Composites and metamaterials

Description

Contents Preface 1 Introduction 1.1 Heterogeneous materials 1.1.1 Overview 1.1.2 Classification and terminology 1.1.3 Assumptions about the material 1.1.4 Materials vs. structures 1.2 Outline 1.3 Role of density 1.3.1 Modulus and density 1.3.2 Strength and density 1.3.3 Soft materials Bibliography 2 Structures, properties, bounds 2.1 Introduction 2.2 Bounds on properties 2.2.1 Bounds on elastic constants of a homogeneous solid 2.2.2 Bounds on heat capacity of a homogeneous solid 2.2.3 Bounds on composite elastic properties 2.2.4 Bounds on composite dielectric constant 2.3 Attaining the bounds on properties 2.3.1 Voigt composite 2.3.2 Reuss composite 2.3.3 Laminates: dielectric constant 2.3.4 Laminates: structural hierarchy 2.3.5 Attaining the Hashin-Shtrikman bounds: spheres 2.3.6 Attaining the Hashin-Shtrikman bounds: laminates 2.4 Inclusion shape: dilute concentration 2.4.1 Spherical inclusions 2.4.2 Fiber inclusions 2.4.3 Platelet inclusions 2.5 Exceeding bounds 2.5.1 Negative structural sti ness and extreme damping 2.5.2 Extreme nonlinear energy dissipation 2.5.3 Phase transformations 2.5.4 Negative and extreme moduli: stored energy 2.5.5 Negative and extreme moduli: energy flux 2.5.6 Negative heat capacity 2.5.7 Negative capacitance 2.6 Summary Bibliography 3 Symmetry and anisotropy 3.1 Introduction and Rationale 3.2 Tensors 3.3 Elastic properties 3.3.1 Hooke's law 3.3.2 Reduced notation: matrix form 3.3.3 Symmetry classes 3.3.4 Quasicrystals 3.3.5 Modulus matrices and symmetry 3.3.6 Isotropy 3.3.7 Physical interpretation: elastic modulus 3.3.8 Physical interpretation: elastic compliance 3.3.9 Physical interpretation: experiment 3.3.10 How to show the effect of symmetry 3.3.11 Neumann's principle 3.4 Stress concentration: anisotropy 3.5 Chirality 3.6 Dielectric and optical properties 3.7 Materials, symmetry and structure 3.7.1 Examples of materials 3.7.2 Poisson's ratio in materials with structure 3.7.3 Quasicrystal elasticity 3.8 Summary Bibliography 4 Coupled fields 4.1 Introduction: piezoelectricity, thermoelasticity 4.2 Piezoelectric properties 4.2.1 Piezoelectric properties and symmetry 4.2.2 Piezoelectric materials 4.2.3 Strongly piezoelectric materials 4.2.4 Lead free piezoelectric materials 4.2.5 Experimental piezoelectric measurement 4.2.6 Electrostriction 4.2.7 Pyroelectric materials 4.2.8 Applications of piezoelectric and pyroelectric solids 4.3 Thermal expansion 4.3.1 Thermoelasticity, symmetry, causes 4.3.2 Thermal expansion anisotropy 4.3.3 Small or negative thermal expansion 4.3.4 Composite thermal expansion bounds 4.3.5 Applications and thermal expansion 4.3.6 Piezocaloric and related effects 4.4 Fluid-solid composites 4.4.1 Constitutive equations 4.4.2 Experimental determination of constants 4.4.3 Applications: geology and geological engineering 4.4.4 Foams 4.4.5 Streaming potentials 4.4.6 Vascular materials 4.5 Hall effect 4.6 Reciprocity 4.6.1 Non-reciprocal and extreme materials 4.7 Slow and fast processes 4.7.1 Overview 4.7.2 Isothermal and adiabatic moduli 4.7.3 Short-/open-circuit moduli 4.7.4 Fluid-solid composites 4.8 Artificial muscles 4.9 Artificial tentacles 4.10 Energy harvesting 4.11 Other coupled fields 4.12 Summary Bibliography 5 Particles, fibers, platelets 5.1 Introduction: structure 5.2 Particulate polymer matrix solids 5.2.1 Dental composites 5.2.2 Asphalt 5.2.3 Toughened polymers 5.2.4 Filled polymers; tire rubber; nano-fillers 5.2.5 Self healing polymers 5.3 Fibrous polymer matrix solids 5.3.1 Why fibers? 5.3.2 Unidirectional fibrous composites 5.3.3 Laminates 5.3.4 Nano-tubes as fibers 5.3.5 Effects of moisture 5.3.6 Damage 5.3.7 Making fibrous composites 5.4 Platelet reinforcement 5.5 Metal matrix composites 5.5.1 Particulate metal matrix composite stiffness and strength 5.5.2 Nano-size particle inclusions in metal 5.5.3 Fiber inclusions in metal 5.6 Composites with renewable constituents 5.7 Thermoelastic composites 5.7.1 Thermal expansion, Voigt 5.7.2 Unidirectional composites: thermal expansion 5.7.3 Thermal benders 5.8 Piezoelectric composites 5.8.1 Piezoelectric composite structure and rationale 5.8.2 Piezoelectric Voigt composite 5.8.3 Piezoelectric benders 5.8.4 Piezoelectric composite uses and fabrication 5.9 In situ composites 5.10 Summary Bibliography 6 Cellular solids and lattices 6.1 Introduction 6.2 Tessellations 6.3 Honeycomb 6.3.1 Honeycomb modulus 6.3.2 Honeycomb Poisson's ratio 6.3.3 Honeycomb strength 6.3.4 Square cell honeycombs 6.3.5 Hierarchical solids: honeycombs 6.3.6 Making honeycomb 6.4 Foams 6.4.1 Foam elastic modulus 6.4.2 Poisson's ratio of foams 6.4.3 Nonlinearity and strength of foams 6.4.4 Toughness of foams 6.4.5 Dense foams and syntactic foams 6.4.6 Making foams 6.5 Lattices 6.5.1 Truss lattices: ribs 6.5.2 Continuous rib lattices 6.5.3 Lattice property bounds 6.5.4 Plate lattices 6.5.5 Surface lattices 6.5.6 Hierarchical lattices 6.5.7 Making lattices 6.6 Poisson's ratio tuning 6.6.1 Poisson's ratio in anisotropic materials 6.6.2 Poisson's tuning ratio in foams: negative or extreme 6.6.3 Poisson's ratio tuning in hinged structures: negative or extreme 6.6.4 Poisson's ratio tuning in lattices: negative or extreme 6.7 Tuning coupled fields 6.7.1 Tuning thermal expansion: negative or extreme 6.7.2 Piezoelectric lattices 6.7.3 Tuning the Hall effect 6.8 Control of waves 6.8.1 Role of resonance 6.8.2 Tuning refraction of waves. Negative index. 6.8.3 Electromagnetic lattices; cloaking 6.8.4 Acoustic lattices; cloaking 6.9 Applications of cellular solids 6.9.1 Applications of foam and honeycomb 6.9.2 Applications of lattices 6.10 Summary Bibliography 7 Biological material structural hierarchy 7.1 Introduction 7.2 Bone and teeth 7.2.1 Compact bone: stiffness and strength 7.2.2 Compact bone: piezoelectricity 7.2.3 Compact bone: adaptation 7.2.4 Compact bone: stress concentration 7.2.5 Spongy bone 7.2.6 Teeth 7.3 Ligaments and tendons 7.4 Wood and other plant tissue 7.4.1 Wood structure, stiffness and strength 7.4.2 Wood piezoelectricity 7.5 Summary Bibliography 8 Size of heterogeneity 8.1 Introduction 8.2 Stress concentrations 8.2.1 Experiment 8.2.2 Analysis: ad hoc criteria 8.2.3 Analysis: generalized elasticity 8.3 Size effects 8.3.1 Size effects: structural example 8.3.2 Size effects: continuum view 8.3.3 Size effects: experiment 8.4 Generalized continuum elasticity 8.4.1 Cosserat theory 8.4.2 Stress and strain fields: effect of microstructure 8.4.3 Physical causes 8.4.4 Homogenization analyses 8.4.5 Hinged structures 8.4.6 Chirality in elasticity 8.4.7 Other generalized continua 8.5 Flexo-electricity: gradient piezoelectricity 8.6 Surface and free edge effects 8.7 Summary Bibliography 9 Viscoelastic composites 9.1 Viscoelastic properties: introduction 9.2 Viscoelastic functions 9.2.1 Creep 9.2.2 Relaxation 9.2.3 Response to sinusoidal input 9.2.4 Viscoelasticity of typical materials 9.3 Viscoelasticity of composites 9.3.1 Viscoelasticity of Voigt laminates 9.3.2 Stiffness-damping maps of extremal composites 9.3.3 Stiffness-damping map: inclusion shape 9.3.4 Bounds on viscoelastic properties 9.3.5 Waves in composites 9.3.6 Negative damping; acoustic amplification 9.3.7 Extreme viscoelastic composites: inclusion shape 9.3.8 Extreme viscoelastic composites: stored energy 9.3.9 Viscoelasticity of fibrous composites 9.3.10 Effect of temperature 9.3.11 Poisson's ratio of viscoelastic materials 9.3.12 Viscoelasticity of cellular solids 9.3.13 Viscoelasticity of bone 9.3.14 Viscoelasticity of tendon and ligament 9.3.15 Viscoelastic damping of metal matrix composites 9.4 Summary Bibliography A Appendix A.1 Solved Problems A.1.1 Transverse, fibrous A.1.2 Physical meaning of C1111 in applications A.1.3 Adiabatic and isothermal compliance A.1.4 Foam stiffness vs. density A.1.5 Steel foam and solid polymer A.1.6 Cardboard honeycomb strength A.1.7 Poisson's ratio of honeycomb A.1.8 Particle inclusion concentration A.1.9 Multiple particle sizes A.1.10 Spongy bone modulus A.1.11 Sneaker sole design A.1.12 Cubic lattice A.1.13 Lattice with tubular ribs A.1.14 Motion from piezoelectric disk A.1.15 Voltage from piezoelectric disk A.1.16 Piezoelectric bender A.1.17 Laminate of steel and rubber A.2 Problems and questions B Symbols B.1 Principal symbols and definitions Index