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英文全書下載 Viscoelastic Materials. Roderic Lakes 2009 《粘彈性材料》
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陳小黑
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2015-1-9 22:34
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英文全書下載 Viscoelastic Materials. Roderic Lakes 2009 《粘彈性材料》
本帖最后由 陳小黑 于 2015-1-9 22:37 編輯
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目錄
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Contents
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Preface page xvii
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1 Introduction: Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
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1.1 Viscoelastic Phenomena 1
9 m, ?2 R [, q/ v- n# M+ f
1.2 Motivations for Studying Viscoelasticity 3
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1.3 Transient Properties: Creep and Relaxation 3
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1.3.1 Viscoelastic Functions J (t), E(t) 3
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1.3.2 Solids and Liquids 7
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1.4 Dynamic Response to Sinusoidal Load: E∗, tanδ 8
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1.5 Demonstration of Viscoelastic Behavior 10
3 A7 E9 N8 A3 s) W/ ~
1.6 Historical Aspects 10
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1.7 Summary 11
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1.8 Examples 11
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1.9 Problems 12
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Bibliography 12
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2 Constitutive Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
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2.1 Introduction 14
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2.2 Prediction of the Response of Linearly Viscoelastic Materials 14
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2.2.1 Prediction of Recovery from Relaxation E(t) 14
& G# v* y" @5 w# _2 `7 w1 x
2.2.2 Prediction of Response to Arbitrary Strain History 15
% ~6 p& I! {) y Y! \
2.3 Restrictions on the Viscoelastic Functions 17
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2.3.1 Roles of Energy and Passivity 17
3 I9 ? j* P5 e& h
2.3.2 Fading Memory 18
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2.4 Relation between Creep and Relaxation 19
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2.4.1 Analysis by Laplace Transforms: J (t) ↔ E(t) 19
4 C( A9 T7 M; x& d
2.4.2 Analysis by Direct Construction: J (t) ↔ E(t) 20
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2.5 Stress versus Strain for Constant Strain Rate 20
: F6 @3 l! N$ g& f8 v
2.6 Particular Creep and Relaxation Functions 21
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2.6.1 Exponentials and Mechanical Models 21
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2.6.2 Exponentials and Internal Causal Variables 26
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2.6.3 Fractional Derivatives 27
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2.6.4 Power-Law Behavior 28
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2.6.5 Stretched Exponential 29
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2.6.6 Logarithmic Creep; Kuhn Model 29
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2.6.7 Distinguishing among Viscoelastic Functions 30
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2.7 Effect of Temperature 30
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2.8 Three-Dimensional Linear Constitutive Equation 33
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2.9 Aging Materials 35
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2.10 Dielectric and Other Forms of Relaxation 35
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2.11 Adaptive and “Smart” Materials 36
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2.12 Effect of Nonlinearity 37
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2.12.1 Constitutive Equations 37
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2.12.2 Creep–Relaxation Interrelation: Nonlinear 40
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2.13 Summary 43
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2.14 Examples 43
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2.15 Problems 51
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Bibliography 52
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3 Dynamic Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
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3.1 Introduction and Rationale 55
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3.2 The Linear Dynamic Response Functions E∗, tanδ 56
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3.2.1 Response to Sinusoidal Input 57
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3.2.2 Dynamic Stress–Strain Relation 59
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3.2.3 Standard Linear Solid 62
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3.3 Kramers–Kronig Relations 63
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3.4 Energy Storage and Dissipation 65
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3.5 Resonance of Structural Members 67
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3.5.1 Resonance, Lumped System 67
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3.5.2 Resonance, Distributed System 71
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3.6 Decay of Resonant Vibration 74
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3.7 Wave Propagation and Attenuation 77
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3.8 Measures of Damping 79
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3.9 Nonlinear Materials 79
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3.10 Summary 81
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3.11 Examples 81
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3.12 Problems 88
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Bibliography 89
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4 Conceptual Structure of Linear Viscoelasticity . . . . . . . . . . . . . . . 91
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4.1 Introduction 91
4 O( I! q) I6 u F- `& ]3 h
4.2 Spectra in Linear Viscoelasticity 92
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4.2.1 Definitions H(τ ), L(τ ) and Exact Interrelations 92
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4.2.2 Particular Spectra 93
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4.3 Approximate Interrelations of Viscoelastic Functions 95
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4.3.1 Interrelations Involving the Spectra 95
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4.3.2 Interrelations Involving Measurable Functions 98
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4.3.3 Summary, Approximate Relations 101
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4.4 Conceptual Organization of the Viscoelastic Functions 101
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4.5 Summary 104
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4.6 Examples 104
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4.7 Problems 109
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Bibliography 109
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5 Viscoelastic Stress and Deformation Analysis . . . . . . . . . . . . . . . 111
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5.1 Introduction 111
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5.2 Three-Dimensional Constitutive Equation 111
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5.3 Pure Bending by Direct Construction 112
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5.4 Correspondence Principle 114
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5.5 Pure Bending by Correspondence 116
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5.6 Correspondence Principle in Three Dimensions 116
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5.6.1 Constitutive Equations 116
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5.6.2 Rigid Indenter on a Semi-Infinite Solid 117
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5.6.3 Viscoelastic Rod Held at Constant Extension 119
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5.6.4 Stress Concentration 119
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5.6.5 Saint Venant’s Principle 120
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5.7 Poisson’s Ratio ν(t) 121
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5.7.1 Relaxation in Tension 121
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5.7.2 Creep in Tension 123
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5.8 Dynamic Problems: Effects of Inertia 124
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5.8.1 Longitudinal Vibration and Waves in a Rod 124
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5.8.2 Torsional Waves and Vibration in a Rod 125
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5.8.3 Bending Waves and Vibration 128
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5.8.4 Waves in Three Dimensions 129
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5.9 Noncorrespondence Problems 131
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5.9.1 Solution by Direct Construction: Example 131
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5.9.2 A Generalized Correspondence Principle 132
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5.9.3 Contact Problems 132
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5.10 Bending in Nonlinear Viscoelasticity 133
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5.11 Summary 134
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5.12 Examples 134
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5.13 Problems 142
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Bibliography 142
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6 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
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6.1 Introduction and General Requirements 145
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6.2 Creep 146
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6.2.1 Creep: Simple Methods to Obtain J (t) 146
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6.2.2 Effect of Risetime in Transient Tests 146
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6.2.3 Creep in Anisotropic Media 148
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6.2.4 Creep in Nonlinear Media 148
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6.3 Inference of Moduli 150
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6.3.1 Use of Analytical Solutions 150
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6.3.2 Compression of a Block 151
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6.4 Displacement and Strain Measurement 152
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6.5 Force Measurement 156
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6.6 Load Application 157
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6.7 Environmental Control 157
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6.8 Subresonant Dynamic Methods 158
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6.8.1 Phase Determination 158
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6.8.2 Nonlinear Materials 160
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6.8.3 Rebound Test 161
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6.9 Resonance Methods 161
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6.9.1 General Principles 161
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6.9.2 Particular Resonance Methods 163
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6.9.3 Methods for Low-Loss or High-Loss Materials 166
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6.9.4 Resonant Ultrasound Spectroscopy 168
7 ^% J5 d& `& e& ]; N( Q
6.10 Achieving a Wide Range of Time or Frequency 171
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6.10.1 Rationale 171
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6.10.2 Multiple Instruments and Long Creep 172
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6.10.3 Time–Temperature Superposition 172
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6.11 Test Instruments for Viscoelasticity 173
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6.11.1 Servohydraulic Test Machines 173
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6.11.2A Relaxation Instrument 174
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6.11.3 Driven Torsion Pendulum Devices 174
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6.11.4 Commercial Viscoelastic Instrumentation 178
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6.11.5 Instruments for a Wide Range of Time and Frequency 179
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6.11.6 Fluctuation–Dissipation Relation 182
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6.11.7 Mapping Properties by Indentation 183
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6.12 Wave Methods 184
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6.13 Summary 188
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6.14 Examples 188
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6.15 Problems 200
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Bibliography 201
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7 Viscoelastic Properties of Materials . . . . . . . . . . . . . . . . . . . . . 207
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7.1 Introduction 207
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7.1.1 Rationale 207
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7.1.2 Overview: Some Common Materials 207
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7.2 Polymers 208
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7.2.1 Shear and Extension in Amorphous Polymers 208
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7.2.2 Bulk Relaxation in Amorphous Polymers 212
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7.2.3 Crystalline Polymers 213
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7.2.4 Aging and other Relaxations 214
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7.2.5 Piezoelectric Polymers 214
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7.2.6 Asphalt 214
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7.3 Metals 215
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7.3.1 Linear Regime of Metals 215
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7.3.2 Nonlinear Regime of Metals 217
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7.3.3 High-Damping Metals and Alloys 219
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7.3.4 Creep-Resistant Alloys 224
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7.3.5 Semiconductors and Amorphous Elements 225
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7.3.6 Semiconductors and Acoustic Amplification 226
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7.3.7 Nanoscale Properties 226
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7.4 Ceramics 227
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7.4.1 Rocks 227
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7.4.2 Concrete 229
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7.4.3 Inorganic Glassy Materials 231
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7.4.4 Ice 231
+ } ^6 |! l2 x( Z8 \
7.4.5 Piezoelectric Ceramics 232
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7.5 Biological Composite Materials 233
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7.5.1 Constitutive Equations 234
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7.5.2 Hard Tissue: Bone 234
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7.5.3 Collagen, Elastin, Proteoglycans 236
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7.5.4 Ligament and Tendon 237
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7.5.5 Muscle 240
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7.5.6 Fat 243
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7.5.7 Brain 243
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7.5.8 Vocal Folds 244
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7.5.9 Cartilage and Joints 244
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7.5.10 Kidney and Liver 246
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7.5.11 Uterus and Cervix 246
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7.5.12 Arteries 247
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7.5.13 Lung 248
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7.5.14 The Ear 248
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7.5.15 The Eye 249
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7.5.16 Tissue Comparison 251
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7.5.17 Plant Seeds 252
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7.5.18 Wood 252
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7.5.19 Soft Plant Tissue: Apple, Potato 253
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7.6 Common Aspects 253
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7.6.1 Temperature Dependence 253
6 O% C/ i) p$ H K8 J
7.6.2 High-Temperature Background 254
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7.6.3 Negative Damping and Acoustic Emission 255
! W H2 H4 N) K& e; @
7.7 Summary 255
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7.8 Examples 255
4 b3 n3 g: z9 N& z$ b% R
7.9 Problems 256
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Bibliography 257
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8 Causal Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
4 A7 U: ?5 R! K9 k: B! d% V
8.1 Introduction 271
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8.1.1 Rationale 271
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8.1.2 Survey of Viscoelastic Mechanisms 271
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8.1.3 Coupled Fields 273
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8.2 Thermoelastic Relaxation 274
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8.2.1 Thermoelasticity in One Dimension 274
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8.2.2 Thermoelasticity in Three Dimensions 275
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8.2.3 Thermoelastic Relaxation Kinetics 276
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8.2.4 Heterogeneity and Thermoelastic Damping 278
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8.2.5 Material Properties and Thermoelastic Damping 280
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8.3 Relaxation by Stress-Induced Fluid Motion 280
% }# k2 t) p h( P0 ^
8.3.1 Fluid Motion in One Dimension 280
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8.3.2 Biot Theory: Fluid Motion in Three Dimensions 281
$ J$ r6 \* r. X4 e4 [6 c% j
8.4 Relaxation by Molecular Rearrangement 286
8 [5 _- B& H# c* X. p! n3 Q
8.4.1 Glassy Region 286
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8.4.2 Transition Region 287
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8.4.3 Rubbery Behavior 289
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8.4.4 Crystalline Polymers 291
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8.4.5 Biological Macromolecules 292
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8.4.6 Polymers and Metals 292
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8.5 Relaxation by Interface Motion 292
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8.5.1 Grain Boundary Slip in Metals 292
7 I; L, z* E+ X# {7 g$ c
8.5.2 Interface Motion in Composites 294
3 h3 V3 L! D; h, a& J& U* F+ U
8.5.3 Structural Interface Motion 294
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8.6 Relaxation Processes in Crystalline Materials 294
2 N+ S, }9 ?: n y; g: ?8 a
8.6.1 Snoek Relaxation: Interstitial Atoms 294
1 T* L _! `: I9 Z
8.6.2 Zener Relaxation in Alloys: Pairs of Atoms 298
1 T0 s: } e$ v
8.6.3 Gorsky Relaxation 299
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8.6.4 Granato–L ¨ ucke Relaxation: Dislocations 300
7 [7 N) q1 B& }! ]. `1 a
8.6.5 Bordoni Relaxation: Dislocation Kinks 303
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8.6.6 Relaxation Due to Phase Transformations 305
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8.6.7 High-Temperature Background 314
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8.6.8 Nonremovable Relaxations 315
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8.6.9 Damping Due to Wave Scattering 316
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8.7 Magnetic and Piezoelectric Materials 316
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8.7.1 Relaxation in Magnetic Media 316
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8.7.2 Relaxation in Piezoelectric Materials 318
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8.8 Nonexponential Relaxation 322
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8.9 Concepts for Material Design 323
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8.9.1 Multiple Causes: Deformation Mechanism Maps 323
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8.9.2 Damping Mechanisms in High-Loss Alloys 326
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8.9.3 Creep Mechanisms in Creep-Resistant Alloys 326
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8.10 Relaxation at Very Long Times 327
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8.11 Summary 327
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8.12 Examples 328
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8.13 Problems and Questions 332
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Bibliography 332
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9 Viscoelastic Composite Materials . . . . . . . . . . . . . . . . . . . . . . . 341
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9.1 Introduction 341
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9.2 Composite Structures and Properties 341
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9.2.1 Ideal Structures 341
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9.2.2 Anisotropy due to Structure 342
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9.3 Prediction of Elastic and Viscoelastic Properties 344
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9.3.1 Basic Structures: Correspondence Solutions 344
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9.3.2 Voigt Composite 345
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9.3.3 Reuss Composite 345
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9.3.4 Hashin–Shtrikman Composite 346
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9.3.5 Spherical Particulate Inclusions 347
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9.3.6 Fiber Inclusions 349
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9.3.7 Platelet Inclusions 349
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9.3.8 Stiffness-Loss Maps 350
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9.4 Bounds on the Viscoelastic Properties 353
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9.5 Extremal Composites 354
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9.6 Biological Composite Materials 356
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9.7 Poisson’s Ratio of Viscoelastic Composites 357
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9.8 Particulate and Fibrous Composite Materials 358
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9.8.1 Structure 358
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9.8.2 Particulate Polymer Matrix Composites 359
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9.8.3 Fibrous Polymer Matrix Composites 361
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9.8.4 Metal–Matrix Composites 362
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9.9 Cellular Solids 363
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9.10 Piezoelectric Composites 366
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9.11 Dispersion of Waves in Composites 366
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9.12 Summary 367
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9.13 Examples 367
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9.14 Problems 370
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Bibliography 370
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10 Applications and Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . 377
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10.1 Introduction 377
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10.2 A Viscoelastic Earplug: Use of Recovery 377
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10.3 Creep and Relaxation of Materials and Structures 378
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10.3.1 Concrete 378
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10.3.2 Wood 378
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10.3.3 Power Lines 379
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10.3.4 Glass Sag: Flowing Window Panes 380
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10.3.5 Indentation: Road Rutting 380
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10.3.6 Leather 381
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10.3.7 Creep-Resistant Alloys and Turbine Blades 381
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10.3.8 Loosening of Bolts and Screws 382
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10.3.9 Computer Disk Drive: Case Study of Relaxation 384
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10.3.10 Earth, Rock, and Ice 385
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10.3.11 Solder 386
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10.3.12 Filamentsi nL ight Bulbs and Other Devices 387
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10.3.13Tires: Flat-Spotting and Swelling 388
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10.3.14Cushionsfor Seats and Wheelchairs 388
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10.3.15 Artificial Joints 389
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10.3.16 Dental Fillings 389
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10.3.17 Food Products 389
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10.3.18 Seals and Gaskets 390
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10.3.19 Relaxationi nM usical Instrument Strings 390
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10.3.20 Winding of Tape 391
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10.4 Creep and Recovery in Human Tissue 391
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10.4.1 Spinal Discs: Height Change 391
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10.4.2 The Nose 392
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10.4.3 Skin 392
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10.4.4 The Head 393
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10.5 Creep Damage and Creep Rupture 394
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10.5.1 Vajont Slide 394
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10.5.2 Collapse of a Tunnel Segment 394
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10.6 Vibration Control and Waves 394
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10.6.1 Analysis of Vibration Transmission 394
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10.6.2 Resonant (Tuned) Damping 397
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10.6.3 Rotating Equipment Vibration 397
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10.6.4 Large Structure Vibration: Bridges and Buildings 398
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10.6.5 Damping Layers for Plate and Beam Vibration 399
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10.6.6 Structural Damping Materials 400
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10.6.7 Piezoelectric Transducers 402
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10.6.8 Aircraft Noise and Vibration 402
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10.6.9 Solid Fuel Rocket Vibration 404
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10.6.10 Sports Equipment Vibration 404
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10.6.11 Seat Cushions and Automobiles: Protection of People 404
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10.6.12 Vibrationi n ScientificI nstruments 406
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10.6.13 Waves 406
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10.7 “Smart” Materials and Structures 407
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10.7.1 “Smart” Materials 407
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10.7.2 Shape Memory Materials 408
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10.7.3 Self-Healing Materials 409
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10.7.4 Piezoelectric Solid Damping 409
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10.7.5 Active Vibration Control: “Smart” Structures 409
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10.8 Rolling Friction 409
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10.8.1 Rolling Analysis 410
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10.8.2 Rolling of Tires 411
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10.9 Uses of Low-Loss Materials 412
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10.9.1 Timepieces 412
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10.9.2 Frequency Stabilization and Control 413
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10.9.3 Gravitational Measurements 413
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10.9.4 Nanoscale Resonators 414
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10.10 Impulses, Rebound, and Impact Absorption 414
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10.10.1 Rationale 414
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10.10.2 Analysis 415
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10.10.3 Bumpers and Pads 418
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10.10.4 Shoe Insoles, Athletic Tracks, and Glove Liners 419
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10.10.5 Toughness of Materials 419
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10.10.6 Tissue Viscoelasticity in Medical Diagnosis 420
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10.11Rebound of a Ball 421
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10.11.1 Analysis 421
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10.11.2 Applications in Sports 422
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10.12 Applications of Soft Materials 424
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10.12.1 Viscoelastic Gels in Surgery 424
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10.12.2 Hand Strength Exerciser 424
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10.12.3 Viscoelastic Toys 424
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10.12.4 No-Slip Flooring, Mats, and Shoe Soles 425
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10.13 Applications Involving Thermoviscoelasticity 425
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10.14 Satellite Dynamics and Stability 426
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10.15 Summary 428
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10.16 Examples 429
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10.17 Problems 431
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Bibliography 431
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A: Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441
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A.1 Mathematical Preliminaries 441
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A.1.1 Introduction 441
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A.1.2 Functionals and Distributions 441
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A.1.3 Heaviside Unit Step Function 442
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A.1.4 Dirac Delta 442
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A.1.5 Doublet 443
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A.1.6 Gamma Function 445
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A.1.7 Liebnitz Rule 445
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A.2 Transforms 445
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A.2.1 Laplace Transform 446
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A.2.2 Fourier Transform 446
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A.2.3 Hartley Transform 447
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A.2.4 Hilbert Transform 447
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A.3 Laplace Transform Properties 448
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A.4 Convolutions 449
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A.5 Interrelations in Elasticity Theory 451
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A.6 Other Works on Viscoelasticity 451
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Bibliography 452
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B: Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455
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B.1 Principal Symbols 455
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Index 457
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