{"product_id":"dynamics-of-lattice-materials-hardback-9781118729595","title":"Dynamics of Lattice Materials (Hardback) 9781118729595","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eDynamics of Lattice Materials\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eA. Srikantha Phani (Edited by), Mahmoud I. Hussein (Edited by)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781118729595, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 22 September 2017\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e312 pages\u003cbr\u003e24.6 x 17.3 x 2 cm, 0.658 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cul\u003e \u003cli\u003eProvides a comprehensive introduction to the dynamic response of lattice materials, covering the fundamental theory and applications in engineering practice\u003c\/li\u003e \u003cli\u003eOffers comprehensive treatment of dynamics of lattice materials and periodic materials in general, including phononic crystals and elastic metamaterials\u003c\/li\u003e \u003cli\u003eProvides an in depth introduction to elastostatics and elastodynamics of lattice materials\u003c\/li\u003e \u003cli\u003eCovers advanced topics such as damping, nonlinearity, instability, impact and nanoscale systems\u003c\/li\u003e \u003cli\u003eIntroduces contemporary concepts including pentamodes, local resonance and inertial amplification\u003c\/li\u003e \u003cli\u003eIncludes chapters on fast computation and design optimization tools\u003c\/li\u003e \u003cli\u003eTopics are introduced using simple systems and generalized to more complex structures with a focus on dispersion characteristics\u003c\/li\u003e \u003c\/ul\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003eList of Contributors xiii\u003c\/p\u003e \u003cp\u003eForeword xv\u003c\/p\u003e \u003cp\u003ePreface xxv\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction to Lattice Materials 1\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eA. Srikantha Phani andMahmoud I. Hussein\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e1.1 Introduction 1\u003c\/p\u003e \u003cp\u003e1.2 Lattice Materials and Structures 2\u003c\/p\u003e \u003cp\u003e1.2.1 Material versus Structure 3\u003c\/p\u003e \u003cp\u003e1.2.2 Motivation 3\u003c\/p\u003e \u003cp\u003e1.2.3 Classification of Lattices and Maxwell’s Rule 4\u003c\/p\u003e \u003cp\u003e1.2.4 ManufacturingMethods 6\u003c\/p\u003e \u003cp\u003e1.2.5 Applications 7\u003c\/p\u003e \u003cp\u003e1.3 Overview of Chapters 8\u003c\/p\u003e \u003cp\u003eAcknowledgment 10\u003c\/p\u003e \u003cp\u003eReferences 10\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Elastostatics of Lattice Materials 19\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eD. Pasini and S. Arabnejad\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 19\u003c\/p\u003e \u003cp\u003e2.2 The RVE 21\u003c\/p\u003e \u003cp\u003e2.3 Surface Average Approach 22\u003c\/p\u003e \u003cp\u003e2.4 Volume Average Approach 25\u003c\/p\u003e \u003cp\u003e2.5 Force-based Approach 25\u003c\/p\u003e \u003cp\u003e2.6 Asymptotic Homogenization Method 26\u003c\/p\u003e \u003cp\u003e2.7 Generalized Continuum Theory 29\u003c\/p\u003e \u003cp\u003e2.8 Homogenization via BlochWave Analysis and the Cauchy–Born Hypothesis 32\u003c\/p\u003e \u003cp\u003e2.9 Multiscale Matrix-based Computational Technique 34\u003c\/p\u003e \u003cp\u003e2.10 Homogenization based on the Equation of Motion 36\u003c\/p\u003e \u003cp\u003e2.11 Case Study: Property Predictions for a Hexagonal Lattice 38\u003c\/p\u003e \u003cp\u003e2.12 Conclusions 42\u003c\/p\u003e \u003cp\u003eReferences 43\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Elastodynamics of Lattice Materials 53\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eA. Srikantha Phani\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 53\u003c\/p\u003e \u003cp\u003e3.2 One-dimensional Lattices 55\u003c\/p\u003e \u003cp\u003e3.2.1 Bloch’s Theorem 57\u003c\/p\u003e \u003cp\u003e3.2.2 Application of Bloch’s Theorem 59\u003c\/p\u003e \u003cp\u003e3.2.3 Dispersion Curves and Unit-cell Resonances 59\u003c\/p\u003e \u003cp\u003e3.2.4 Continuous Lattices: Local Resonance and sub-Bragg Band Gaps 61\u003c\/p\u003e \u003cp\u003e3.2.5 Dispersion Curves of a Beam Lattice 62\u003c\/p\u003e \u003cp\u003e3.2.6 Receptance Method 64\u003c\/p\u003e \u003cp\u003e3.2.7 Synopsis of 1D Lattices 67\u003c\/p\u003e \u003cp\u003e3.3 Two-dimensional Lattice Materials 67\u003c\/p\u003e \u003cp\u003e3.3.1 Application of Bloch’s Theorem to 2D Lattices 67\u003c\/p\u003e \u003cp\u003e3.3.2 Discrete Square Lattice 70\u003c\/p\u003e \u003cp\u003e3.4 Lattice Materials 72\u003c\/p\u003e \u003cp\u003e3.4.1 Finite Element Modelling of the Unit Cell 75\u003c\/p\u003e \u003cp\u003e3.4.2 Band Structure of Lattice Topologies 77\u003c\/p\u003e \u003cp\u003e3.4.3 Directionality ofWave Propagation 84\u003c\/p\u003e \u003cp\u003e3.5 Tunneling and EvanescentWaves 85\u003c\/p\u003e \u003cp\u003e3.6 Concluding Remarks 87\u003c\/p\u003e \u003cp\u003e3.7 Acknowledgments 87\u003c\/p\u003e \u003cp\u003eReferences 87\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Wave Propagation in Damped Lattice Materials 93\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eDimitri Krattiger, A. Srikantha Phani andMahmoud I. Hussein\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 93\u003c\/p\u003e \u003cp\u003e4.2 One-dimensionalMass–Spring–DamperModel 95\u003c\/p\u003e \u003cp\u003e4.2.1 1D Model Description 95\u003c\/p\u003e \u003cp\u003e4.2.2 Free-wave Solution 96\u003c\/p\u003e \u003cp\u003eState-spaceWave Calculation 97\u003c\/p\u003e \u003cp\u003eBloch–Rayleigh Perturbation Method 97\u003c\/p\u003e \u003cp\u003e4.2.3 Driven-wave Solution 98\u003c\/p\u003e \u003cp\u003e4.2.4 1D Damped Band Structures 98\u003c\/p\u003e \u003cp\u003e4.3 Two-dimensional Plate–Plate Lattice Model 99\u003c\/p\u003e \u003cp\u003e4.3.1 2D Model Description 99\u003c\/p\u003e \u003cp\u003e4.3.2 Extension of Driven-wave Calculations to 2D Domains 100\u003c\/p\u003e \u003cp\u003e4.3.3 2D Damped Band Structures 101\u003c\/p\u003e \u003cp\u003eReferences 104\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Wave Propagation in Nonlinear Lattice Materials 107\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eKevin L.Manktelow,Massimo Ruzzene andMichael J. Leamy\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e5.1 Overview 107\u003c\/p\u003e \u003cp\u003e5.2 Weakly Nonlinear Dispersion Analysis 108\u003c\/p\u003e \u003cp\u003e5.3 Application to a 1D Monoatomic Chain 114\u003c\/p\u003e \u003cp\u003e5.3.1 Overview 114\u003c\/p\u003e \u003cp\u003e5.3.2 Model Description and Nonlinear Governing Equation 114\u003c\/p\u003e \u003cp\u003e5.3.3 Single-wave Dispersion Analysis 115\u003c\/p\u003e \u003cp\u003e5.3.4 Multi-wave Dispersion Analysis 116\u003c\/p\u003e \u003cp\u003eCase 1. GeneralWave–Wave Interactions 117\u003c\/p\u003e \u003cp\u003eCase 2. Long-wavelength LimitWave–Wave Interactions 119\u003c\/p\u003e \u003cp\u003e5.3.5 Numerical Verification and Discussion 122\u003c\/p\u003e \u003cp\u003e5.4 Application to a 2D Monoatomic Lattice 123\u003c\/p\u003e \u003cp\u003e5.4.1 Overview 123\u003c\/p\u003e \u003cp\u003e5.4.2 Model Description and Nonlinear Governing Equation 124\u003c\/p\u003e \u003cp\u003e5.4.3 Multiple-scale Perturbation Analysis 125\u003c\/p\u003e \u003cp\u003e5.4.4 Analysis of Predicted Dispersion Shifts 127\u003c\/p\u003e \u003cp\u003e5.4.5 Numerical Simulation Validation Cases 129\u003c\/p\u003e \u003cp\u003eAnalysis Method 130\u003c\/p\u003e \u003cp\u003eOrthogonal and Oblique Interaction 131\u003c\/p\u003e \u003cp\u003e5.4.6 Application: Amplitude-tunable Focusing 133\u003c\/p\u003e \u003cp\u003eSummary 134\u003c\/p\u003e \u003cp\u003eAcknowledgements 135\u003c\/p\u003e \u003cp\u003eReferences 135\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Stability of Lattice Materials 139\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eFilippo Casadei, PaiWang and Katia Bertoldi\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 139\u003c\/p\u003e \u003cp\u003e6.2 Geometry, Material, and Loading Conditions 140\u003c\/p\u003e \u003cp\u003e6.3 Stability of Finite-sized Specimens 141\u003c\/p\u003e \u003cp\u003e6.4 Stability of Infinite Periodic Specimens 142\u003c\/p\u003e \u003cp\u003e6.4.1 Microscopic Instability 142\u003c\/p\u003e \u003cp\u003e6.5 Post-buckling Analysis 145\u003c\/p\u003e \u003cp\u003e6.6 Effect of Buckling and Large Deformation on the Propagation Of Elastic Waves 146\u003c\/p\u003e \u003cp\u003e6.7 Conclusions 150\u003c\/p\u003e \u003cp\u003eReferences 151\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Impact and Blast Response of Lattice Materials 155\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eMatthew Smith,Wesley J. Cantwell and Zhongwei Guan\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 155\u003c\/p\u003e \u003cp\u003e7.2 Literature Review 155\u003c\/p\u003e \u003cp\u003e7.2.1 Dynamic Response of Cellular Structures 155\u003c\/p\u003e \u003cp\u003e7.2.2 Shock- and Blast-loading Responses of Cellular Structures 157\u003c\/p\u003e \u003cp\u003e7.2.3 Dynamic Indentation Performance of Cellular Structures 158\u003c\/p\u003e \u003cp\u003e7.3 Manufacturing Process 159\u003c\/p\u003e \u003cp\u003e7.3.1 The Selective Laser Melting Technique 159\u003c\/p\u003e \u003cp\u003e7.3.2 Sandwich Panel Manufacture 160\u003c\/p\u003e \u003cp\u003e7.4 Dynamic and Blast Loading of Lattice Materials 161\u003c\/p\u003e \u003cp\u003e7.4.1 ExperimentalMethod – Drop-hammer Impact Tests 161\u003c\/p\u003e \u003cp\u003e7.4.2 ExperimentalMethod – Blast Tests on Lattice Cubes 162\u003c\/p\u003e \u003cp\u003e7.4.3 ExperimentalMethod – Blast Tests on Composite-lattice Sandwich Structures 163\u003c\/p\u003e \u003cp\u003e7.5 Results and Discussion 165\u003c\/p\u003e \u003cp\u003e7.5.1 Drop-hammer Impact Tests 165\u003c\/p\u003e \u003cp\u003e7.5.2 Blast Tests on the Lattice Structures 167\u003c\/p\u003e \u003cp\u003e7.5.3 Blast Tests on the Sandwich Panels 170\u003c\/p\u003e \u003cp\u003eConcluding Remarks 173\u003c\/p\u003e \u003cp\u003eAcknowledgements 174\u003c\/p\u003e \u003cp\u003eReferences 174\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Pentamode Lattice Structures 179\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eAndrew N. Norris\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 179\u003c\/p\u003e \u003cp\u003e8.2 Pentamode Materials 183\u003c\/p\u003e \u003cp\u003e8.2.1 General Properties 183\u003c\/p\u003e \u003cp\u003e8.2.2 Small Rigidity and Poisson’s Ratio of a PM 185\u003c\/p\u003e \u003cp\u003e8.2.3 Wave Motion in a PM 186\u003c\/p\u003e \u003cp\u003e8.3 Lattice Models for PM 187\u003c\/p\u003e \u003cp\u003e8.3.1 Effective PM Properties of 2D and 3D Lattices 187\u003c\/p\u003e \u003cp\u003e8.3.2 Transversely Isotropic PM Lattice 188\u003c\/p\u003e \u003cp\u003eEffective Moduli: 2D 190\u003c\/p\u003e \u003cp\u003e8.4 Quasi-static Pentamode Properties of a Lattice in 2D and 3D 192\u003c\/p\u003e \u003cp\u003e8.4.1 General Formulation with Rigidity 192\u003c\/p\u003e \u003cp\u003e8.4.2 Pentamode Limit 194\u003c\/p\u003e \u003cp\u003e8.4.3 Two-dimensional Results for Finite Rigidity 195\u003c\/p\u003e \u003cp\u003e8.5 Conclusion 195\u003c\/p\u003e \u003cp\u003eAcknowledgements 196\u003c\/p\u003e \u003cp\u003eReferences 196\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Modal Reduction of Lattice Material Models 199\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eDimitri Krattiger and Mahmoud I. Hussein\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 199\u003c\/p\u003e \u003cp\u003e9.2 Plate Model 200\u003c\/p\u003e \u003cp\u003e9.2.1 Mindlin–Reissner Plate Finite Elements 200\u003c\/p\u003e \u003cp\u003e9.2.2 Bloch Boundary Conditions 202\u003c\/p\u003e \u003cp\u003e9.2.3 Example Model 203\u003c\/p\u003e \u003cp\u003e9.3 Reduced Bloch Mode Expansion 204\u003c\/p\u003e \u003cp\u003e9.3.1 RBME Formulation 204\u003c\/p\u003e \u003cp\u003e9.3.2 RBME Example 205\u003c\/p\u003e \u003cp\u003e9.3.3 RBME Additional Considerations 207\u003c\/p\u003e \u003cp\u003e9.4 Bloch Mode Synthesis 208\u003c\/p\u003e \u003cp\u003e9.4.1 BMS Formulation 208\u003c\/p\u003e \u003cp\u003e9.4.2 BMS Example 210\u003c\/p\u003e \u003cp\u003e9.4.3 BMS Additional Considerations 210\u003c\/p\u003e \u003cp\u003e9.5 Comparison of RBME and BMS 212\u003c\/p\u003e \u003cp\u003e9.5.1 Model Size 212\u003c\/p\u003e \u003cp\u003e9.5.2 Computational Efficiency 213\u003c\/p\u003e \u003cp\u003e9.5.3 Ease of Implementation 214\u003c\/p\u003e \u003cp\u003eReferences 214\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Topology Optimization of Lattice Materials 217\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eOsama R. Bilal and Mahmoud I. Hussein\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 217\u003c\/p\u003e \u003cp\u003e10.2 Unit-cell Optimization 218\u003c\/p\u003e \u003cp\u003e10.2.1 Parametric, Shape, and Topology Optimization 218\u003c\/p\u003e \u003cp\u003e10.2.2 Selection of Studies from the Literature 218\u003c\/p\u003e \u003cp\u003e10.2.3 Design Search Space 219\u003c\/p\u003e \u003cp\u003e10.3 Plate-based Lattice Material Unit Cell 220\u003c\/p\u003e \u003cp\u003e10.3.1 Equation of Motion and FE Model 221\u003c\/p\u003e \u003cp\u003e10.3.2 Mathematical Formulation 222\u003c\/p\u003e \u003cp\u003e10.4 Genetic Algorithm 223\u003c\/p\u003e \u003cp\u003e10.4.1 Objective Function 223\u003c\/p\u003e \u003cp\u003e10.4.2 Fitness Function 224\u003c\/p\u003e \u003cp\u003e10.4.3 Selection 224\u003c\/p\u003e \u003cp\u003e10.4.4 Reproduction 224\u003c\/p\u003e \u003cp\u003e10.4.5 Initialization and Termination 225\u003c\/p\u003e \u003cp\u003e10.4.6 Implementation 225\u003c\/p\u003e \u003cp\u003e10.5 Appendix 226\u003c\/p\u003e \u003cp\u003eReferences 228\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Dynamics of Locally Resonant and Inertially Amplified Lattice Materials 233\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eCetin Yilmaz and Gregory M. Hulbert\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 233\u003c\/p\u003e \u003cp\u003e11.2 Locally Resonant Lattice Materials 234\u003c\/p\u003e \u003cp\u003e11.2.1 1D Locally Resonant Lattices 234\u003c\/p\u003e \u003cp\u003e11.2.2 2D Locally Resonant Lattices 241\u003c\/p\u003e \u003cp\u003e11.2.3 3D Locally Resonant Lattices 243\u003c\/p\u003e \u003cp\u003e11.3 Inertially Amplified Lattice Materials 246\u003c\/p\u003e \u003cp\u003e11.3.1 1D Inertially Amplified Lattices 246\u003c\/p\u003e \u003cp\u003e11.3.2 2D Inertially Amplified Lattices 248\u003c\/p\u003e \u003cp\u003e11.3.3 3D Inertially Amplified Lattices 253\u003c\/p\u003e \u003cp\u003e11.4 Conclusions 255\u003c\/p\u003e \u003cp\u003eReferences 256\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Dynamics of Nanolattices: Polymer-Nanometal Lattices 259\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eCraig A. Steeves, Glenn D. Hibbard,Manan Arya, and Ante T. Lausic\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e12.1 Introduction 259\u003c\/p\u003e \u003cp\u003e12.2 Fabrication 259\u003c\/p\u003e \u003cp\u003e12.2.1 Case Study 262\u003c\/p\u003e \u003cp\u003e12.3 Lattice Dynamics 263\u003c\/p\u003e \u003cp\u003e12.3.1 Lattice Properties 264\u003c\/p\u003e \u003cp\u003eGeometries of 3D Lattices 264\u003c\/p\u003e \u003cp\u003eEffective Material Properties of Nanometal-coated Polymer Lattices 265\u003c\/p\u003e \u003cp\u003e12.3.2 Finite-elementModel 266\u003c\/p\u003e \u003cp\u003eDisplacement Field 266\u003c\/p\u003e \u003cp\u003eKinetic Energy 268\u003c\/p\u003e \u003cp\u003eStrain Potential Energy 269\u003c\/p\u003e \u003cp\u003eCollected Equation of Motion 270\u003c\/p\u003e \u003cp\u003e12.3.3 Floquet–Bloch Principles 271\u003c\/p\u003e \u003cp\u003eGeneralized Forces in Bloch Analysis 272\u003c\/p\u003e \u003cp\u003eReduced Equation of Motion 274\u003c\/p\u003e \u003cp\u003e12.3.4 Dispersion Curves for the Octet Lattice 275\u003c\/p\u003e \u003cp\u003e12.3.5 Lattice Tuning 277\u003c\/p\u003e \u003cp\u003eBandgap Placement 277\u003c\/p\u003e \u003cp\u003eLattice Optimization 277\u003c\/p\u003e \u003cp\u003e12.4 Conclusions 278\u003c\/p\u003e \u003cp\u003e12.5 Appendix: Shape Functions for a Timoshenko Beam with Six Nodal Degrees\u003c\/p\u003e \u003cp\u003eof Freedom 279\u003c\/p\u003e \u003cp\u003eReferences 280\u003c\/p\u003e \u003cp\u003eIndex 283\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mechanical engineering \u0026amp; materials [\u003ca title=\"See our other books on Mechanical engineering \u0026amp; materials\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mechanical%20engineering%20\u0026amp;%20materials%20%5BTG%5D%22\"\u003eTG\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley","offers":[{"title":"Brand New","offer_id":52511411568920,"sku":"9781118729595","price":94.46,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781118729595.jpg?v=1786599557","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/dynamics-of-lattice-materials-hardback-9781118729595","provider":"Freshly Printed Books","version":"1.0","type":"link"}