Dynamic Damage and Fragmentation

David Edward Lambert is a member of the scientific and professional cadre of Senior Executives, and Chief Scientist of the Air Force Research Laboratory, Munitions Directorate, Eglin, USA.Crystal L. Pasiliao is a Senior Research Scientist at the Air Force Research Laboratory, Munitions Directorate, Eglin, USA.Benjamin Erzar is a Senior Research Scientist at the Commissariat à l’Energie Atomique, Gramat, France.Benoit Revil-Baudard is a Research Scientist in the Department of Mechanical and Aerospace Engineering at the University of Florida, REEF, Shalimar, USA.Oana Cazacu is Professor in the Department of Mechanical and Aerospace Engineering at the University of Florida, REEF, Shalimar, USA.

• Preface xiiiChapter 1. Some Issues Related to the Modeling of Dynamic Shear Localization-assisted Failure 1Patrice LONGÈRE1.1. Introduction 11.2. Preliminary/fundamental considerations 31.2.1. Localization and discontinuity 31.2.2. Isothermal versus adiabatic conditions 61.2.3. Sources of softening 91.2.4. ASB onset 221.2.5. Scale postulate 261.3. Small-scale postulate-based approaches 271.3.1. Material of the band viewed as an extension of the solid material behavior before ASB onset 281.3.2. Material of the band viewed as a fluid material 291.3.3. ASB viewed as a damage mechanism 311.3.4. Assessment 321.4. Embedded band-based approaches (large-scale postulate) 331.4.1. Variational approaches 341.4.2. Enriched finite element kinematics 381.4.3. Enriched constitutive model 411.4.4. Discussion 431.5. Conclusion 441.6. Acknowledgments 451.7. References 45Chapter 2. Analysis of the Localization Process Prior to the Fragmentation of a Ring in Dynamic Expansion 53Skander EL MAÏ, Sébastien MERCIER and Alain MOLINARI2.1. Introduction 532.1.1. Fragmentation experiments 542.1.2. Fragmentation theories 542.2. An extension of a linear stability analysis developed in [MER 03] 592.2.1. Position of the problem 592.2.2. Classical linear stability analysis 602.2.3. Evolution of the cross-section perturbation 622.2.4. Analysis of the potential sites of necking 652.3. Outcomes of the approach 702.3.1. Effects of the loading velocity on neck spacing distribution 702.3.2. Effects of an imposed dominant mode in the initial perturbation 722.3.3. Comparison of the approach with numerical simulations 832.4. Conclusion 892.5. References 90Chapter 3. Gradient Damage Models Coupled with Plasticity and Their Application to Dynamic Fragmentation 95Arthur GEROMEL FISCHER and Jean-Jacques MARIGO3.1. Introduction 953.2. Theoretical aspects 963.2.1. Gradient damage models 963.2.2. Damage coupled with plasticity 1063.2.3. Dynamic gradient damage 1173.3. Numerical implementation 1223.4. Applications 1233.4.1. 1D fracture 1243.4.2. Material behavior 1243.4.3. Dimensionless parameters 1263.4.4. 1D period bar 1313.4.5. Cylinder under internal pressure 1353.5. Conclusion 1383.6. References 139Chapter 4. Plastic Deformation of Pure Polycrystalline Molybdenum 143Geremy J. KLEISER, Benoit REVIL-BAUDARD and Oana CAZACU4.1. Introduction 1434.2. Quasi-static and dynamic data on a pure polycrystalline Mo 1444.2.1. Analysis of the quasi-static uniaxial tension test results on smooth specimens 1474.2.2. Split Hopkinson pressure bar data 1544.2.3. Taylor cylinder impact data 1554.3. Constitutive model for polycrystalline Mo 1584.4. Predictions of the mechanical response 1624.4.1. FE. predictions of the quasi-static uniaxial tensile response for notched specimens 1624.5. Conclusions 1724.6. References 173Chapter 5. Some Advantages of Advanced Inverse Methods to Identify Viscoplastic and Damage Material Model Parameters 177Bertrand LANGRAND, Delphine NOTTA-CUVIER, Thomas FOUREST and Eric MARKIEWICZ5.1. Introduction 1775.2. Experimental devices for material characterization over a large range of strain rates 1805.3. Identification of elasto-viscoplastic and damage material Parameters 1845.3.1. Direct approach for material parameter identification 1845.3.2. Inverse approaches for material parameter identification 1925.4. Conclusions 2045.5. Acknowledgments 2055.6. References 205Chapter 6. Laser Shock Experiments to Investigate Fragmentation at Extreme Strain Rates 213Thibaut DE RESSÉGUIER, Didier LOISON, Benjamin JODAR, Emilien LESCOUTE,Caroline ROLAND, Loïc SIGNOR and André DRAGON6.1. Introduction 2146.2. Phenomenology of laser shock-induced fragmentation 2156.3. Spall fracture 2176.4. Microspall after shock-induced melting 2226.5. Microjetting from geometrical defects 2256.6. Conclusion 2306.7. References 231Chapter 7. One-dimensional Models for Dynamic Fragmentation of Brittle Materials 237David CERECEDA, Nitin DAPHALAPURKAR and Lori GRAHAM BRADY7.1. Introduction 2377.2. Methods 2427.3. Results 2447.3.1. Mono-phase materials 2447.3.2. Multi-phase materials 2517.4. Conclusions 2587.5. References 259Chapter 8. Damage and Wave Propagation in Brittle Materials 263Quriaky GOMEZ, Jia LI and Ioan R. IONESCU8.1. Introduction 2638.2. Short overview of damage models 2648.2.1. Effective elasticity of a cracked solid 2668.2.2. Damage evolution 2688.3. 1D wave propagation 2758.3.1. Problem statement 2768.3.2. A single family of micro-cracks 2788.3.3. Three families of micro-cracks 2808.4. Two-dimensional anti-plane wave propagation 2808.4.1. Anisotropic damage under isotropic loading 2818.4.2. Anisotropic loading of an initial isotropic damaged material 2848.5. Blast impact and damage evolution 2868.6. Conclusions and perspectives 2918.7. Acknowledgments 2928.8. References 292Chapter 9. Discrete Element Analysis to Predict Penetration and Perforation of Concrete Targets Struck by Rigid Projectiles 297Laurent DAUDEVILLE, Andria ANTONIOU, Ahmad OMAR, Philippe MARIN, Serguei POTAPOV and Christophe PONTIROLI9.1. Introduction 2979.2. Discrete element model 2999.2.1. Definition of interactions 2999.2.2. Constitutive behavior of concrete: Discrete element model 3009.2.3. Linear elastic constitutive behavior 3019.2.4. Nonlinear constitutive behavior 3029.2.5. Strain rate dependency 3059.3. Simulation of impacts 3079.3.1. Impact experiments 3079.3.2. Modeling of impact experiments 3089.4. Conclusion 3119.5. References 311Chapter 10. Bifurcation Micromechanics in Granular Materials 315Antoine WAUTIER, Jiaying LIU, François NICOT and Félix DARVE10.1. Introduction 31510.2. Application of the second-order work criterion at representative volume element scale 31810.3. From macro to micro analysis of instability 32210.3.1. Local second-order work and contact sliding 32210.3.2. Role of strong contact network in stable and unstable loading directions 32310.3.3. From contact sliding to mesoscale mechanisms 32610.3.4. Micromechanisms leading to bifurcation at the representative volume element scale 32910.4. Diffuse and localized failure in a unified framework 33110.4.1. Diffuse and localized failure pattern 33110.4.2. Common micromechanisms and microstructures 33210.5. Conclusion 33410.6. References 335Chapter 11. Influence of Specimen Size on the Dynamic Response of Concrete 339Xu NIE, William F. HEARD and Bradley E. MARTIN11.1. Introduction 33911.2. Materials and specimens 34111.3. Experimental techniques 34311.3.1. Kolsky compression bar theory and set-up 34311.3.2. Pulse shaping technique 34511.4. Results and discussion 35011.4.1. Pulse shaper design for Kolsky compression bar systems 35011.4.2. Rate and specimen size effect on failure strength 35511.5. Conclusion 36011.6. Acknowledgments 36211.7. References 362Chapter 12. Shockless Characterization of Ceramics Using High-Pulsed Power Technologies 365Jean-Luc ZINSZNER, Benjamin ERZAR and Pascal FORQUIN12.1. Introduction 36512.1.1. Presentation of the silicon carbide grades 36712.2. Principle of the GEPI generator 36812.3. Dynamic compression of ceramics 37012.3.1. Lagrangian analysis of velocity profiles 37112.3.2. Experimental results 37212.4. Dynamic tensile strength of ceramics 37412.4.1. Experimental methodology and data processing 37512.4.2. Characterization of two silicon carbide grades 37712.4.3. Post-mortem analyses of damaged samples 37812.5. Conclusions 38012.6. Acknowledgments 38112.7. References 381Chapter 13. A Eulerian Level Set-based Framework for Reactive Meso-scale Analysis of Heterogeneous Energetic Materials 387Nirmal KUMAR RAI and H.S. UDAYKUMAR13.1. Introduction 38713.2. Numerical framework 39013.2.1. Governing equations 39013.2.2. Constitutive model for HMX 39013.2.3. Reactive modeling of HMX 39313.2.4. Level set representation of embedded interface 39513.2.5. Image processing approach: Representing real geometries 39513.3. Results 39813.3.1. Grid refinement study 40013.3.2. Collapse behavior of voids present in the pressed HMX material 40113.3.3. Criticality conditions for Class III and Class V samples 40313.3.4. Meso-scale criticality conditions for pressed energetic materials 40513.4. Conclusions 41113.5. Acknowledgments 41213.6. References 412Chapter 14. A Well-posed Hypoelastic Model Derived From a Hyperelastic One 417Nicolas FAVRIE and Sergey GAVRILYUK14.1. Introduction 41714.2. A general hyperelastic model formulation 41814.3. Evolution equation for the deviatoric part of the stress tensor: neo-Hookean solids 42014.3.1. Expression of tr(b) as a function of the invariants of S 42114.3.2. Hypoelastic formulation 42314.4. Conclusions 42414.5. Acknowledgments 42514.6. References 425Appendix A: Case a = 0.5 429List of Authors 433Index 437