Dynamics of Lattice Materials (eBook, PDF)

Redaktion: Phani, A. Srikantha; Hussein, Mahmoud I.

• Format: PDF

Produktbeschreibung

* Provides a comprehensive introduction to the dynamic response of lattice materials, covering the fundamental theory and applications in engineering practice * Offers comprehensive treatment of dynamics of lattice materials and periodic materials in general, including phononic crystals and elastic metamaterials * Provides an in depth introduction to elastostatics and elastodynamics of lattice materials * Covers advanced topics such as damping, nonlinearity, instability, impact and nanoscale systems * Introduces contemporary concepts including pentamodes, local resonance and inertial amplification * Includes chapters on fast computation and design optimization tools * Topics are introduced using simple systems and generalized to more complex structures with a focus on dispersion characteristics

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Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 312
• Erscheinungstermin: 10. Juli 2017
• Englisch
• ISBN-13: 9781118729564
• Artikelnr.: 52554504

Autorenporträt

Editors A. Srikantha Phani, University of British Columbia, Canada Mahmoud I. Hussein, University of Colorado Boulder, USA

Inhaltsangabe

List of Contributors xiii Foreword xv Preface xxv 1 Introduction to Lattice
Materials 1 A. Srikantha Phani andMahmoud I. Hussein 1.1 Introduction 1 1.2
Lattice Materials and Structures 2 1.2.1 Material versus Structure 3 1.2.2
Motivation 3 1.2.3 Classification of Lattices and Maxwell's Rule 4 1.2.4
ManufacturingMethods 6 1.2.5 Applications 7 1.3 Overview of Chapters 8
Acknowledgment 10 References 10 2 Elastostatics of Lattice Materials 19 D.
Pasini and S. Arabnejad 2.1 Introduction 19 2.2 The RVE 21 2.3 Surface
Average Approach 22 2.4 Volume Average Approach 25 2.5 Force-based Approach
25 2.6 Asymptotic Homogenization Method 26 2.7 Generalized Continuum Theory
29 2.8 Homogenization via BlochWave Analysis and the Cauchy-Born Hypothesis
32 2.9 Multiscale Matrix-based Computational Technique 34 2.10
Homogenization based on the Equation of Motion 36 2.11 Case Study: Property
Predictions for a Hexagonal Lattice 38 2.12 Conclusions 42 References 43 3
Elastodynamics of Lattice Materials 53 A. Srikantha Phani 3.1 Introduction
53 3.2 One-dimensional Lattices 55 3.2.1 Bloch's Theorem 57 3.2.2
Application of Bloch's Theorem 59 3.2.3 Dispersion Curves and Unit-cell
Resonances 59 3.2.4 Continuous Lattices: Local Resonance and sub-Bragg Band
Gaps 61 3.2.5 Dispersion Curves of a Beam Lattice 62 3.2.6 Receptance
Method 64 3.2.7 Synopsis of 1D Lattices 67 3.3 Two-dimensional Lattice
Materials 67 3.3.1 Application of Bloch's Theorem to 2D Lattices 67 3.3.2
Discrete Square Lattice 70 3.4 Lattice Materials 72 3.4.1 Finite Element
Modelling of the Unit Cell 75 3.4.2 Band Structure of Lattice Topologies 77
3.4.3 Directionality ofWave Propagation 84 3.5 Tunneling and
EvanescentWaves 85 3.6 Concluding Remarks 87 3.7 Acknowledgments 87
References 87 4 Wave Propagation in Damped Lattice Materials 93 Dimitri
Krattiger, A. Srikantha Phani andMahmoud I. Hussein 4.1 Introduction 93 4.2
One-dimensionalMass-Spring-DamperModel 95 4.2.1 1D Model Description 95
4.2.2 Free-wave Solution 96 State-spaceWave Calculation 97 Bloch-Rayleigh
Perturbation Method 97 4.2.3 Driven-wave Solution 98 4.2.4 1D Damped Band
Structures 98 4.3 Two-dimensional Plate-Plate Lattice Model 99 4.3.1 2D
Model Description 99 4.3.2 Extension of Driven-wave Calculations to 2D
Domains 100 4.3.3 2D Damped Band Structures 101 References 104 5 Wave
Propagation in Nonlinear Lattice Materials 107 Kevin L.Manktelow,Massimo
Ruzzene andMichael J. Leamy 5.1 Overview 107 5.2 Weakly Nonlinear
Dispersion Analysis 108 5.3 Application to a 1D Monoatomic Chain 114 5.3.1
Overview 114 5.3.2 Model Description and Nonlinear Governing Equation 114
5.3.3 Single-wave Dispersion Analysis 115 5.3.4 Multi-wave Dispersion
Analysis 116 Case 1. GeneralWave-Wave Interactions 117 Case 2.
Long-wavelength LimitWave-Wave Interactions 119 5.3.5 Numerical
Verification and Discussion 122 5.4 Application to a 2D Monoatomic Lattice
123 5.4.1 Overview 123 5.4.2 Model Description and Nonlinear Governing
Equation 124 5.4.3 Multiple-scale Perturbation Analysis 125 5.4.4 Analysis
of Predicted Dispersion Shifts 127 5.4.5 Numerical Simulation Validation
Cases 129 Analysis Method 130 Orthogonal and Oblique Interaction 131 5.4.6
Application: Amplitude-tunable Focusing 133 Summary 134 Acknowledgements
135 References 135 6 Stability of Lattice Materials 139 Filippo Casadei,
PaiWang and Katia Bertoldi 6.1 Introduction 139 6.2 Geometry, Material, and
Loading Conditions 140 6.3 Stability of Finite-sized Specimens 141 6.4
Stability of Infinite Periodic Specimens 142 6.4.1 Microscopic Instability
142 6.5 Post-buckling Analysis 145 6.6 Effect of Buckling and Large
Deformation on the Propagation Of Elastic Waves 146 6.7 Conclusions 150
References 151 7 Impact and Blast Response of Lattice Materials 155 Matthew
Smith,Wesley J. Cantwell and Zhongwei Guan 7.1 Introduction 155 7.2
Literature Review 155 7.2.1 Dynamic Response of Cellular Structures 155
7.2.2 Shock- and Blast-loading Responses of Cellular Structures 157 7.2.3
Dynamic Indentation Performance of Cellular Structures 158 7.3
Manufacturing Process 159 7.3.1 The Selective Laser Melting Technique 159
7.3.2 Sandwich Panel Manufacture 160 7.4 Dynamic and Blast Loading of
Lattice Materials 161 7.4.1 ExperimentalMethod - Drop-hammer Impact Tests
161 7.4.2 ExperimentalMethod - Blast Tests on Lattice Cubes 162 7.4.3
ExperimentalMethod - Blast Tests on Composite-lattice Sandwich Structures
163 7.5 Results and Discussion 165 7.5.1 Drop-hammer Impact Tests 165 7.5.2
Blast Tests on the Lattice Structures 167 7.5.3 Blast Tests on the Sandwich
Panels 170 Concluding Remarks 173 Acknowledgements 174 References 174 8
Pentamode Lattice Structures 179 Andrew N. Norris 8.1 Introduction 179 8.2
Pentamode Materials 183 8.2.1 General Properties 183 8.2.2 Small Rigidity
and Poisson's Ratio of a PM 185 8.2.3 Wave Motion in a PM 186 8.3 Lattice
Models for PM 187 8.3.1 Effective PM Properties of 2D and 3D Lattices 187
8.3.2 Transversely Isotropic PM Lattice 188 Effective Moduli: 2D 190 8.4
Quasi-static Pentamode Properties of a Lattice in 2D and 3D 192 8.4.1
General Formulation with Rigidity 192 8.4.2 Pentamode Limit 194 8.4.3
Two-dimensional Results for Finite Rigidity 195 8.5 Conclusion 195
Acknowledgements 196 References 196 9 Modal Reduction of Lattice Material
Models 199 Dimitri Krattiger and Mahmoud I. Hussein 9.1 Introduction 199
9.2 Plate Model 200 9.2.1 Mindlin-Reissner Plate Finite Elements 200 9.2.2
Bloch Boundary Conditions 202 9.2.3 Example Model 203 9.3 Reduced Bloch
Mode Expansion 204 9.3.1 RBME Formulation 204 9.3.2 RBME Example 205 9.3.3
RBME Additional Considerations 207 9.4 Bloch Mode Synthesis 208 9.4.1 BMS
Formulation 208 9.4.2 BMS Example 210 9.4.3 BMS Additional Considerations
210 9.5 Comparison of RBME and BMS 212 9.5.1 Model Size 212 9.5.2
Computational Efficiency 213 9.5.3 Ease of Implementation 214 References
214 10 Topology Optimization of Lattice Materials 217 Osama R. Bilal and
Mahmoud I. Hussein 10.1 Introduction 217 10.2 Unit-cell Optimization 218
10.2.1 Parametric, Shape, and Topology Optimization 218 10.2.2 Selection of
Studies from the Literature 218 10.2.3 Design Search Space 219 10.3
Plate-based Lattice Material Unit Cell 220 10.3.1 Equation of Motion and FE
Model 221 10.3.2 Mathematical Formulation 222 10.4 Genetic Algorithm 223
10.4.1 Objective Function 223 10.4.2 Fitness Function 224 10.4.3 Selection
224 10.4.4 Reproduction 224 10.4.5 Initialization and Termination 225
10.4.6 Implementation 225 10.5 Appendix 226 References 228 11 Dynamics of
Locally Resonant and Inertially Amplified Lattice Materials 233 Cetin
Yilmaz and Gregory M. Hulbert 11.1 Introduction 233 11.2 Locally Resonant
Lattice Materials 234 11.2.1 1D Locally Resonant Lattices 234 11.2.2 2D
Locally Resonant Lattices 241 11.2.3 3D Locally Resonant Lattices 243 11.3
Inertially Amplified Lattice Materials 246 11.3.1 1D Inertially Amplified
Lattices 246 11.3.2 2D Inertially Amplified Lattices 248 11.3.3 3D
Inertially Amplified Lattices 253 11.4 Conclusions 255 References 256 12
Dynamics of Nanolattices: Polymer-Nanometal Lattices 259 Craig A. Steeves,
Glenn D. Hibbard,Manan Arya, and Ante T. Lausic 12.1 Introduction 259 12.2
Fabrication 259 12.2.1 Case Study 262 12.3 Lattice Dynamics 263 12.3.1
Lattice Properties 264 Geometries of 3D Lattices 264 Effective Material
Properties of Nanometal-coated Polymer Lattices 265 12.3.2
Finite-elementModel 266 Displacement Field 266 Kinetic Energy 268 Strain
Potential Energy 269 Collected Equation of Motion 270 12.3.3 Floquet-Bloch
Principles 271 Generalized Forces in Bloch Analysis 272 Reduced Equation of
Motion 274 12.3.4 Dispersion Curves for the Octet Lattice 275 12.3.5
Lattice Tuning 277 Bandgap Placement 277 Lattice Optimization 277 12.4
Conclusions 278 12.5 Appendix: Shape Functions for a Timoshenko Beam with
Six Nodal Degrees of Freedom 279 References 280 Index 283