Linear And Nonlinear Mechanics 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 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

This book describes behavior of crystalline solids primarily via methods of modern continuum mechanics. Emphasis is given to geometrically nonlinear descriptions, i.e., finite deformations. Primary topics include anisotropic crystal elasticity, plasticity, and methods for representing effects of defects in the solid on the material's mechanical response. Defects include crystal dislocations, point defects, twins, voids or pores, and micro-cracks. Thermoelastic, dielectric, and piezoelectric behaviors are addressed. Traditional and higher-order gradient theories of mechanical behavior of crystalline solids are discussed. Differential-geometric representations of kinematics of finite deformations and lattice defect distributions are presented. Multi-scale modeling concepts are described in the context of elastic and plastic material behavior. Representative substances towards which modeling techniques may be applied are single- and poly- crystalline metals and alloys, ceramics, and minerals. This book is intended for use by scientists and engineers involved in advanced constitutive modeling of nonlinear mechanical behavior of solid crystalline materials. Knowledge of fundamentals of continuum mechanics and tensor calculus is a prerequisite for accessing much of the text. This book could be used as supplemental material for graduate courses on continuum mechanics, elasticity, plasticity, micromechanics, or dislocation mechanics, for students in various disciplines of engineering, materials science, applied mathematics, and condensed matter physics.

This book presents contributions on the current problems in a number of topical areas of nonlinear dynamics and physics, written by experts from Russia, Ukraine, Israel, Germany, Poland, Italy, the Netherlands, the USA, and France. The book is dedicated to Professor Leonid I. Manevitch, an outstanding scholar in the fields of Mechanics of Solids, Nonlinear Dynamics, and Polymer Physics, on the occasion of his 80th birthday.

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

Novel mathematical and modeling approaches to problems in graded materials, biological materials, fluid mechanics and more Covers nanomechanics, multi-scale modeling, interface mechanics and microstructure This series volume contains 128 not previously published research presentations on using nonlinear mechanics to understand and model a wide variety of materials, including polymers, metals and composites, as well as subcellular and cellular tissues. Focus is on numerical and physics approaches to representing multiscale relationships within complex solids and fluids systems, with applications in materials science, energy storage, medical diagnostics and treatment, and biotechnology. TABLE OF CONTENTS Preface Committees SESSION 1: INVITED LECTURES Micro-Macro Analysis of Creep and Damage Behavior of Multi-Pass Welds Some New Developments in Non-Linear Solid Mechanics Design of Material Systems: Mathematics and Physics of the Archetype-Genome Exemplar Criticism of Generally Accepted Fundamentals and Methodologies of Traffic and Transportation Theory SESSION 2: NONLINEAR CONTINUUM MECHANICS Geometrically Nonlinear Analysis of Simple Plane Frames of Functionally Graded Materials Thermal Post-Buckling of FG Circular Plates Under Transversely Point-Space Constraint Tunability of Longitudinal Wave Band Gap in One Dimensional Magneto-Elastic Phononic Crystal Teaching Nonlinear Mechanics at the Undergraduate and Graduate Level—Two Examples Geometrically Nonlinear FE Instability Simulations of Hinged Composite Laminated Cylindrical Shells Constitutive Relation of Martensitic Transformation in CuAlNi Based on Atomistic Simulations Soft Behaviors of Beam Shaped Liquid Crystal Elastomers Under Light Actuations XFEM Based Discontinuity Simulation for Saturated Soil Numerical Algorithm of Solving the Problem of Large Elastic-Plastic Deformation by FEM Finite Deformation for Everted Compressible Hypereleastic Cylindrical Tubes Modelling and Non-Linear Free Vibrations of Cable-Stayed Beam Wavelet Solution of a Class of Nonlinear Boundary Value Problems Axial Compression of a Rectangular Rubber Ring Composed of an Incompressible Mooney-Rivlin Material Influence of Concentration-Dependent Elastic Modulus and Charge or Discharge Rate on Tensile Stress in Anode An Integral Equation Approach to the Fully Nonlinear Fluid Flow Problem in an Infinite Channel Over Arbitrary Bottom Topography Analysis of Nonlinear Dynamical Characteristics for Thermoelastic Half-Plane with Voids Tensor Model for Dynamic Damage of Ductile Metals Over a Wide Range of Strain Rates SESSION 3: MULTI-SCALE MECHANICS AND MULTI-PHYSICS MODELING The Nonlinear Magnetoelectric Effect of Layered Magnetoelectric Composite Cylinder with an Imperfect Interface A Solution for Nonlinear Poisson-Neumann Problem of Nb3Sn Superconducting Transport Current Temperature Effect on the Tensile Mechanical Properties of Graphene Nanoribbons Square Inclusion with a Nonlinear Eigenstrain in an Anisotropic Piezoelectric Full Plane Nonlinear Analysis of the Threaded Connection with Three-Dimensional Finite Element Model Effects of Particle Volume Fraction on the Macro-Thermo-Mechanical Behaviors in Plate-Type Dispersion Nuclear Fuel Elements Mechanics of Semiflexible Polymer Chains Under Confinements Study on the Solution of Reynolds Equation for Micro Gas Bearings Using the Alternating-Direction Implication Algorithm Atomistic Study of Li Concentration Dependence of the Mechanical Properties of Graphite Anode in Li-ion Battery 3D Extrusion Simulation of the Single Screw Head and Optimization Design Buckling Behavior of Defective Carbon Nanotubes Elastic Properties of Single-Stranded DNA Biofilm with Strong Interactions Analysis on Thickness Dependence of Jc Caused by Dislocations and Grain Boundaries in YBCO Superconducting Films Operating Strain Response in CICC Coils Through Nonlinear Finite Element Modeling Dynamics Analysis of a Multi-Degree-of-Freedom Electro-Hydraulic Mix-Drive Motion Simulator by KANE Equation Multiscale 3D Fracture Simulation Integrating Tomographic Characterization Research into Compressive Mechanical Properties of Special Piezomagnetic Material Sheets A Numerical Study on Detonation Wave Propagation Using High-Precision and High-Resolution Schemes SESSION 4: STRUCTURAL DYNAMIC AND STRUCTURE-FLUID INTERACTIONS A Study on Pure IL VIV of a Marine Riser in Shear Current Parametric Studies on Nonlinear Flutter of High-Aspect-Ratio Flexible Wings Model Reduction of a Flexible Beam Rotating at High Speed Considering Dynamic Stiffening Vibration Modal Analysis of Cantilever Beams with Complicated Elasticity Boundary Constraint Numerical Simulation of Ahmed Model in Consideration of the FSI Effect Aerodynamic Damping of a Hammerhead Launch Vehicle in Transonic Flow Symmetry Reductions and Explicit Solutions of (3 + 1)-Dimensional Kadomtsev-Petviashvili (KP) Equation Nonlinear Behaviors of an Isotropic Incompressible Hyperelastic Spherical Membrane Under Different Dynamic Loads Creep Buckling of Viscoelastic Plate Consdering Higher Order Modes SESSION 5: COMPLEX FLUID FLOW AND NONLINEAR STABILITY Homotopy Analysis of Korteweg-de Vries Equation with Time Delay Homotopy Analysis Method for Bubble Pulsation Equation with Nonlinear Term of Fractional Power Chebyshev Finite Spectral Method for Boussinesq-Type Equations on Staggered Grids Twin Jets in Crossflow Application of Fixed Point Method to Obtain a Semi-Analytical Solution of Stagnation Flow On the Nonlinear Stability of Laminar Flow Between Parallel Planes Boundary Treatments in Lattice Boltzmann Method A Lattice Boltzmann Based Immersed Boundary Method for Fluid-Structure Interaction Numerical Solutions of Convection-Diffusion Equations by Hybrid Discontinuous Galerkin Methods Steady-State Solutions of the Wave-Bottom Resonant Interaction Lattice Boltzmann Simulation of the Shock Damping and the Shock Increased by Means of Lorentz Force Analysis of the Effects of Nonlinear Characteristics of Lag Dampers on Helicopter Ground Resonance Flow Structures and Sound Radiation in Supersonic Mixing Layers with Nonlinear PSE Method Turbulent Structures in Subsonic Jet Flow Forced by Random Disturbances Exponential p-Stability for a Delayed Recurrent Neural Networks with Impulses Spatial Variation of Scaling Exponents for Structure Functions in a Decaying Turbulence SESSION 6: NONLINEAR DYNAMIC OF STRUCTURE Analysis of Chaos Behavior of Single Mode Vibration of Cable-Stayed Chaotification of Fractional Maps Nonlinear Finite Element Analysis of the Dynamic Axial Crushing of Empty Hexagonal Tube Active Control of a Nonlinear Aeroelastic System Using the Receptance Method Dynamics Analysis of the FHN Neuronal Model Analyzing the Effect of the Axial Force to the Natural Frequencies of Arch Stable Periodic Response of One-Way Clutches in a Two-Pulley Belt-Drive Model Supercritical Nonlinear Dynamics of an Axially Moving Viscoelastic Beam with Speed Fluctuation Nonlinear Dynamic Response to a Moving Force of Timoshenko Beams Resting on Pasternak Foundations An Improved Method for the Construction of Nonlinear Operator in Homotopy Analysis Method A Nonlinear Integration Scheme for Evolutionary Differential Equations A Comparative Study of Civil Aircraft Crashworthiness with Different Ground Conditions Improved Dynamic Analysis of Development of Pulmonary Edema The Timescale Function Method for Solving Free Vibration of Nonlinear Oscillator Nonlinear Aeroelastic Analysis of Flexible Wings with High-Aspect-Ratio Considering Large Deflection Differential Quadrature Method for Vibration Analysis of Finite Beams on Nonlinear Viscoelastic Foundations Numerical Simulation on the Strength and Sealing Performance for High-Pressure Isolating Flange Nonlinear Dynamical Stability of the Lattices with Initial Material and Geometric Imperfection Nonlinear Vibration of Symmetric Angle-Ply Laminated Piezoelectric Plates with Linearly Varying Thickness An Exact Free Vibration Frequency Formula for Oscillator with Single-Term Positive-Power Restoring Force An Exact Solution of Synchronization State for a Class of Networked Mass-Spring-Damper Oscillator Systems SESSION 7: INTERFACE MECHANICS AND ENGINEERING APPLICATION Numerical Simulation of Free Surface Collapse in Propellant Tank Restudy on the Adaptive Mesh Technique for Seepage Problems High-Order Series Solutions of Wave and Current Interactions Deformation and Stress Distribution of Arterial Walls of the Aged A p53-Mdm2 Dynamical Model Induced by Laminar Shear Stress in Endothelial Cells Optimized Image Processing Based on CUDA in a Combined Measurement Technique of PIV and Shadowgraph 3D Visualization of the Flow Fields Using Digital In-Line Holography Analysis and Experimental Study on Air Foam Flooding Seepage Flow Mechanics Experimental Measurements for Mechanical and Electrical Conductive Properties of CNT Bundles Analysis on Dynamic Response of Bedding Rock Slope with Bolts under Earthquakes Numerical Prediction of Aerodynamic Noise Radiated from High Speed Train Pantograph Effects of Length on Aerodynamics of High Speed Train Models Free Convection Nanofluid Flow in the Stagnation-Point Region of a Three Dimensional Body Vertical Distribution and Dynamic Release Characteristics of Pollutants from Resuspended Sediment Numerical Simulation of the Contaminant Release Through the Sediment-Overlying Water Interface Analysis on the Aerodynamic and Aero-Noise of MIRA Model Radial Squeeze Force of MR Fluid Between Two Cylinders Nonlinear Buckling Analysis and Ultimate Extended Capacity Research of Downhole Pipe Strings in Ultra-Deep Horizontal Wells A Novel Method of Generating Nonlinear Internal Wave in a Stratified Fluid Tank and Its Theoretical Model SESSION 8: MINI-SYMPOSIUM ON TRAFFIC FLUID Study on Correlation Analysis of Synchronized Flow in the Kerner-Klenov-Wolf Cellular Automation Model Numerical Simulation of Traffic Flow in the Rain or Snow Weather Condition First Order Phase Transitions in the Brake Light Cellular Automation Model Within the Fundamental Diagram Approach The Leader-Follower Winding Behavior of Pedestrians in a Queue Effect of Overpasses in Two-Dimensional Traffic Flow Model with Random Update Rule Analysis of the Density Wave in a New Continuum Model The Phenomenon of High-Speed-Car-Following on Chinese Highways A Lattice Hydrodynamic Model Considering the Difference of Density and its Analysis Experimental Feature of Car-Following Behaviors in a Platoon of 25 Vehicles Car-Following Model for Manual Transmission Vehicles The Mechanism of Synchronized Flow in Traffic Flow Modeling An Asymmetric Stochastic Car-Following Model Based on Extended Tau Theory A Gaussian Distribution Based Dual-Cognition Driver Behavior Model at Cross Traffic A New Traffic Kinetic Model Considering Potential Influence The Effect of Marks on the Pedestrian Evacuation Equilibrium Velocity Distribution Function for Traffic Flow Effects of Antilock Braking System on Driving Behavior Under Emergent Stability Analysis of Pedestrian Flow in Two-Dimensional Optimal Velocity Model with Asymmetric Interaction Simulation-Based Stability Analysis of Car-Following Models Under Heterogeneous Traffic Crossing Speed of Pedestrian at an Unsignalized Intersection Modeling Mixed Traffic Flow at a Crosswalk with Push Button Effects of Game Strategy Update on Pedestrian Evacuation in a Hall Study on Long-Term Correlation of CO and CO2 from Vehicle Emissions on Roadsides with the Detrended Fluctuation Analysis Method Bottleneck Effect on a Bidirectional Two-Lane Mixed Traffic Flow

Soliton theory, the theory of nonlinear waves in lattices composed of particles interacting by nonlinear forces, is treated rigorously in this book. The presentation is coherent and self-contained, starting with pioneering work and extending to the most recent advances in the field. Special attention is focused on exact methods of solution of nonlinear problems and on the exact mathematical treatment of nonlinear lattice vibrations. This new edition updates the material to take account of important new advances.

The aim of this book is to provide a unified presentation of modern mechanics of structures in a form which is suitable for graduate students as well as for engineers and scientists working in the field of applied mechanics. Traditionally, students at technical universities have been taught subjects such as continuum mechanics, elasticity, plates and shells, frames or finite element techniques in an entirely separate manner. The authors' teaching experience clearly suggests that this situation frequently tends to create in students' minds an incomplete and inconsistent picture of the contemporary structural mechanics. Thus, it is very common that the fundamental laws of physics appear to students hardly related to simplified equations of different "technical" theories of structures, numerical solution techniques are studied independently of the essence of mechanical models they describe, and so on. The book is intended to combine in a reasonably connected and unified manner all these problems starting with the very fundamental postulates of nonlinear continuum mechanics via different structural models of "engineer ing" accuracy to numerical solution methods which can effectively be used for solving boundary-value problems of technological importance. The authors have tried to restrict the mathematical background required to that which is normally familiar to a mathematically minded engineering graduate.

This book uses asymptotic methods to obtain simple approximate analytic solutions to various problems within mechanics, notably wave processes in heterogeneous materials. Presenting original solutions to common issues within mechanics, this book builds upon years of research to demonstrate the benefits of implementing asymptotic techniques within mechanical engineering and material science. Focusing on linear and nonlinear wave phenomena in complex micro-structured solids, the book determines their global characteristics through analysis of their internal structure, using homogenization and asymptotic procedures, in line with the latest thinking within the field. The book’s cutting-edge methodology can be applied to optimal design, non-destructive control and in deep seismic sounding, providing a valuable alternative to widely used numerical methods. Using case studies, the book covers topics such as elastic waves in nonhomogeneous materials, regular and chaotic dynamics based on continualisation and discretization and vibration localization in 1D Linear and Nonlinear lattices. The book will be of interest to students, research engineers, and professionals specialising in mathematics and physics as well as mechanical and civil engineering.

This book is a printed edition of the Special Issue "Non-Linear Lattice" that was published in Entropy