage 63
2.1. On the main schemes for modeling the behavior of materiallysimple continuous media 64
2.2. Behavior and fracture of metals and alloys: some physicaland phenomenological aspects 69
2.3. Theoretical framework of modeling and main hypotheses91
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 deformablesolids 200
2.8. Nonlocal modeling of damageable behavior of micromorphiccontinua 215
2.9. On the micro-macro modeling of inelastic flow withductile damage 226
Chapter 3. Numerical Methods for Solving Metal FormingProblems 243
3.1. Initial and boundary value problem associated with virtualmetal 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 computation304
3.5. Adaptive analysis of damageable elasto-inelastic structures337
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 processes484
Appendix: Legendre-Fenchel Transformation 493
Bibliography 499
Index 515