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Format: 1 online resource

ISBN: 9781118729564 , 1118729560 , 9781118729588 , 1118729587

Note: Cover -- Title Page -- Copyright -- Dedication -- Contents -- List of Contributors -- Foreword -- Preface -- Chapter 1 Introduction to Lattice Materials -- 1.1 Introduction -- 1.2 Lattice Materials and Structures -- 1.2.1 Material versus Structure -- 1.2.2 Motivation -- 1.2.3 Classification of Lattices and Maxwell's Rule -- 1.2.4 Manufacturing Methods -- 1.2.5 Applications -- 1.3 Overview of Chapters -- Acknowledgment -- References -- Chapter 2 Elastostatics of Lattice Materials -- 2.1 Introduction -- 2.2 The RVE -- 2.3 Surface Average Approach -- 2.4 Volume Average Approach -- 2.5 Force-based Approach -- 2.6 Asymptotic Homogenization Method -- 2.7 Generalized Continuum Theory -- 2.8 Homogenization via Bloch Wave Analysis and the Cauchy-Born Hypothesis -- 2.9 Multiscale Matrix-based Computational Technique -- 2.10 Homogenization based on the Equation of Motion -- 2.11 Case Study: Property Predictions for a Hexagonal Lattice -- 2.12 Conclusions -- References -- Chapter 3 Elastodynamics of Lattice Materials -- 3.1 Introduction -- 3.2 One-dimensional Lattices -- 3.2.1 Bloch's Theorem -- 3.2.2 Application of Bloch's Theorem -- 3.2.3 Dispersion Curves and Unit-cell Resonances -- 3.2.4 Continuous Lattices: Local Resonance and sub-Bragg Band Gaps -- 3.2.5 Dispersion Curves of a Beam Lattice -- 3.2.6 Receptance Method -- 3.2.7 Synopsis of 1D Lattices -- 3.3 Two-dimensional Lattice Materials -- 3.3.1 Application of Bloch's Theorem to 2D Lattices -- 3.3.2 Discrete Square Lattice -- 3.4 Lattice Materials -- 3.4.1 Finite Element Modelling of the Unit Cell -- 3.4.2 Band Structure of Lattice Topologies -- 3.4.3 Directionality of Wave Propagation -- 3.5 Tunneling and Evanescent Waves -- 3.6 Concluding Remarks -- 3.7 Acknowledgments -- References -- Chapter 4 Wave Propagation in Damped Lattice Materials -- 4.1 Introduction. , 4.2 One-dimensional Mass-Spring-Damper Model -- 4.2.1 1D Model Description -- 4.2.2 Free-wave Solution -- State-space Wave Calculation -- Bloch-Rayleigh Perturbation Method -- 4.2.3 Driven-wave Solution -- 4.2.4 1D Damped Band Structures -- 4.3 Two-dimensional Plate-Plate Lattice Model -- 4.3.1 2D Model Description -- 4.3.2 Extension of Driven-wave Calculations to 2D Domains -- 4.3.3 2D Damped Band Structures -- References -- Chapter 5 Wave Propagation in Nonlinear Lattice Materials -- 5.1 Overview -- 5.2 Weakly Nonlinear Dispersion Analysis -- 5.3 Application to a 1D Monoatomic Chain -- 5.3.1 Overview -- 5.3.2 Model Description and Nonlinear Governing Equation -- 5.3.3 Single-wave Dispersion Analysis -- 5.3.4 Multi-wave Dispersion Analysis -- Case 1. General Wave-Wave Interactions -- Case 2. Long-wavelength Limit Wave-Wave Interactions -- 5.3.5 Numerical Verification and Discussion -- 5.4 Application to a 2D Monoatomic Lattice -- 5.4.1 Overview -- 5.4.2 Model Description and Nonlinear Governing Equation -- 5.4.3 Multiple-scale Perturbation Analysis -- 5.4.4 Analysis of Predicted Dispersion Shifts -- 5.4.5 Numerical Simulation Validation Cases -- Analysis Method -- Orthogonal and Oblique Interaction -- 5.4.6 Application: Amplitude-tunable Focusing -- Summary -- Acknowledgements -- References -- Chapter 6 Stability of Lattice Materials -- 6.1 Introduction -- 6.2 Geometry, Material, and Loading Conditions -- 6.3 Stability of Finite-sized Specimens -- 6.4 Stability of Infinite Periodic Specimens -- 6.4.1 Microscopic Instability -- 6.5 Post-buckling Analysis -- 6.6 Effect of Buckling and Large Deformation on the Propagation Of Elastic Waves -- 6.7 Conclusions -- References -- Chapter 7 Impact and Blast Response of Lattice Materials -- 7.1 Introduction -- 7.2 Literature Review -- 7.2.1 Dynamic Response of Cellular Structures. , 7.2.2 Shock- and Blast-loading Responses of Cellular Structures -- 7.2.3 Dynamic Indentation Performance of Cellular Structures -- 7.3 Manufacturing Process -- 7.3.1 The Selective Laser Melting Technique -- 7.3.2 Sandwich Panel Manufacture -- 7.4 Dynamic and Blast Loading of Lattice Materials -- 7.4.1 Experimental Method -- Drop-hammer Impact Tests -- 7.4.2 Experimental Method -- Blast Tests on Lattice Cubes -- 7.4.3 Experimental Method -- Blast Tests on Composite-lattice Sandwich Structures -- 7.5 Results and Discussion -- 7.5.1 Drop-hammer Impact Tests -- 7.5.2 Blast Tests on the Lattice Structures -- 7.5.3 Blast Tests on the Sandwich Panels -- Concluding Remarks -- Acknowledgements -- References -- Chapter 8 Pentamode Lattice Structures -- 8.1 Introduction -- 8.2 Pentamode Materials -- 8.2.1 General Properties -- 8.2.2 Small Rigidity and Poisson's Ratio of a PM -- 8.2.3 Wave Motion in a PM -- 8.3 Lattice Models for PM -- 8.3.1 Effective PM Properties of 2D and 3D Lattices -- 8.3.2 Transversely Isotropic PM Lattice -- Effective Moduli: 2D -- 8.4 Quasi-static Pentamode Properties of a Lattice in 2D and 3D -- 8.4.1 General Formulation with Rigidity -- 8.4.2 Pentamode Limit -- 8.4.3 Two-dimensional Results for Finite Rigidity -- 8.5 Conclusion -- Acknowledgements -- References -- Chapter 9 Modal Reduction of Lattice Material Models -- 9.1 Introduction -- 9.2 Plate Model -- 9.2.1 Mindlin-Reissner Plate Finite Elements -- 9.2.2 Bloch Boundary Conditions -- 9.2.3 Example Model -- 9.3 Reduced Bloch Mode Expansion -- 9.3.1 RBME Formulation -- 9.3.2 RBME Example -- 9.3.3 RBME Additional Considerations -- 9.4 Bloch Mode Synthesis -- 9.4.1 BMS Formulation -- 9.4.2 BMS Example -- 9.4.3 BMS Additional Considerations -- 9.5 Comparison of RBME and BMS -- 9.5.1 Model Size -- 9.5.2 Computational Efficiency -- 9.5.3 Ease of Implementation -- References. , Chapter 10 Topology Optimization of Lattice Materials -- 10.1 Introduction -- 10.2 Unit-cell Optimization -- 10.2.1 Parametric, Shape, and Topology Optimization -- 10.2.2 Selection of Studies from the Literature -- 10.2.3 Design Search Space -- 10.3 Plate-based Lattice Material Unit Cell -- 10.3.1 Equation of Motion and FE Model -- 10.3.2 Mathematical Formulation -- 10.4 Genetic Algorithm -- 10.4.1 Objective Function -- 10.4.2 Fitness Function -- 10.4.3 Selection -- 10.4.4 Reproduction -- 10.4.5 Initialization and Termination -- 10.4.6 Implementation -- 10.5 Appendix -- References -- Chapter 11 Dynamics of Locally Resonant and Inertially Amplified Lattice Materials -- 11.1 Introduction -- 11.2 Locally Resonant Lattice Materials -- 11.2.1 1D Locally Resonant Lattices -- 11.2.2 2D Locally Resonant Lattices -- 11.2.3 3D Locally Resonant Lattices -- 11.3 Inertially Amplified Lattice Materials -- 11.3.1 1D Inertially Amplified Lattices -- 11.3.2 2D Inertially Amplified Lattices -- 11.3.3 3D Inertially Amplified Lattices -- 11.4 Conclusions -- References -- Chapter 12 Dynamics of Nanolattices: Polymer-Nanometal Lattices -- 12.1 Introduction -- 12.2 Fabrication -- 12.2.1 Case Study -- 12.3 Lattice Dynamics -- 12.3.1 Lattice Properties -- Geometries of 3D Lattices -- Effective Material Properties of Nanometal-coated Polymer Lattices -- 12.3.2 Finite-element Model -- Displacement Field -- Kinetic Energy -- Strain Potential Energy -- Collected Equation of Motion -- 12.3.3 Floquet-Bloch Principles -- Generalized Forces in Bloch Analysis -- Reduced Equation of Motion -- 12.3.4 Dispersion Curves for the Octet Lattice -- 12.3.5 Lattice Tuning -- Bandgap Placement -- Lattice Optimization -- 12.4 Conclusions -- 12.5 Appendix: Shape Functions for a Timoshenko Beam with Six Nodal Degrees of Freedom -- References -- Index -- EULA.

Additional Edition: Print version: Dynamics of lattice materials. Chichester, West Sussex, United Kingdom : John Wiley & Sons, Inc., 2017 ISBN 9781118729595

Language: English

Keywords: Electronic books.

URL: https://onlinelibrary.wiley.com/doi/book/10.1002/9781118729588