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標(biāo)題: 英文全書下載 Viscoelastic Materials. Roderic Lakes 2009 《粘彈性材料》 [打印本頁]

作者: 陳小黑    時間: 2015-1-9 22:34
標(biāo)題: 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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( ?& \$ {; c" ^Contents
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; h% x* M& j, G: fPreface page xvii( b& F; z% i( n
1 Introduction: Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 t- b- \- s2 @+ R9 p  P
1.1 Viscoelastic Phenomena 16 Z1 o2 L, H' J/ H1 w
1.2 Motivations for Studying Viscoelasticity 3
) U' X4 S0 [3 r5 }; s" |1.3 Transient Properties: Creep and Relaxation 3
& w( _0 x$ x, l9 n4 q' ?  E1.3.1 Viscoelastic Functions J (t), E(t) 3
; B( M1 E# s9 w/ t( x6 L1.3.2 Solids and Liquids 77 w( R7 V( h1 p& d
1.4 Dynamic Response to Sinusoidal Load: E∗, tanδ 87 n1 k0 U4 X8 V3 ?; E: m9 t$ \! X
1.5 Demonstration of Viscoelastic Behavior 109 x& T. a# J. m/ |* g" W. O
1.6 Historical Aspects 10
. [& P# J- K, j1 _1.7 Summary 118 U0 G$ ?& v9 ^$ A5 {' \
1.8 Examples 11
; }4 j/ L6 Q0 a  x. g4 d4 [3 T1.9 Problems 12, W- }) |% r) Z0 q" U( q
Bibliography 12( S  M! D4 m4 {( a4 `

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2 Constitutive Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
) I; G0 i" O1 D; _2.1 Introduction 14  j; Z$ C9 V2 W/ E# @2 {
2.2 Prediction of the Response of Linearly Viscoelastic Materials 14
6 ~$ D2 w8 k! R1 ^$ N2.2.1 Prediction of Recovery from Relaxation E(t) 14
. r! Q7 ~- N. h+ F  L2.2.2 Prediction of Response to Arbitrary Strain History 153 B5 I. t% e  y
2.3 Restrictions on the Viscoelastic Functions 17
7 W# C" U# h! {0 Q% @" e. T2.3.1 Roles of Energy and Passivity 17; j& ~( |0 z5 G7 B5 y0 K
2.3.2 Fading Memory 18! J0 v$ u6 L. X" j& c4 u$ k
2.4 Relation between Creep and Relaxation 193 M  @# o$ x. b9 Y3 t
2.4.1 Analysis by Laplace Transforms: J (t) ↔ E(t) 19- d/ X' x1 o6 D
2.4.2 Analysis by Direct Construction: J (t) ↔ E(t) 207 N* ^5 C5 F% I
2.5 Stress versus Strain for Constant Strain Rate 20
2 r3 v& x! t( h" h+ _. U2.6 Particular Creep and Relaxation Functions 21" X, m7 m4 Y  ~, \, b0 W
2.6.1 Exponentials and Mechanical Models 21
  O! y' R, ?8 W/ e. Y& V6 O/ h2.6.2 Exponentials and Internal Causal Variables 26
9 m2 y/ ?# j: ?' e/ O; }' H2.6.3 Fractional Derivatives 27
2 n3 c7 d5 q: L- B% H2.6.4 Power-Law Behavior 28
  D7 s1 Q7 i! ~! V2 N! a( b2.6.5 Stretched Exponential 29
+ H9 m/ r' n6 _" e8 _& ?; N5 V% u2.6.6 Logarithmic Creep; Kuhn Model 29
. b. N/ L4 Z! ^6 l& f: J2.6.7 Distinguishing among Viscoelastic Functions 305 f) i  _# L3 V+ f9 q) w9 p) o7 Y  v
2.7 Effect of Temperature 30
" y$ N4 `. t3 @0 C2 Y, {2 ~) E* {2.8 Three-Dimensional Linear Constitutive Equation 33
( Z# F! w4 n& P7 u: c2.9 Aging Materials 354 ^9 G. {. C. J
2.10 Dielectric and Other Forms of Relaxation 35
7 g/ b0 _: V: {4 u  f2.11 Adaptive and “Smart” Materials 36
7 Z/ D# u7 |. o, I' m7 a; U  w. b2.12 Effect of Nonlinearity 37$ q; Z/ V% T3 x# V9 Q2 q
2.12.1 Constitutive Equations 371 u7 r0 K2 H' ]2 b
2.12.2 Creep–Relaxation Interrelation: Nonlinear 400 Q) H1 w4 _7 D) W& `
2.13 Summary 43
8 |9 g+ ^( `  H& ]* x/ M2 U4 |2.14 Examples 43, c1 d! W8 `3 Y& Q! E' j/ ~
2.15 Problems 51
# m  P0 h! R6 S5 Q9 uBibliography 52+ F' L% E$ }# |9 P1 }! g

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3 Dynamic Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
1 e0 U/ z2 i6 x8 v; U6 C3 Q6 ^3.1 Introduction and Rationale 55
6 i' g- q! w8 ~  P3.2 The Linear Dynamic Response Functions E∗, tanδ 56
$ t0 A) P" m  I# }. C  o5 B3.2.1 Response to Sinusoidal Input 57# h: R* s; E, P; K" @( j
3.2.2 Dynamic Stress–Strain Relation 593 t5 x% R# h' M& G
3.2.3 Standard Linear Solid 62
* o5 a1 f" ^+ P# |3.3 Kramers–Kronig Relations 63
+ y, z! r/ M6 [5 [: b& ?3.4 Energy Storage and Dissipation 655 F; d/ g/ @( R0 J# p7 ]" X  G
3.5 Resonance of Structural Members 67; r& {8 |; k+ h4 C! e
3.5.1 Resonance, Lumped System 67
. y* g9 D, O; G/ v& V. K% J% k3.5.2 Resonance, Distributed System 71) B) _. w# A# h  d: R" D  w3 @
3.6 Decay of Resonant Vibration 74
9 O4 M$ P% l6 B# v8 n3.7 Wave Propagation and Attenuation 770 ^4 A$ G: B, I. J
3.8 Measures of Damping 79  |$ T4 Z" O/ t. b/ o) i
3.9 Nonlinear Materials 79: z1 p  K& @. g# m  g: G3 K8 U1 X
3.10 Summary 81
, ]# D8 {& h8 E0 d3.11 Examples 81
4 X& d' v! ^2 M6 U3.12 Problems 88) l# @* O( g2 n: h4 \
Bibliography 893 F* B1 j; M/ |! q( Z" c6 T& j) q1 @

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4 Conceptual Structure of Linear Viscoelasticity . . . . . . . . . . . . . . . 91
, G) Q3 X8 @; ]0 t8 l4.1 Introduction 91/ f+ C5 J( Z0 t5 t) Y- m
4.2 Spectra in Linear Viscoelasticity 92
7 C* y" b4 O  L+ B+ F3 K6 ^* u6 o4.2.1 Definitions H(τ ), L(τ ) and Exact Interrelations 92
8 l5 F! e+ ^8 S/ Q) Q% W4.2.2 Particular Spectra 935 C; Q8 m2 m4 E* s% |
4.3 Approximate Interrelations of Viscoelastic Functions 95
8 V! ]7 X7 o: M$ b- x' S* k# _; ^* f4.3.1 Interrelations Involving the Spectra 95& ?: y$ H4 X7 _( Y. ]  ]0 O6 F
4.3.2 Interrelations Involving Measurable Functions 98
6 Z  @. ~6 g0 h7 J' a2 A8 H4.3.3 Summary, Approximate Relations 1017 ]' @( r: R7 [. F1 {7 v) ]0 j
4.4 Conceptual Organization of the Viscoelastic Functions 101
/ u: o8 o) K  w2 `7 d) Y4.5 Summary 104
' c( h" N: ^2 Y  ~4.6 Examples 104* A% I' X  Q2 @3 N$ B2 ]* j
4.7 Problems 109& C: z6 Z- z  m4 W" ?7 \' d2 ]& a
Bibliography 109
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5 Viscoelastic Stress and Deformation Analysis . . . . . . . . . . . . . . . 111
1 j$ }6 p6 P" q: Q  x( n5 F5.1 Introduction 1117 e+ |* j& G3 Z) m
5.2 Three-Dimensional Constitutive Equation 111* c& l  ]" z- r: i. I- z, P9 h
5.3 Pure Bending by Direct Construction 112
* \' n% H, v* a% e7 ]" j- y' Y! o5.4 Correspondence Principle 1141 ?/ a7 C' x6 T" _1 o( l: C" R
5.5 Pure Bending by Correspondence 116
: ]+ L: F" b2 ~3 I5 J$ C5.6 Correspondence Principle in Three Dimensions 116( T2 _. l7 H: D- f% A  m
5.6.1 Constitutive Equations 1162 B9 V& ~, u' ]3 F
5.6.2 Rigid Indenter on a Semi-Infinite Solid 117' e# |+ `3 N6 J3 @5 S2 |2 R
5.6.3 Viscoelastic Rod Held at Constant Extension 119
; a* ]' r4 c* X$ y9 h- d. H5.6.4 Stress Concentration 119
0 W0 i; b/ d* n; y% ~5.6.5 Saint Venant’s Principle 120
3 D/ F  _2 E) \' _: E8 U5.7 Poisson’s Ratio ν(t) 121
5 E" A$ s2 _, I( G( m) G; [5.7.1 Relaxation in Tension 121. }/ ~! {/ r2 ~
5.7.2 Creep in Tension 123
0 C- R, S$ a+ p5.8 Dynamic Problems: Effects of Inertia 1245 b0 f. k" |4 B" P6 `4 F6 [
5.8.1 Longitudinal Vibration and Waves in a Rod 124
5 V; i' @& J7 I5 `3 P" J) M6 s8 x5.8.2 Torsional Waves and Vibration in a Rod 1257 L1 \0 g* z& V
5.8.3 Bending Waves and Vibration 128# n: }( o$ u9 W( ~
5.8.4 Waves in Three Dimensions 129- u6 }, ]0 A6 r4 A# ]6 g3 A
5.9 Noncorrespondence Problems 131. U* S1 y1 v( O
5.9.1 Solution by Direct Construction: Example 1318 n- p7 c. K: ?- B" }
5.9.2 A Generalized Correspondence Principle 132+ P6 A9 D: f1 @4 R+ s
5.9.3 Contact Problems 132# X, P, q- N8 o2 ~
5.10 Bending in Nonlinear Viscoelasticity 133
1 ?  U! R$ T/ b1 P5.11 Summary 134: J) i( q0 D$ r1 W0 H# j$ n& h1 y
5.12 Examples 134
+ v6 m9 ~; s  q) Z2 J6 n; {  t9 T0 S5.13 Problems 1429 H+ t1 V0 g, Z" A2 z4 T/ y
Bibliography 1429 ^: o/ B. Z' d' |. T& ?% Q4 K4 D

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. L& o* l7 D. P) N7 W* m6 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1451 v" i3 u- r/ L! |
6.1 Introduction and General Requirements 145; i1 `+ K5 m; k4 J5 I
6.2 Creep 146  m, x( G" n/ |" x
6.2.1 Creep: Simple Methods to Obtain J (t) 146
6 N/ |& q: [# y/ e, A9 Z; J! C$ y6.2.2 Effect of Risetime in Transient Tests 146
. f4 v* v  O5 g1 M) y6.2.3 Creep in Anisotropic Media 148! I6 a+ X- n' Y7 ]4 b. g' m" r
6.2.4 Creep in Nonlinear Media 148
( R) |) v  S; @- K  C6.3 Inference of Moduli 150" c7 H1 g0 b. m/ q7 _) }* I
6.3.1 Use of Analytical Solutions 150
: X7 K* I# I& P/ H, A6.3.2 Compression of a Block 151
, U/ t" Q9 l/ s$ A3 b6.4 Displacement and Strain Measurement 1524 `+ V+ H- @- }% q& ?0 y, X! f
6.5 Force Measurement 1563 k! S: l  E2 V& Q6 M1 \
6.6 Load Application 1573 q' Z/ x" J4 A, x
6.7 Environmental Control 157
/ n% d( D. k. d# E& `6.8 Subresonant Dynamic Methods 158
" W5 b: R9 J! |6.8.1 Phase Determination 158
' N5 o, \" E4 i6 T6.8.2 Nonlinear Materials 160
% _6 }" s/ y' G! K" M; }8 R# y6.8.3 Rebound Test 1618 [& l: `4 `7 J* t3 P! ^. O
6.9 Resonance Methods 1619 t3 z6 B* ?6 k7 C9 t4 s, A4 X) V
6.9.1 General Principles 1613 W8 x* l5 ]' d0 C
6.9.2 Particular Resonance Methods 163' x% m- a0 h0 A+ M/ f
6.9.3 Methods for Low-Loss or High-Loss Materials 166
) I4 _+ H& g/ R. Z$ S6 m7 B6.9.4 Resonant Ultrasound Spectroscopy 168
% |6 k+ `$ l& _$ P6.10 Achieving a Wide Range of Time or Frequency 171
3 A+ k! h) @, }6.10.1 Rationale 171
$ |- G! j' p6 p2 g5 V6.10.2 Multiple Instruments and Long Creep 172, b7 p) d' d2 [6 q' u, \
6.10.3 Time–Temperature Superposition 172
' @. ]$ C' ?" z6.11 Test Instruments for Viscoelasticity 173) y3 k1 e+ D5 A3 j7 B! X& q* R* g
6.11.1 Servohydraulic Test Machines 173) W* q5 O$ a3 P2 o/ F4 c- S0 P: o/ a
6.11.2A Relaxation Instrument 174
$ `6 _: h$ O' ^) D+ s( Z9 O. [6.11.3 Driven Torsion Pendulum Devices 174  @5 K/ y2 a' P7 d
6.11.4 Commercial Viscoelastic Instrumentation 178
# a5 G' [9 g$ f- E$ T7 u5 ?6.11.5 Instruments for a Wide Range of Time and Frequency 179
; R* _2 p2 v' o6.11.6 Fluctuation–Dissipation Relation 182) _6 \! [  s0 U- i2 z, P
6.11.7 Mapping Properties by Indentation 183
" A  _; @, d; a6.12 Wave Methods 184
  @6 E& F+ t) ]9 w, v! R+ m4 @6.13 Summary 188# j- ?6 G& T6 U% P0 b# c
6.14 Examples 188/ V& x3 F& p5 v- B* f' F4 o
6.15 Problems 2008 `( M' Y1 w6 N6 x
Bibliography 201
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7 Viscoelastic Properties of Materials . . . . . . . . . . . . . . . . . . . . . 207
, M) R% O- j- i. f7.1 Introduction 207, t2 L( h- @" R( K' ^# M4 k7 k7 x
7.1.1 Rationale 207
2 b8 s) v% \1 m+ w" E; I) u7.1.2 Overview: Some Common Materials 207
5 {0 H8 e1 M2 A# _- S- I7.2 Polymers 2088 t2 k: T7 g4 b4 M
7.2.1 Shear and Extension in Amorphous Polymers 208
( e; z4 q- F" C- B! G" T7.2.2 Bulk Relaxation in Amorphous Polymers 212
3 O, K: f+ Q: K. f6 m* B7.2.3 Crystalline Polymers 2130 l" U& M' y- t0 D: l) l5 u
7.2.4 Aging and other Relaxations 214
# V) `; h4 b" ?' e( {# q7.2.5 Piezoelectric Polymers 214
3 g5 N1 _. [  B# U6 I# z( r; E4 h7.2.6 Asphalt 214( K5 n4 G; }2 B2 H3 r' f" w
7.3 Metals 215
$ T& A4 O" Y. [# O- g7.3.1 Linear Regime of Metals 215# }1 J0 ~# M4 C- Q
7.3.2 Nonlinear Regime of Metals 217
# i# y9 d) ]% p3 D7.3.3 High-Damping Metals and Alloys 2193 A' ]% ]/ ^0 O
7.3.4 Creep-Resistant Alloys 224
  O+ H! R; g3 I' ~# A8 }, Q7.3.5 Semiconductors and Amorphous Elements 225
7 e- s4 O% @5 C+ R$ Z. l1 t7.3.6 Semiconductors and Acoustic Amplification 2260 w- E/ f1 p7 u  Q
7.3.7 Nanoscale Properties 226
" Y- A* m. n  W0 Z6 {9 i% B7.4 Ceramics 227* z* f5 W! n; V
7.4.1 Rocks 2273 B0 _* Q6 s+ m/ _1 c0 g1 l0 @
7.4.2 Concrete 229
" O& @" \3 n) q  s* r7.4.3 Inorganic Glassy Materials 2311 {8 T7 [, L( X0 v. U4 y* w7 v
7.4.4 Ice 231/ H7 y4 z7 o" I
7.4.5 Piezoelectric Ceramics 232
8 C4 q- [1 h, q6 ?7.5 Biological Composite Materials 233
7 m& d5 |, t& G) J4 i% O. y7.5.1 Constitutive Equations 234
: }* A2 e5 B; C$ T1 J8 ?$ {7.5.2 Hard Tissue: Bone 234
4 @* |  K8 V2 ~, o/ l7.5.3 Collagen, Elastin, Proteoglycans 236  O; X9 a5 N4 P; i' b
7.5.4 Ligament and Tendon 237& Q/ i7 u+ Q- g2 d  `) r+ a+ R
7.5.5 Muscle 240
' @; D& Z2 C" K* t7.5.6 Fat 243( |% u  J( g. Q0 R1 y
7.5.7 Brain 243
6 S1 B2 H" \: Q& ]7.5.8 Vocal Folds 2446 y* P! `1 T# T) L" ~
7.5.9 Cartilage and Joints 2448 V9 Q/ s& Y/ I( b5 c4 V
7.5.10 Kidney and Liver 246
; d( Z  C4 p) i0 [7.5.11 Uterus and Cervix 246
+ H2 e2 l. m) Z; j7.5.12 Arteries 247
3 O; E; {. r7 D- H3 r7 W+ p7.5.13 Lung 248
  Z3 a. B1 c2 Y7.5.14 The Ear 2482 ~( D1 m% b- v3 W6 r! c& j# x
7.5.15 The Eye 249+ H5 s& `( ~" _0 |
7.5.16 Tissue Comparison 251
) L( B$ W3 o' X8 _  Q( N4 x4 ?7.5.17 Plant Seeds 2529 z! Y4 s8 p- \7 d5 U. d+ M
7.5.18 Wood 252* \4 e2 F7 X; A/ j# d
7.5.19 Soft Plant Tissue: Apple, Potato 253' V  `& ?3 E0 k
7.6 Common Aspects 253
/ ?) W1 X$ @" H% G' V$ _7 M7.6.1 Temperature Dependence 253
7 k/ V3 |/ X( d+ R7.6.2 High-Temperature Background 254
) ^' K9 E, S7 M% P7.6.3 Negative Damping and Acoustic Emission 255! Z0 R: S' ?5 V* E. w9 y) t
7.7 Summary 2555 j+ W4 X; k8 G/ |5 u" c
7.8 Examples 255! a0 T0 _: ~/ Y  X% @/ w
7.9 Problems 256
6 Q9 z" U0 H4 ?% bBibliography 257- s' L% t! I8 M8 P

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8 Causal Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
$ a8 v+ q, S* I4 v5 h4 a2 L8.1 Introduction 271
# {- b/ D. w! ^, ^7 n0 z7 @, h) m8.1.1 Rationale 271. h- j- `$ H& w5 o, V# F! J
8.1.2 Survey of Viscoelastic Mechanisms 271
$ Y) E% C/ E+ r" T2 x( B1 Q8.1.3 Coupled Fields 273: }+ J" b* `, j' v* X4 c9 N
8.2 Thermoelastic Relaxation 274* U  y. M8 s0 [$ a* q8 `% l
8.2.1 Thermoelasticity in One Dimension 274. c+ F2 X; d/ j7 r
8.2.2 Thermoelasticity in Three Dimensions 275$ E! L% G% N. J$ |' d
8.2.3 Thermoelastic Relaxation Kinetics 276/ A9 @& Z0 V' T8 r* K
8.2.4 Heterogeneity and Thermoelastic Damping 278$ C  u, o4 y1 v( p. R3 \/ y
8.2.5 Material Properties and Thermoelastic Damping 280( Y) E& w/ _; r; J  j
8.3 Relaxation by Stress-Induced Fluid Motion 280
$ |# ~& v2 M$ W: u9 R7 o" N/ E- Y8.3.1 Fluid Motion in One Dimension 280* B, K4 b+ C/ F3 M# d# C
8.3.2 Biot Theory: Fluid Motion in Three Dimensions 281
( t: s3 N+ G8 Z9 ^0 ]+ C8.4 Relaxation by Molecular Rearrangement 286$ O: d! J' ]4 ]3 g
8.4.1 Glassy Region 286
6 D$ |/ g! \' n& D8.4.2 Transition Region 287
: T  ^/ o/ h; U* O8 d, |6 X8.4.3 Rubbery Behavior 2899 ^6 x; L, e5 g/ D5 ?/ \
8.4.4 Crystalline Polymers 291* D$ {/ l3 q& K; @( i
8.4.5 Biological Macromolecules 2922 A- d' _% e7 z( y% G, v0 F
8.4.6 Polymers and Metals 292
# W* L; V6 R8 B9 Y6 a8.5 Relaxation by Interface Motion 2929 d' a. f& ~- _+ u( S, l
8.5.1 Grain Boundary Slip in Metals 292
+ `3 I9 e& }6 w& S8.5.2 Interface Motion in Composites 294# T" \! B8 V1 [% }3 W
8.5.3 Structural Interface Motion 294
8 C! V6 r7 r- r0 V# k8.6 Relaxation Processes in Crystalline Materials 294
% J: Q6 n4 ?9 K' X0 G/ s# H8.6.1 Snoek Relaxation: Interstitial Atoms 294) D* z; b0 S2 r/ |* B; v( u& n
8.6.2 Zener Relaxation in Alloys: Pairs of Atoms 2988 [) E9 I& L1 k1 E
8.6.3 Gorsky Relaxation 299' J1 r$ }2 y4 w
8.6.4 Granato–L ¨ ucke Relaxation: Dislocations 300- _% {* n3 v+ q6 s+ }0 Y
8.6.5 Bordoni Relaxation: Dislocation Kinks 303
- j# J/ _; B2 b6 w0 q  Z5 h1 [8.6.6 Relaxation Due to Phase Transformations 305
* f; v0 W  {( Y: r# O8.6.7 High-Temperature Background 314
# T+ D, ?  h, {; j) @8 I8.6.8 Nonremovable Relaxations 315+ Z7 L; v: M) O7 {7 c
8.6.9 Damping Due to Wave Scattering 316; t4 Z0 I8 T5 d
8.7 Magnetic and Piezoelectric Materials 316- N; k1 R: ]4 O2 B9 r
8.7.1 Relaxation in Magnetic Media 316
2 n- W! N) B7 {4 k9 v8.7.2 Relaxation in Piezoelectric Materials 3183 n  z3 c% X' L  `8 F! b4 c% m
8.8 Nonexponential Relaxation 322# \! Q, F7 a/ e( ?9 [3 F! B- F2 G$ n. o
8.9 Concepts for Material Design 323
* [2 j7 h6 f0 s( v8 c5 k6 j8 F% |8.9.1 Multiple Causes: Deformation Mechanism Maps 323. r3 C0 X  }2 ]  s4 Z+ _, K
8.9.2 Damping Mechanisms in High-Loss Alloys 3263 r, p$ {) a# V7 C. d4 c1 b
8.9.3 Creep Mechanisms in Creep-Resistant Alloys 3260 M/ F$ X1 h- _0 s$ v  p& x
8.10 Relaxation at Very Long Times 327! l1 ]- I1 T) D0 o% X4 _4 `% s; d$ z, K
8.11 Summary 327
8 t7 _% D. V: `& T$ g! A8.12 Examples 328
) v( J: B6 }$ y, y5 s8.13 Problems and Questions 332- u% g$ q/ S& O5 `
Bibliography 3326 W+ \& i7 s/ O0 O- e
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" d0 n( q( L* K. Q; e: \9 Viscoelastic Composite Materials . . . . . . . . . . . . . . . . . . . . . . . 3412 q6 b9 c* Y: d! ~4 n1 ?8 I8 y
9.1 Introduction 341
+ `; X  s' M6 U' m: m9.2 Composite Structures and Properties 341
9 g* b; g9 r! x1 }5 j2 O9.2.1 Ideal Structures 3416 }# S4 q: ], `- `
9.2.2 Anisotropy due to Structure 342
+ e' j) e2 v% r  b8 \9.3 Prediction of Elastic and Viscoelastic Properties 3441 ], Y  i( }" H
9.3.1 Basic Structures: Correspondence Solutions 344
0 G+ @4 q1 Q# f" B. |9.3.2 Voigt Composite 345
, m" j$ ~  \! N% Z" [( ]9.3.3 Reuss Composite 345
& H8 ~  c, s& E- |& T8 ]9.3.4 Hashin–Shtrikman Composite 346
6 d8 ?- f/ ~  W5 {9.3.5 Spherical Particulate Inclusions 347
  [% M. }  K  w! K7 B) b7 h9.3.6 Fiber Inclusions 349% X, d* Z9 ]7 B0 I; k1 b# d7 P" C
9.3.7 Platelet Inclusions 349; H' ]) z0 X5 q* L
9.3.8 Stiffness-Loss Maps 350
3 F1 s7 \% Q% }& }2 @  U  P& D* h9.4 Bounds on the Viscoelastic Properties 3539 ]- f' N% A- F% x3 a$ u+ C
9.5 Extremal Composites 354: C: U5 U0 U1 W$ V( Q* L8 K
9.6 Biological Composite Materials 356) f  F  G  x0 \7 W
9.7 Poisson’s Ratio of Viscoelastic Composites 357
! Y4 [: \, O. H4 {* `) y9.8 Particulate and Fibrous Composite Materials 358% e; Z# c) Y6 ^2 B& [& e2 l
9.8.1 Structure 358$ L. n6 H1 I2 P8 K$ V
9.8.2 Particulate Polymer Matrix Composites 359: @# f* D6 Y; Q4 ]3 O$ l- L
9.8.3 Fibrous Polymer Matrix Composites 361
2 t$ l" B, `! N3 Z1 K9.8.4 Metal–Matrix Composites 362
4 m+ G/ e/ H& @9 |/ y& \9.9 Cellular Solids 363
6 |5 W8 f( _: h. s9.10 Piezoelectric Composites 3661 f+ I. R; P& ~8 P
9.11 Dispersion of Waves in Composites 366
" X" p* q/ g. H# [9.12 Summary 367
$ v8 W8 Q/ _! F" l9.13 Examples 367
0 V+ i$ X1 E0 d" h9.14 Problems 370
) i5 X& r" [2 @9 e; O! eBibliography 370
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6 T5 B7 E8 {- S* `$ v6 L
  k5 d$ m+ |: e6 p10 Applications and Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . 377( Z( P' \1 O# V* L# n) Y  h
10.1 Introduction 377# a' B+ v1 w" d" D: ^- V. ?) e( M- o& k
10.2 A Viscoelastic Earplug: Use of Recovery 377
; l9 @; O! K3 h4 R/ ^6 w: T( D10.3 Creep and Relaxation of Materials and Structures 378% `/ l, x. j- d# l/ @& W$ d
10.3.1 Concrete 378
$ K0 _* k4 t9 z2 f, ?: x% Q10.3.2 Wood 378
9 E, o- G: E5 Z- h* g1 U/ o. n9 c10.3.3 Power Lines 379
3 v, U7 A( T# n10.3.4 Glass Sag: Flowing Window Panes 380
) q  z  g- T" ?9 `- V. G( K10.3.5 Indentation: Road Rutting 380, m4 o( ?$ I5 u' k% i1 n
10.3.6 Leather 381; h, w& y) u: V7 a  s. R7 y
10.3.7 Creep-Resistant Alloys and Turbine Blades 381
4 H9 j5 b* \  h) F10.3.8 Loosening of Bolts and Screws 382( F7 y% j8 U5 f/ D/ j, p
10.3.9 Computer Disk Drive: Case Study of Relaxation 384& `$ F" `/ u4 Y& K. r4 O# l4 }
10.3.10 Earth, Rock, and Ice 385
4 @' ]; b% h2 i* L# J10.3.11 Solder 386
; E" b' k. }8 W/ O10.3.12 Filamentsi nL ight Bulbs and Other Devices 3870 K( c5 }& _1 ]# p/ C- o
10.3.13Tires: Flat-Spotting and Swelling 3880 q' \2 a6 X, t1 V) v
10.3.14Cushionsfor Seats and Wheelchairs 388
; l! W! H; J: X/ V  I# f; S10.3.15 Artificial Joints 389
8 T; M. y  ^+ \5 I% k10.3.16 Dental Fillings 389
4 @% O  P+ p! q+ b- ]) P% d10.3.17 Food Products 389  U* b) _, T6 D0 i+ y
10.3.18 Seals and Gaskets 390
4 w( R6 h) ]/ C( u" ^9 V. n10.3.19 Relaxationi nM usical Instrument Strings 390
' x. B6 O* ~6 t5 B) o+ k10.3.20 Winding of Tape 391
( U+ N+ g, _+ o5 o; p10.4 Creep and Recovery in Human Tissue 391
3 U* n7 h) ~8 l, H10.4.1 Spinal Discs: Height Change 391
) Y% G) u/ H# E  Z% U* j10.4.2 The Nose 392# \) J) t1 J- T4 b8 _9 X! N* [
10.4.3 Skin 392
9 t3 z4 P/ S4 ?  ]% y, v10.4.4 The Head 3932 m4 a* p7 t) a* _& F
10.5 Creep Damage and Creep Rupture 3942 e- X, C+ U3 s, A& @( _" j
10.5.1 Vajont Slide 394
/ k5 X! L2 m( b6 @$ A0 s$ l2 j10.5.2 Collapse of a Tunnel Segment 394
0 F0 b" d6 T5 K3 |: C9 V' d4 m3 e+ S10.6 Vibration Control and Waves 394# S# e- k$ k: K5 C0 H( w/ ?
10.6.1 Analysis of Vibration Transmission 394
, a9 l  k% x3 R( A: W10.6.2 Resonant (Tuned) Damping 397
6 d3 h- b; h6 U; p10.6.3 Rotating Equipment Vibration 397
. j/ R! |& r- B3 a0 _+ n10.6.4 Large Structure Vibration: Bridges and Buildings 398" W) N# E2 l; l
10.6.5 Damping Layers for Plate and Beam Vibration 399
  R6 f$ O0 @: ?8 u3 m/ _10.6.6 Structural Damping Materials 400# Z4 a9 O2 _2 {* _7 V
10.6.7 Piezoelectric Transducers 4023 A* q+ J  \) g8 R4 Z1 [# l: N. g: G
10.6.8 Aircraft Noise and Vibration 402
% t7 Q  K+ e, y' D, P3 S10.6.9 Solid Fuel Rocket Vibration 404
/ r  o! K; I5 y  C7 P3 k1 T10.6.10 Sports Equipment Vibration 404- `3 N0 ]% C/ q9 Z( H. P% c! G% N
10.6.11 Seat Cushions and Automobiles: Protection of People 404
: o5 i, R' C$ j$ W. ]+ X5 h# {10.6.12 Vibrationi n ScientificI nstruments 406
5 \, k  G7 q' @6 V9 W7 _) O# C: p10.6.13 Waves 406
  F  l% L- ^% ?. U& I5 t10.7 “Smart” Materials and Structures 407
8 E* Y" v) h& p& [$ `& O10.7.1 “Smart” Materials 407
* |5 A- A9 p5 r9 H7 L10.7.2 Shape Memory Materials 408
- g$ u1 c2 v$ J, ~10.7.3 Self-Healing Materials 409
. s( s+ _' ]. K9 N7 q- w$ P% L9 o10.7.4 Piezoelectric Solid Damping 4096 v* O9 }6 K) k- @* |; _, m/ C- q
10.7.5 Active Vibration Control: “Smart” Structures 409
1 C- C9 I6 \. Y9 N" G0 o( L10.8 Rolling Friction 409
! z+ G7 Y7 K. v10.8.1 Rolling Analysis 410
% U# j6 y( y6 d% H. B5 n1 p+ O10.8.2 Rolling of Tires 411
. `0 ]! ]0 j. }% ?5 p4 e10.9 Uses of Low-Loss Materials 412
2 ^2 k9 ?$ B' n9 a$ L10.9.1 Timepieces 412& \9 F- l. t% a1 s! R
10.9.2 Frequency Stabilization and Control 413: l! O2 t7 q- A" n# ~  a
10.9.3 Gravitational Measurements 413
7 i" R: T# \: U& j7 U$ D4 ~& v- P! B6 I10.9.4 Nanoscale Resonators 414
! U3 N/ W, z6 R- j2 e+ a10.10 Impulses, Rebound, and Impact Absorption 414
! t& e- }: `" L$ x" p1 F10.10.1 Rationale 414: i  @' O% p( D+ d5 u# o
10.10.2 Analysis 415. d# T/ e& ~# s# y. x; z
10.10.3 Bumpers and Pads 418
( `6 f- d+ c6 D# K( @10.10.4 Shoe Insoles, Athletic Tracks, and Glove Liners 419+ E/ X% h, @* f' R% \& v1 C% }! A
10.10.5 Toughness of Materials 4198 ^/ A% C. f  u" P7 c7 h
10.10.6 Tissue Viscoelasticity in Medical Diagnosis 420! l) t7 _/ u7 L! g0 O
10.11Rebound of a Ball 421- F! e0 n/ l: k
10.11.1 Analysis 421" w, p: i9 V* y1 S
10.11.2 Applications in Sports 422
' e% ~1 b4 y- }8 z) p10.12 Applications of Soft Materials 424
' h. N, M1 E6 `7 V2 X& ]. E10.12.1 Viscoelastic Gels in Surgery 4243 D, W1 P6 e0 G# N$ _6 o+ V
10.12.2 Hand Strength Exerciser 424/ U4 F8 v' O& Q- V
10.12.3 Viscoelastic Toys 424
% v: t# a) @- \7 q% K; G7 o5 d10.12.4 No-Slip Flooring, Mats, and Shoe Soles 425' h. O/ i& U9 ~
10.13 Applications Involving Thermoviscoelasticity 425! z; ^8 g% ?! J$ L  J! x; F. K! S" @
10.14 Satellite Dynamics and Stability 426
2 e' V; t2 n9 `9 S) |$ I' l  T10.15 Summary 428
8 l  Z* x! t3 p10.16 Examples 4292 Y' f7 J6 X: ~! Y1 \+ W( ~$ [
10.17 Problems 431' t" K+ D$ \- P3 u; y5 E0 I/ Q
Bibliography 431# Z' i! N( T3 g+ T4 M4 l) R6 s; ^

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" z! X& y/ h& I) b: oA: Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4419 r: v3 z2 ~7 ?8 Z: l. B3 H
A.1 Mathematical Preliminaries 441
, ]# [. A6 q' O8 b8 qA.1.1 Introduction 441
0 R5 ~/ W" \3 Y: iA.1.2 Functionals and Distributions 441
) }' e7 A& i' K- pA.1.3 Heaviside Unit Step Function 442
5 [) X( e3 w4 D# E' A- v8 d8 jA.1.4 Dirac Delta 442
3 f6 j. [  F% W/ Q3 RA.1.5 Doublet 443
! s2 @1 n6 e. K6 jA.1.6 Gamma Function 4454 F2 x& ^+ z8 V  ^
A.1.7 Liebnitz Rule 445  e: u6 }' ^# L, A* j2 l: q
A.2 Transforms 445
! x$ A- D4 p/ y, BA.2.1 Laplace Transform 446' Y# `" n# i, o: J; I
A.2.2 Fourier Transform 446
% V$ k& }: z5 h  Z8 q2 o3 tA.2.3 Hartley Transform 447% M& o: [" \7 ?
A.2.4 Hilbert Transform 447
: L; V6 E' B% J/ _* V3 F9 `A.3 Laplace Transform Properties 448" W" F; Y+ X9 _4 f, |
A.4 Convolutions 449
( o. c+ u/ V$ l& eA.5 Interrelations in Elasticity Theory 451# q' D9 O7 n5 G+ c; X( `
A.6 Other Works on Viscoelasticity 451
8 ~# o) ], _) fBibliography 452
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( a3 [, [0 ]4 Z3 |B: Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455% A2 c- N( F! K/ A; M
B.1 Principal Symbols 455# @( ~7 ?5 o% ^& G
Index 457  j' \" ]( t! J# m! }, l+ C* W

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