Dynamics of lattice materials /

* 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...

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Bibliographic Details
Other Authors:	Phani, A. Srikantha (Editor), Hussein, Mahmoud I. (Editor)
Format:	eBook
Language:	English
Published:	Chichester, West Sussex, United Kingdom : John Wiley & Sons, Inc., 2017.
Subjects:	Lattice dynamics.
Online Access:	Connect to the full text of this electronic book

Table of Contents:

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.