Bouchaib Radi is Full Professor of FST at Hassan Premier University, Settat, Morocco. His research interests include forming, optimization and reliability. Abdelkhalak El Hami is Full Professor at INSA Rouen, University of Normandy, France. His research interests include optimization, reliability and structural dynamics.

• Preface xiChapter 1. Forming Processes 11.1. Introduction& 11.2. Different processes 11.2.1. Smelting 21.2.2. Machining 31.2.3. Powder metallurgy 51.3. Hot and cold forming 61.3.1. Influence of the static parameters 91.3.2. Hydroforming 121.3.3. The limitations of the process 131.3.4. Deep drawing 141.4. Experimental characterization 141.5. Forming criteria 161.5.1. Influence of the structure of sheet metal 181.5.2. Physical strain mechanisms 201.5.3. Different criteria 21Chapter 2. Contact and Large Deformation Mechanics 232.1. Introduction 232.2. Large transformation kinematics 232.2.1. Kinematics of the problem in spatial coordinates 242.3. Transformation gradient 252.4. Strain measurements 262.4.1. Polar decomposition of F 262.4.2. Strain rate tensor 272.4.3. Canonical decomposition of F 282.4.4. Kinematics of the problem in convective coordinates 282.4.5. Transformation tensor 292.4.6. Strain rate measures 322.4.7. Strain tensor 352.5. Constitutive relations 362.5.1. Large elastoplastic transformations 382.5.2. Kinematic decomposition of the transformation 412.6. Incremental behavioral problem 422.6.1. Stress incrementation 422.6.2. Strain incrementation 442.6.3. Solution of the behavior problem 462.7. Definition of the P.V.W. in major transformations 492.7.1. Equilibrium equations 492.7.2. Definition of the P.V.W 502.7.3. Incremental formulation 512.8. Contact kinematics 522.8.1. Definition of the problem and notations 522.8.2. Contact formulation 532.8.3. Formulation of the friction problem 532.8.4. Friction laws 542.8.5. Coulomb's law 542.8.6. Tresca's law 55Chapter 3. Stamping 573.1. Introduction 573.2. Forming limit curve 593.3. Stamping modeling: incremental problem 603.3.1. Modeling of sheet metal 613.3.2. Spatial discretization: finite elements method 623.3.3. Choice of sheet metal and finite element approximation 633.4. Modeling tools 643.4.1. Tool surface meshing into simple geometry elements 643.4.2. Analytical representation of tools 653.4.3. Bezier patches 653.5. Stamping numerical processing 723.5.1. Problem statement 733.5.2. The augmented Lagrangian method 753.6. Numerical simulations 793.6.1. Sollac test 81Chapter 4. Hydroforming 834.1. Introduction  834.2. Hydroforming 854.2.1. Tube hydroforming 854.2.2. Sheet metal hydroforming 864.3. Plastic instabilities in hydroforming 874.3.1. Tube buckling 884.3.2. Wrinkling 904.3.3. Necking 914.3.4. Springback 924.4. Forming limit curve 924.5. Material characterization for hydroforming 944.5.1. Tensile testing 954.5.2. Bulge testing 954.6. Analytical modeling of a inflation test 974.6.1. Hill48 criterion in planar stresses 974.7. Numerical simulation 1004.8. Mechanical characteristic of tube behavior 101Chapter 5. Additive Manufacturing 1055.1. Introduction 1055.2. RP and stratoconception 1075.3. Additive manufacturing definitions 1095.4. Principle 1135.4.1. Principle of powder bed laser sintering/melting 1145.4.2. Principle of laser sintering/melting by projecting powder 1165.5. Additive manufacturing in the IT-based development process 1175.5.1. Concept "from the object to the object" 1175.5.2. Key element of the IT development process 118Chapter 6. Optimization and Reliability in Forming 1216.1. Introduction 1216.2. Different approaches to optimization processes 1226.2.1. Limitations of the deterministic approaches 1246.3. Characterization of forming processes by objective functions 1256.4. Deterministic and probabilistic optimization of a T-shaped tube 1266.4.1. Problem description 1266.4.2. Choice of the objective function and definition of the stresses 1276.4.3. Choice of the uncertain parameters 1286.4.4. Choice of the objective function and the stresses 1306.4.5. Deterministic formulation of the optimization problem 1326.4.6. Probabilistic formulation of the optimization problem 1336.4.7. Optima sensitivity to uncertainties 1406.5. Deterministic and optimization-based reliability of a tube with two expansion regions 1426.5.1. Problem description 1426.5.2. Deterministic and reliabilist formulation of the optimization problem 1476.6. Optimization-based reliability of circular sheet metal hydroforming 1506.6.1. Problem description 1506.6.2. Construction of the objective function and of the stresses 1516.6.3. Effects diagram 1516.6.4. Deterministic solution of the optimization problem 1556.6.5. Reliabilist solution of the optimization problem 1576.6.6. Effect of uncertainties on the optimal variables 1596.7. Deterministic and robust optimization of a square plate 1606.7.1. Robust resolution of the optimization problem 1666.8. Optimization of thin sheet metal 168Chapter 7. Application of Metamodels to Hydroforming 1717.1. Introduction 1717.2. Sources of uncertainty in forming 1727.3. Failure criteria 1737.3.1. Failure criteria for necking 1747.3.2. Failure criteria for wrinkling 1747.4. Evaluation strategy of the probability of failure 1757.4.1. Finite element model and choice of uncertainty parameters 1767.4.2. Identification of failure modes and definition of boundary states 1807.4.3. Identification of elements and critical areas 1817.5. Critical strains probabilistic characterization 1857.5.1. Choice of numerical experimental design 1867.5.2. Construction of metamodels 1867.5.3. Validation and statistical analysis of metamodels 1877.5.4. Fitting of distributions 1877.6. Necking and wrinkling probabilistic study 1937.7. Effects of the correlations on the probability of failure 1967.7.1. Spatial estimation of the probability of failures 197Chapter 8. Parameters Identification in Metal Forming 1998.1. Introduction 1998.2. Identification methods 1998.2.1. Validation test 2008.3. Welded tube hydroforming 2038.3.1. Thin sheet metal hydroforming 205Appendices  213Appendix 1. Optimization in Mechanics 215Appendix 2. Reliability in Mechanics 223Appendix 3. Metamodels 233Bibliography 243Index 253