Engineering structures may be subjected to extreme high-rate loading conditions, like those associated with natural disasters (earthquakes, tsunamis, rock falls, etc.) or those of anthropic origin (impacts, fluid–structure interactions, shock wave transmissions, etc.). Characterization and modeling of the mechanical behavior of materials under these environments is important in predicting the response of structures and improving designs. This book gathers contributions by eminent researchers in academia and government research laboratories on the latest advances in the understanding of the dynamic process of damage, cracking and fragmentation. It allows the reader to develop an understanding of the key features of the dynamic mechanical behavior of brittle (e.g. granular and cementitious), heterogeneous (e.g. energetic) and ductile (e.g. metallic) materials.

Table of Contents:
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. References 90 Chapter 3. Gradient Damage Models Coupled with Plasticity and Their Application to Dynamic Fragmentation 95 Arthur GEROMEL FISCHER and Jean-Jacques MARIGO 3.1. Introduction 95 3.2. Theoretical aspects 96 3.2.1. Gradient damage models 96 3.2.2. Damage coupled with plasticity 106 3.2.3. Dynamic gradient damage 117 3.3. Numerical implementation 122 3.4. Applications 123 3.4.1. 1D fracture 124 3.4.2. Material behavior 124 3.4.3. Dimensionless parameters 126 3.4.4. 1D period bar 131 3.4.5. Cylinder under internal pressure 135 3.5. Conclusion 138 3.6. References 139 Chapter 4. Plastic Deformation of Pure Polycrystalline Molybdenum 143 Geremy J. KLEISER, Benoit REVIL-BAUDARD and Oana CAZACU 4.1. Introduction 143 4.2. Quasi-static and dynamic data on a pure polycrystalline Mo 144 4.2.1. 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. Kolsky compression bar theory and set-up 343 11.3.2. Pulse shaping technique 345 11.4. Results and discussion 350 11.4.1. Pulse shaper design for Kolsky compression bar systems 350 11.4.2. Rate and specimen size effect on failure strength 355 11.5. Conclusion 360 11.6. Acknowledgments 362 11.7. References 362 Chapter 12. Shockless Characterization of Ceramics Using High-Pulsed Power Technologies 365 Jean-Luc ZINSZNER, Benjamin ERZAR and Pascal FORQUIN 12.1. Introduction 365 12.1.1. Presentation of the silicon carbide grades 367 12.2. Principle of the GEPI generator 368 12.3. Dynamic compression of ceramics 370 12.3.1. Lagrangian analysis of velocity profiles 371 12.3.2. Experimental results 372 12.4. Dynamic tensile strength of ceramics 374 12.4.1. Experimental methodology and data processing 375 12.4.2. Characterization of two silicon carbide grades 377 12.4.3. Post-mortem analyses of damaged samples 378 12.5. Conclusions 380 12.6. Acknowledgments 381 12.7. References 381 Chapter 13. A Eulerian Level Set-based Framework for Reactive Meso-scale Analysis of Heterogeneous Energetic Materials 387 Nirmal KUMAR RAI and H.S. UDAYKUMAR 13.1. Introduction 387 13.2. Numerical framework 390 13.2.1. Governing equations 390 13.2.2. Constitutive model for HMX 390 13.2.3. Reactive modeling of HMX 393 13.2.4. Level set representation of embedded interface 395 13.2.5. Image processing approach: Representing real geometries 395 13.3. Results 398 13.3.1. Grid refinement study 400 13.3.2. Collapse behavior of voids present in the pressed HMX material 401 13.3.3. Criticality conditions for Class III and Class V samples 403 13.3.4. Meso-scale criticality conditions for pressed energetic materials 405 13.4. Conclusions 411 13.5. Acknowledgments 412 13.6. References 412 Chapter 14. A Well-posed Hypoelastic Model Derived From a Hyperelastic One 417 Nicolas FAVRIE and Sergey GAVRILYUK 14.1. Introduction 417 14.2. A general hyperelastic model formulation 418 14.3. Evolution equation for the deviatoric part of the stress tensor: neo-Hookean solids 420 14.3.1. Expression of tr(b) as a function of the invariants of S 421 14.3.2. Hypoelastic formulation 423 14.4. Conclusions 424 14.5. Acknowledgments 425 14.6. References 425 Appendix A: Case a = 0.5 429 List of Authors 433 Index 437