Preface xiii Chapter 1. Some Issues Related to the Modeling of Dynamic Shear Localization-assisted Failure 1; Patrice LONGÈRE 1.1. Introduction 1 1.2. Preliminary/fundamental considerations 3 1.2.1. Localization and discontinuity 3 1.2.2. Isothermal versus adiabatic conditions 6 1.2.3. Sources of softening 9 1.2.4. ASB onset 22 1.2.5. Scale postulate 26 1.3. Small-scale postulate-based approaches 27 1.3.1. Material of the band viewed as an extension of the solid material behavior before ASB onset 28 1.3.2. Material of the band viewed as a fluid material 29 1.3.3. ASB viewed as a damage mechanism 31 1.3.4. Assessment 32 1.4. Embedded band-based approaches (large-scale postulate) 33 1.4.1. Variational approaches 34 1.4.2. Enriched finite element kinematics 38 1.4.3. Enriched constitutive model 41 1.4.4. Discussion 43 1.5.

Conclusion 44 1.6. Acknowledgments 45 1.7. References 45 Chapter 2. Analysis of the Localization Process Prior to the Fragmentation of a Ring in Dynamic Expansion 53; Skander EL MAÏ, Sébastien MERCIER and Alain MOLINARI 2.1. Introduction 53 2.1.1. Fragmentation experiments 54 2.1.2. Fragmentation theories 54 2.2. An extension of a linear stability analysis developed in [MER 03] 59 2.2.1. Position of the problem 59 2.2.2. Classical linear stability analysis 60 2.2.3. Evolution of the cross-section perturbation 62 2.2.4. Analysis of the potential sites of necking 65 2.3. Outcomes of the approach 70 2.3.1. Effects of the loading velocity on neck spacing distribution 70 2.3.2. Effects of an imposed dominant mode in the initial perturbation 72 2.3.3. Comparison of the approach with numerical simulations 83 2.4. Conclusion 89 2.5.

Analysis of the quasi-static uniaxial tension test results on smooth specimens 147 4.2.2. Split Hopkinson pressure bar data 154 4.2.3. Taylor cylinder impact data 155 4.3. Constitutive model for polycrystalline Mo 158 4.4. Predictions of the mechanical response 162 4.4.1. FE. predictions of the quasi-static uniaxial tensile response for notched specimens 162 4.5. Conclusions 172 4.6. References 173 Chapter 5. Some Advantages of Advanced Inverse Methods to Identify Viscoplastic and Damage Material Model Parameters 177; Bertrand LANGRAND, Delphine NOTTA-CUVIER, Thomas FOUREST and Eric MARKIEWICZ 5.1. Introduction 177 5.2. Experimental devices for material characterization over a large range of strain rates 180 5.3. Identification of elasto-viscoplastic and damage material Parameters 184 5.3.1. Direct approach for material parameter identification 184 5.3.2.

Inverse approaches for material parameter identification 192 5.4. Conclusions 204 5.5. Acknowledgments 205 5.6. References 205 Chapter 6. Laser Shock Experiments to Investigate Fragmentation at Extreme Strain Rates 213; Thibaut DE RESSÉGUIER, Didier LOISON, Benjamin JODAR, Emilien LESCOUTE, Caroline ROLAND, Loïc SIGNOR and André DRAGON 6.1. Introduction 214 6.2. Phenomenology of laser shock-induced fragmentation 215 6.3. Spall fracture 217 6.4. Microspall after shock-induced melting 222 6.5. Microjetting from geometrical defects 225 6.6. Conclusion 230 6.7. References 231 Chapter 7. One-dimensional Models for Dynamic Fragmentation of Brittle Materials 237; David CERECEDA, Nitin DAPHALAPURKAR and Lori GRAHAM BRADY 7.1. Introduction 237 7.2. Methods 242 7.3. Results 244 7.3.1. Mono-phase materials 244 7.3.2.

Multi-phase materials 251 7.4. Conclusions 258 7.5. References 259 Chapter 8. Damage and Wave Propagation in Brittle Materials 263; Quriaky GOMEZ, Jia LI and Ioan R. IONESCU 8.1. Introduction 263 8.2. Short overview of damage models 264 8.2.1. Effective elasticity of a cracked solid 266 8.2.2. Damage evolution 268 8.3. 1D wave propagation 275 8.3.1. Problem statement 276 8.3.2. A single family of micro-cracks 278 8.3.3. Three families of micro-cracks 280 8.4. Two-dimensional anti-plane wave propagation 280 8.4.1. Anisotropic damage under isotropic loading 281 8.4.2. Anisotropic loading of an initial isotropic damaged material 284 8.5. Blast impact and damage evolution 286 8.6. Conclusions and perspectives 291 8.7. Acknowledgments 292 8.8. References 292 Chapter 9.

Discrete Element Analysis to Predict Penetration and Perforation of Concrete Targets Struck by Rigid Projectiles 297; Laurent DAUDEVILLE, Andria ANTONIOU, Ahmad OMAR, Philippe MARIN, Serguei POTAPOV and Christophe PONTIROLI 9.1. Introduction 297 9.2. Discrete element model 299 9.2.1. Definition of interactions 299 9.2.2. Constitutive behavior of concrete: Discrete element model 300 9.2.3. Linear elastic constitutive behavior 301 9.2.4. Nonlinear constitutive behavior 302 9.2.5. Strain rate dependency 305 9.3. Simulation of impacts 307 9.3.1. Impact experiments 307 9.3.2. Modeling of impact experiments 308 9.4. Conclusion 311 9.5. References 311 Chapter 10. Bifurcation Micromechanics in Granular Materials 315; Antoine WAUTIER, Jiaying LIU, François NICOT and Félix DARVE 10.1. Introduction 315 10.2.

Application of the second-order work criterion at representative volume element scale 318 10.3. From macro to micro analysis of instability 322 10.3.1. Local second-order work and contact sliding 322 10.3.2. Role of strong contact network in stable and unstable loading directions 323 10.3.3. From contact sliding to mesoscale mechanisms 326 10.3.4. Micromechanisms leading to bifurcation at the representative volume element scale 329 10.4. Diffuse and localized failure in a unified framework 331 10.4.1. Diffuse and localized failure pattern 331 10.4.2. Common micromechanisms and microstructures 332 10.5. Conclusion 334 10.6. References 335 Chapter 11. Influence of Specimen Size on the Dynamic Response of Concrete 339; Xu NIE, William F. HEARD and Bradley E. MARTIN 11.1. Introduction 339 11.2. Materials and specimens 341 11.3. Experimental techniques 343 11.3.1.