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Viscoelastic Materials Roderic Lakes 2009 Part 1-2.rar
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Viscoelastic Materials Roderic Lakes 2009 Part 2-2.rar
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目录* |% G, ]9 i& M0 c& {1 @8 |. o4 p
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Contents
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Preface page xvii6 u% Y7 M; M6 `) z
1 Introduction: Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 `2 H4 s: ]- ?4 e% A. h
1.1 Viscoelastic Phenomena 1
" }6 {* t- p, n+ k2 S8 `7 k. m1.2 Motivations for Studying Viscoelasticity 32 ] K# h3 H4 [7 c& t5 C. S
1.3 Transient Properties: Creep and Relaxation 3) M7 i$ p# L* |! _) X
1.3.1 Viscoelastic Functions J (t), E(t) 31 W' ]1 u8 N5 x
1.3.2 Solids and Liquids 7
$ W2 F2 S- T2 z/ R% M1.4 Dynamic Response to Sinusoidal Load: E∗, tanδ 8
2 C& V9 h- F+ ]; i) u* k$ t8 N1.5 Demonstration of Viscoelastic Behavior 10
% G7 y! V& I( a% L# |# n1.6 Historical Aspects 10: P2 J+ k r- }
1.7 Summary 112 j3 V" {9 V |3 f- V5 \
1.8 Examples 116 I" w1 @" E# @- o p' E; C8 d
1.9 Problems 12/ T7 G! ]$ J5 |2 v( I9 D# F5 L
Bibliography 12
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# [' R2 r7 C' W' {# v2 Constitutive Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4 ?3 ~8 i6 v/ e5 F1 S# T* A% t2.1 Introduction 143 S7 j5 m& L5 A2 j3 x
2.2 Prediction of the Response of Linearly Viscoelastic Materials 14/ f! b% P: h& l/ t
2.2.1 Prediction of Recovery from Relaxation E(t) 14 P$ u8 J% b6 D# w% _8 m
2.2.2 Prediction of Response to Arbitrary Strain History 15
$ O7 w9 x3 ?4 c v4 z' W/ s- w2.3 Restrictions on the Viscoelastic Functions 17# V" ?* c: g3 p2 s* o' o
2.3.1 Roles of Energy and Passivity 177 |7 |' p. n) `4 ]
2.3.2 Fading Memory 183 i$ ~0 [9 W& ^' F6 a
2.4 Relation between Creep and Relaxation 19! ~: z3 Q* G7 o% M
2.4.1 Analysis by Laplace Transforms: J (t) ↔ E(t) 198 S6 B3 C# D0 c3 ^/ }
2.4.2 Analysis by Direct Construction: J (t) ↔ E(t) 20
2 b0 X$ ]9 g& O8 Q0 M2.5 Stress versus Strain for Constant Strain Rate 20
# g0 U( r2 U, q# Z7 N. ?2.6 Particular Creep and Relaxation Functions 21
& B8 k3 V4 a. U, x! h2.6.1 Exponentials and Mechanical Models 21
0 M7 \2 D; c7 _0 N) A: n5 L) `5 k2.6.2 Exponentials and Internal Causal Variables 26
# k5 }; N4 x$ Z6 }0 v n% q2.6.3 Fractional Derivatives 27* Z$ d* H/ z; |7 \5 a
2.6.4 Power-Law Behavior 286 N: i5 S$ l) z M. n, M6 q& n
2.6.5 Stretched Exponential 299 g( h8 f6 L i1 ^/ w
2.6.6 Logarithmic Creep; Kuhn Model 29" `$ C+ z$ q) t1 C, ^
2.6.7 Distinguishing among Viscoelastic Functions 30! x6 I9 _* [5 c+ S5 A) m
2.7 Effect of Temperature 30% V' M; a6 A, [
2.8 Three-Dimensional Linear Constitutive Equation 33
+ c& o( b+ W8 s& z V2.9 Aging Materials 359 K+ L V6 I; T7 G K
2.10 Dielectric and Other Forms of Relaxation 35
9 Z g& i( C* f. c2.11 Adaptive and “Smart” Materials 36
8 T( \8 I1 Y8 r7 x- @1 ]* o6 G( X2.12 Effect of Nonlinearity 37
+ g$ i' E! b0 j' J. Y2.12.1 Constitutive Equations 37
9 e2 F7 E3 Q( f' R+ d$ V# s2.12.2 Creep–Relaxation Interrelation: Nonlinear 406 Y# e( K5 } |
2.13 Summary 43
4 R' u3 V- V- @$ ?$ Z2.14 Examples 43
! y/ a p. \ x- W# ~3 ^4 \7 p1 b2.15 Problems 51 x' W/ F* a1 R
Bibliography 525 P6 s J6 V. h2 U& G: ]
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( x" [8 X1 a; Z) ]3 I3 Dynamic Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55: e/ |6 w1 A; |/ d. s% H$ m
3.1 Introduction and Rationale 554 Y [+ L+ E6 d0 `: c4 ^2 m
3.2 The Linear Dynamic Response Functions E∗, tanδ 56/ ~& J& a" b4 y5 S$ i& L' g2 Q
3.2.1 Response to Sinusoidal Input 57" h6 X+ |- R# ?# }
3.2.2 Dynamic Stress–Strain Relation 59
% x$ {$ f8 [) n/ D# l7 b3.2.3 Standard Linear Solid 62
6 Q7 Z* X) p3 h$ t3.3 Kramers–Kronig Relations 63: ?; _4 U- s2 } j( i: u' B5 c6 J0 N
3.4 Energy Storage and Dissipation 65/ f& r `2 G6 V# d/ R& Y# x
3.5 Resonance of Structural Members 67
: F& n2 e+ Q2 x. d5 K$ _8 c3.5.1 Resonance, Lumped System 67
+ L! O* i# S, `4 [5 u/ g3.5.2 Resonance, Distributed System 71
" z9 v. P9 x; t2 x! P3.6 Decay of Resonant Vibration 74! }" L9 A4 B& S/ o! o" c
3.7 Wave Propagation and Attenuation 77
0 E' w2 U/ B, n) y3.8 Measures of Damping 79
5 G; `: h+ }) V. m4 ]3.9 Nonlinear Materials 79
$ ?: r- A% t, W! w& M. j$ e( E3.10 Summary 81
7 H2 E* h# D: t C: T. P3.11 Examples 81
- r" m9 X' Q& F8 u3 F2 S( c3 Q* @3.12 Problems 88. G# O( p- D( N, O8 ?( [* d1 M3 I
Bibliography 89
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4 Conceptual Structure of Linear Viscoelasticity . . . . . . . . . . . . . . . 91) L7 T( ~8 ?- r7 X+ W
4.1 Introduction 91! L. Y5 ]6 n, S( A) c. ~
4.2 Spectra in Linear Viscoelasticity 92
1 J6 L* E: ]0 d0 f& k4.2.1 Definitions H(τ ), L(τ ) and Exact Interrelations 92
% M" _* t. O# h* V" i! |$ N) e4.2.2 Particular Spectra 93
. X4 S9 ~1 W$ m0 M1 w4.3 Approximate Interrelations of Viscoelastic Functions 95
5 U0 \( `1 G6 M% r3 T4.3.1 Interrelations Involving the Spectra 952 K9 }6 I& h0 ?+ z" R( L: _- E
4.3.2 Interrelations Involving Measurable Functions 987 ^0 M5 t2 s; d6 M$ E0 j t
4.3.3 Summary, Approximate Relations 101: \1 J! r* ?' p: R# @* z" @4 Z
4.4 Conceptual Organization of the Viscoelastic Functions 101
/ K- }9 k! e" m5 c; I+ z- ~$ J9 b4.5 Summary 104, ^4 q/ k: o' a: |8 f, W
4.6 Examples 1041 d F* ^- i2 W+ R2 _. n! R
4.7 Problems 109# [4 T- W0 e+ T6 v/ E* @7 ^! M
Bibliography 109/ J8 M: p7 p4 Y- e
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/ w7 b3 G* h6 k. \7 d5 Viscoelastic Stress and Deformation Analysis . . . . . . . . . . . . . . . 111
0 d4 r, o" h8 k5.1 Introduction 111
$ {- g9 j1 ~. k5 }+ _5.2 Three-Dimensional Constitutive Equation 111! ~% Q z. Y0 @0 G4 m W% f
5.3 Pure Bending by Direct Construction 112
8 q+ w: r/ w+ ]! S) v3 I5.4 Correspondence Principle 114
5 x$ M$ Q" z: ~+ p- J9 Q9 [8 A5.5 Pure Bending by Correspondence 1165 t# p3 F Z$ F
5.6 Correspondence Principle in Three Dimensions 1168 `0 Z: }4 t- |
5.6.1 Constitutive Equations 1164 z; Q5 t5 [/ n7 T) \. o! h2 n
5.6.2 Rigid Indenter on a Semi-Infinite Solid 117' o, f1 J7 Q5 l
5.6.3 Viscoelastic Rod Held at Constant Extension 119- x# \; z; q0 r5 V. Z& [
5.6.4 Stress Concentration 119- F5 V' {- J+ |2 I; t8 ^: k
5.6.5 Saint Venant’s Principle 120- i) C# u4 g/ H2 N& B
5.7 Poisson’s Ratio ν(t) 121
, B# q- U8 j: X( _2 }/ E8 A5.7.1 Relaxation in Tension 121
6 F. ?. m* d1 X M5.7.2 Creep in Tension 123. }) d, U2 ~1 ?$ m
5.8 Dynamic Problems: Effects of Inertia 124
- _3 m. p/ ?9 h3 l f$ s2 p5.8.1 Longitudinal Vibration and Waves in a Rod 124
) z" h, I) I9 e4 }, @0 Q0 z5.8.2 Torsional Waves and Vibration in a Rod 1252 T$ g8 j! k7 Q+ S
5.8.3 Bending Waves and Vibration 128" ^! W+ I3 _ T0 x x
5.8.4 Waves in Three Dimensions 129
# [- i3 `; M1 {; I2 l, B$ E5.9 Noncorrespondence Problems 131# B. {; a, i4 \: C
5.9.1 Solution by Direct Construction: Example 131) g' i5 G2 E) O- a7 u4 g+ c
5.9.2 A Generalized Correspondence Principle 132, u3 L0 V; W5 p' F$ V* |* s/ `4 k
5.9.3 Contact Problems 132
! K$ |2 U; O# ^: [1 U; H# l5.10 Bending in Nonlinear Viscoelasticity 133
. U- Z! {9 q$ @9 C5.11 Summary 134
4 S/ g: Z, n+ q" ^: u Z5.12 Examples 134
' O3 T7 t' n2 R+ ~, b: ?5.13 Problems 142
) a, _! ]& ^ zBibliography 142
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6 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1450 `! A+ W9 s. V5 {/ a- i
6.1 Introduction and General Requirements 145; [5 A1 J- y& \! X3 Z
6.2 Creep 146 O0 ]: W0 V5 t; ]# D. B) C+ P
6.2.1 Creep: Simple Methods to Obtain J (t) 146
0 A, t( j8 D3 {6.2.2 Effect of Risetime in Transient Tests 146# P3 T* \ D3 K s0 c2 ]/ ^+ U
6.2.3 Creep in Anisotropic Media 1487 h. I/ f7 q0 q2 S# p* {7 F! w8 W& Q
6.2.4 Creep in Nonlinear Media 148
6 @) l0 b& G( o$ m5 W8 H6.3 Inference of Moduli 150. n4 {, q8 p, l1 u7 B' C- b2 [7 C
6.3.1 Use of Analytical Solutions 150; D7 Y: c+ j" O* o
6.3.2 Compression of a Block 151! J" G5 ^: a$ s- e* o
6.4 Displacement and Strain Measurement 152( ^8 D, @( F/ I# y$ z/ D+ J$ ?+ i
6.5 Force Measurement 156
3 W- R" ?, V4 E# N7 ^& v3 I6.6 Load Application 1571 W( @2 U5 z! W: p( N
6.7 Environmental Control 157
( y: L' q- J9 S" S0 d2 u8 N6.8 Subresonant Dynamic Methods 158
. y/ c: Z ^( p0 R2 x6.8.1 Phase Determination 1586 [( T% G! O3 c% }
6.8.2 Nonlinear Materials 160
- [- M% D, b7 d) T! D( z z3 W6.8.3 Rebound Test 161+ _2 F- }# e6 }) f, b6 M
6.9 Resonance Methods 1614 D" n9 x8 u: d
6.9.1 General Principles 161
; D! ]1 {4 X3 o. R8 Q, ^6.9.2 Particular Resonance Methods 1632 Z1 r" S* @2 F% J
6.9.3 Methods for Low-Loss or High-Loss Materials 1667 _, p1 X) z! @3 F2 @/ [# `
6.9.4 Resonant Ultrasound Spectroscopy 168
# ~+ K4 P! J" n2 n9 s# L6.10 Achieving a Wide Range of Time or Frequency 171* c# f* o8 }' h+ D- B6 j
6.10.1 Rationale 171
Q4 B* F1 q* C1 v6.10.2 Multiple Instruments and Long Creep 172" L- W$ F; s( m! ?1 f5 O0 m* i
6.10.3 Time–Temperature Superposition 172
+ E% i# W: M8 n; g; q3 a% }6.11 Test Instruments for Viscoelasticity 173
9 _ F! C% s/ Z. \# `6 ^6.11.1 Servohydraulic Test Machines 173
* ?1 i0 }+ F8 f5 {$ x6 o( L6.11.2A Relaxation Instrument 174" P4 g9 o1 B4 G; O' D% G
6.11.3 Driven Torsion Pendulum Devices 174. C; c. ?+ ~" |% {' j
6.11.4 Commercial Viscoelastic Instrumentation 178/ Z3 B! [% |- y% ?6 l
6.11.5 Instruments for a Wide Range of Time and Frequency 179! a4 u5 q3 q0 t# o
6.11.6 Fluctuation–Dissipation Relation 1820 b5 K9 C5 Y3 ], a; ]/ T, Z
6.11.7 Mapping Properties by Indentation 183
, N/ P( U4 w$ q U6.12 Wave Methods 184
- D! `( D# q# M z- d$ ^6.13 Summary 188
. e: Y; c0 @* \0 H% ~# ^6.14 Examples 188
/ _5 f% d9 O$ p. x* z! h* g3 |/ s6.15 Problems 200& G! v0 ?- ?0 i7 o4 j/ T
Bibliography 2012 S: v! t8 U1 ]+ {, c, w2 g! L9 Z
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7 Viscoelastic Properties of Materials . . . . . . . . . . . . . . . . . . . . . 2076 f$ d4 d6 q2 S" K+ I* ?# s
7.1 Introduction 2072 V8 j7 J2 Q4 L0 L$ Y \! {/ W8 q
7.1.1 Rationale 207# Q8 C% _0 n+ z7 I0 m& ^
7.1.2 Overview: Some Common Materials 207) J' f! r% i. @' n! F
7.2 Polymers 208# t ~9 S5 N2 n* o
7.2.1 Shear and Extension in Amorphous Polymers 208# N7 m9 w2 j: f7 n: ^3 f3 m6 H, n
7.2.2 Bulk Relaxation in Amorphous Polymers 212
7 w& f( R: \/ Y4 C1 C7 {( o+ |5 @7.2.3 Crystalline Polymers 213
6 y$ d) Q/ H/ r; c/ j7.2.4 Aging and other Relaxations 214
4 q+ F R! b5 I2 P# y @- y( Q7.2.5 Piezoelectric Polymers 214
* b3 l7 S. M! o ]* D/ n7.2.6 Asphalt 214
j- m) I2 `% |9 \% p" d7.3 Metals 2153 \/ b' N! l/ u" y; A! ?, N- h
7.3.1 Linear Regime of Metals 215
0 m7 n4 Q7 g z M7.3.2 Nonlinear Regime of Metals 217
( R, s$ |5 W$ f8 v- J! Q7.3.3 High-Damping Metals and Alloys 219
/ r+ p% M0 f( s# H& G1 }* _7.3.4 Creep-Resistant Alloys 224
- K- e0 Q& n- @7.3.5 Semiconductors and Amorphous Elements 225; a( S2 P1 v; c# A7 K2 W0 T6 I
7.3.6 Semiconductors and Acoustic Amplification 226/ D% O8 x" ]6 j5 K! G$ x+ {& V' G) B
7.3.7 Nanoscale Properties 226
( _. g. b- w8 R3 z$ @- s7.4 Ceramics 227
+ ~9 |+ \: W+ b2 S7.4.1 Rocks 227) l4 Q# L( E/ L! L1 W- i
7.4.2 Concrete 2298 p% C* F. l7 H ?* N0 l
7.4.3 Inorganic Glassy Materials 231+ K h) ^5 S8 V3 x3 p, {
7.4.4 Ice 231. j: _7 i. b7 W1 C& ]
7.4.5 Piezoelectric Ceramics 2321 H5 R6 R: x+ p2 R4 s5 G
7.5 Biological Composite Materials 233. ]" I; p7 g/ A. [/ j; g' m
7.5.1 Constitutive Equations 234, {" M' P& S& V8 M
7.5.2 Hard Tissue: Bone 234( A0 C4 c6 ~% o
7.5.3 Collagen, Elastin, Proteoglycans 236
- q' a1 f2 l \7.5.4 Ligament and Tendon 2371 C5 m+ U, J7 g# Q" K: H
7.5.5 Muscle 2404 A8 ]% X* h% O$ H2 ~1 u. G$ T
7.5.6 Fat 243: }3 W% I0 v% x" A9 b
7.5.7 Brain 243+ L: L, M. b' t
7.5.8 Vocal Folds 244* b- n6 z% x3 C
7.5.9 Cartilage and Joints 244" V/ s" V- F$ k4 G( p
7.5.10 Kidney and Liver 2469 t% S& W) X- [) @
7.5.11 Uterus and Cervix 246
6 A3 w2 ~' n& e( ?* l7.5.12 Arteries 247
& g" {) P2 S: }+ \6 D& q* S7.5.13 Lung 248
; A% F! V) b6 h1 g3 ~7.5.14 The Ear 248; q+ ?& A$ G. \0 V
7.5.15 The Eye 249- h0 T, c( M+ v% Y
7.5.16 Tissue Comparison 251
% e l2 c, _+ E, B: o7.5.17 Plant Seeds 252" x1 u3 f- y$ ~
7.5.18 Wood 252& `; C' n ]5 Z4 x2 K
7.5.19 Soft Plant Tissue: Apple, Potato 253* `) X* k$ l' T! z4 X% E
7.6 Common Aspects 253
$ q* s9 M) y( P$ q0 Z1 |7.6.1 Temperature Dependence 253" W2 z: t+ j% j1 D" e }7 d; s
7.6.2 High-Temperature Background 254
! b6 k+ t1 b4 c' P4 ?! O7.6.3 Negative Damping and Acoustic Emission 255( A4 t: G. l7 @/ u1 L) o1 j
7.7 Summary 255! C; h' p* y. Q$ ?8 e
7.8 Examples 255
, M* G/ G2 h ?2 v7.9 Problems 256) `+ R) H- F+ [
Bibliography 257
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) \$ X0 H/ t0 q" e8 Causal Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
- Q% P4 u2 g4 h2 c- R; t. f/ i! F+ R8.1 Introduction 2714 L' q/ R c' J# P) O
8.1.1 Rationale 2711 j: V* `. r* L/ p
8.1.2 Survey of Viscoelastic Mechanisms 271
- S: T, B; r' \+ G1 E/ o8.1.3 Coupled Fields 273
F* x1 a9 J R. q. o. V# D8.2 Thermoelastic Relaxation 2741 z: i+ z2 T X. ?; R, v9 V
8.2.1 Thermoelasticity in One Dimension 274
* t s p+ }! e8.2.2 Thermoelasticity in Three Dimensions 275. ]# a+ J. K, E7 g* O R
8.2.3 Thermoelastic Relaxation Kinetics 276% M* y6 B/ W7 Q# T
8.2.4 Heterogeneity and Thermoelastic Damping 278- \2 i9 N2 [7 V6 D0 z9 B& Y
8.2.5 Material Properties and Thermoelastic Damping 280
# W7 }4 s$ q7 _% X8.3 Relaxation by Stress-Induced Fluid Motion 280
& d+ f+ r! j4 g' `, D9 r8.3.1 Fluid Motion in One Dimension 280; @& I: G5 Q# i; u4 Z& m
8.3.2 Biot Theory: Fluid Motion in Three Dimensions 281* ~ s% ` X0 g: H
8.4 Relaxation by Molecular Rearrangement 2869 n1 S- ~9 d4 h
8.4.1 Glassy Region 286' m) _3 p: w7 k7 Q9 m
8.4.2 Transition Region 287
# s9 y9 B( X# j; s m8.4.3 Rubbery Behavior 2896 h0 X7 E- v2 g8 @4 ]
8.4.4 Crystalline Polymers 2917 N4 |2 ~$ U) T
8.4.5 Biological Macromolecules 292' L8 | l# n: Q# B% @, e+ F
8.4.6 Polymers and Metals 292: a$ u6 y0 u% x" V0 T
8.5 Relaxation by Interface Motion 292
4 A0 Y9 N0 `5 c! J1 ^0 _8.5.1 Grain Boundary Slip in Metals 292
3 d" G, z* C- f$ S' w8.5.2 Interface Motion in Composites 294
5 P% ?6 W) Y; I7 p: y8.5.3 Structural Interface Motion 294
6 `* ]: N. ?0 Q4 J8.6 Relaxation Processes in Crystalline Materials 2947 b8 d2 y1 C, b
8.6.1 Snoek Relaxation: Interstitial Atoms 294- u* w% ]* Y, f# O
8.6.2 Zener Relaxation in Alloys: Pairs of Atoms 298- [8 @+ e& o9 Z% Y
8.6.3 Gorsky Relaxation 2992 X6 y. h/ Z* h% S( X, b1 U1 J- d/ {
8.6.4 Granato–L ¨ ucke Relaxation: Dislocations 300+ {5 a: X7 H% Q" K
8.6.5 Bordoni Relaxation: Dislocation Kinks 303
0 k/ @2 e7 K6 q1 g7 V6 V8.6.6 Relaxation Due to Phase Transformations 3053 {6 A( |2 Q% H, p3 h
8.6.7 High-Temperature Background 314. ^4 ~( ]- t2 _' w& I! {" G
8.6.8 Nonremovable Relaxations 315
$ G5 X) r, }( {2 }) P8.6.9 Damping Due to Wave Scattering 316
$ B+ k6 n- g- a( [5 E8.7 Magnetic and Piezoelectric Materials 316
4 U# ]5 Y0 ] I* T3 x" n6 O' E3 I% c8.7.1 Relaxation in Magnetic Media 316
6 q6 P @+ E& w8 c% _8.7.2 Relaxation in Piezoelectric Materials 3185 L) D5 n2 k- L
8.8 Nonexponential Relaxation 322- ^# U9 H5 T% W/ |
8.9 Concepts for Material Design 323! j* K+ a* n, D: j" Q
8.9.1 Multiple Causes: Deformation Mechanism Maps 323
- U+ o$ c, x( l/ B Z8.9.2 Damping Mechanisms in High-Loss Alloys 326: g! d6 g1 L* Z( O
8.9.3 Creep Mechanisms in Creep-Resistant Alloys 3260 I9 {4 {2 c5 t! j( K
8.10 Relaxation at Very Long Times 3270 ~" \5 f2 j# A/ H0 ~7 [
8.11 Summary 327# Y% p% u. M% U+ w, u7 S
8.12 Examples 328
& r# A. h2 D5 r& }3 q8.13 Problems and Questions 332& J# m- l2 U; A4 @0 |) D
Bibliography 332
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9 Viscoelastic Composite Materials . . . . . . . . . . . . . . . . . . . . . . . 341/ N L2 i6 `3 t" e; Y9 r
9.1 Introduction 341( ? e3 W2 v2 ~* V; D' R
9.2 Composite Structures and Properties 341
& i# h" ^' d$ w" g$ W/ H4 [9.2.1 Ideal Structures 341- X( e+ o/ c4 }! h
9.2.2 Anisotropy due to Structure 3429 q! H+ H/ f( }
9.3 Prediction of Elastic and Viscoelastic Properties 344; h g4 G% @1 k. i" V# z
9.3.1 Basic Structures: Correspondence Solutions 344
3 _$ z/ w' x( F/ I( ]+ c$ p9 B9.3.2 Voigt Composite 345
5 b4 X2 v, m1 M5 h# h6 m9.3.3 Reuss Composite 345
$ n4 C* g l1 m4 g$ b9.3.4 Hashin–Shtrikman Composite 346" a3 m+ z9 s( W/ v8 j8 @
9.3.5 Spherical Particulate Inclusions 347
- B9 R; j' v3 u" K/ m9.3.6 Fiber Inclusions 349! B' J1 _) ]; l+ j
9.3.7 Platelet Inclusions 349
, X' a! g' y2 q9 t5 P- [9.3.8 Stiffness-Loss Maps 3501 l2 j; j3 W9 I) N$ c( K- N' c! W9 c
9.4 Bounds on the Viscoelastic Properties 3538 F% m$ a' u$ e% m4 d1 i
9.5 Extremal Composites 354
6 M7 u- M" z) E# Q7 f9.6 Biological Composite Materials 356
; S- M5 l$ s+ P$ D# ?9.7 Poisson’s Ratio of Viscoelastic Composites 357$ C! h' y$ e4 s. y; {
9.8 Particulate and Fibrous Composite Materials 358 Y; X; s6 r% Z
9.8.1 Structure 358( R+ _' V+ ?2 i5 n& A F! Y
9.8.2 Particulate Polymer Matrix Composites 359
9 L+ s9 \+ z' i8 j) }( o! n {9.8.3 Fibrous Polymer Matrix Composites 3614 S6 M K) L0 B- _* _3 M
9.8.4 Metal–Matrix Composites 3625 Q' ]2 ?$ y0 ]/ o0 O4 @
9.9 Cellular Solids 363 q7 Z4 _5 ^( d8 b
9.10 Piezoelectric Composites 366
1 R0 h# }) X. v$ @! P/ o4 Y9.11 Dispersion of Waves in Composites 366
) c4 ]9 R' B; {8 R9.12 Summary 367
, D. D4 D1 ~0 A) z, w3 R. b9.13 Examples 367
% ~8 U3 S7 Y' K9.14 Problems 370
U4 s, t, T8 x& g1 Y3 PBibliography 3704 Q2 ~8 \1 ]1 F2 M0 q
9 g) G( @+ s! |' ]9 c
) _% S3 b: [5 K9 m9 O, W, j7 h/ W
10 Applications and Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . 377* i2 Z. k4 y( i6 a7 N% j
10.1 Introduction 377
8 x5 L/ Z! |# g6 T0 z7 x* V10.2 A Viscoelastic Earplug: Use of Recovery 377
1 _+ _' x) f! s10.3 Creep and Relaxation of Materials and Structures 378
1 G6 V- {! S5 s( \5 |10.3.1 Concrete 378
X1 m* a( ? x$ x1 u10.3.2 Wood 3783 }, ?2 c% p! i+ }# g" j3 J3 U
10.3.3 Power Lines 379
; B& @1 G0 I& e0 z$ @; O6 Y7 t10.3.4 Glass Sag: Flowing Window Panes 380
+ ^. m. K+ v' Q& L& R" X, ?10.3.5 Indentation: Road Rutting 380
9 B- T. P/ m2 u; {; X0 e5 A10.3.6 Leather 381. Z* x% M. c- u3 U3 i* {
10.3.7 Creep-Resistant Alloys and Turbine Blades 381& E7 B2 F# o# s" {2 i- `6 }
10.3.8 Loosening of Bolts and Screws 3822 J( x5 T! N6 E
10.3.9 Computer Disk Drive: Case Study of Relaxation 384
# e; ?' r% l4 E& @6 _7 F" S10.3.10 Earth, Rock, and Ice 3852 r0 O) U* T' f$ W, C
10.3.11 Solder 386
$ q' C: E6 W1 M- Y1 n5 ^' F* Y9 [10.3.12 Filamentsi nL ight Bulbs and Other Devices 387* ~4 R7 U/ z& ?7 }: M" Y+ m
10.3.13Tires: Flat-Spotting and Swelling 3888 c, X p& y2 X+ \& I
10.3.14Cushionsfor Seats and Wheelchairs 3883 E1 X6 k: [! s- U$ l ]
10.3.15 Artificial Joints 389
) l- }/ A! S+ A M: m! {" \7 g% ]10.3.16 Dental Fillings 389
# i& n9 v9 M% ~* w' ]3 Y10.3.17 Food Products 389# ~% O; C8 T# k
10.3.18 Seals and Gaskets 3909 Z/ [3 H1 ~$ `5 z+ G
10.3.19 Relaxationi nM usical Instrument Strings 390* D$ Z- V% d% l: ^# H# w
10.3.20 Winding of Tape 391
" W# B, g! G* R1 B10.4 Creep and Recovery in Human Tissue 391
5 B3 q0 @ p# y2 O10.4.1 Spinal Discs: Height Change 391
; X; d1 I! I N: V' f9 {- N10.4.2 The Nose 392
$ B# e7 s3 r( t; l10.4.3 Skin 3925 `* D% z( A$ W$ V3 G+ [2 ?0 v
10.4.4 The Head 393
0 Z. u2 o, j0 h6 s @+ v4 h8 Y9 V# e10.5 Creep Damage and Creep Rupture 394+ A+ }, H' A& q, ]
10.5.1 Vajont Slide 394
( r- m/ N4 v' @! j; F8 {( Y10.5.2 Collapse of a Tunnel Segment 394
/ t0 ?5 W( Q" C( J% g" }* E. i10.6 Vibration Control and Waves 394+ I8 n; D5 W& N4 ?# ~! b* Z7 N
10.6.1 Analysis of Vibration Transmission 394
6 J2 ^6 f2 u V9 C* g* L6 b2 H* y [10.6.2 Resonant (Tuned) Damping 397
" ?7 H) ?0 q4 Z: d5 F10.6.3 Rotating Equipment Vibration 397
: {! m9 H- A8 c R( \10.6.4 Large Structure Vibration: Bridges and Buildings 398
& h: ^! n* q" _- R3 e( N9 F10.6.5 Damping Layers for Plate and Beam Vibration 3991 \- S- {+ U( W" B3 O) |* h2 g
10.6.6 Structural Damping Materials 400
- O, z! S' P' @' w9 N$ q5 j10.6.7 Piezoelectric Transducers 4020 P; T2 x5 `5 ~; k7 _; a
10.6.8 Aircraft Noise and Vibration 402
1 ?, |; D, Q; Q$ n F: ?10.6.9 Solid Fuel Rocket Vibration 404
6 o8 a3 t1 E4 g0 j10.6.10 Sports Equipment Vibration 4047 ~+ _7 [2 ~ F0 k0 x8 m R
10.6.11 Seat Cushions and Automobiles: Protection of People 404) f' f) I6 c K5 f1 S, h
10.6.12 Vibrationi n ScientificI nstruments 406& v2 W$ J3 N8 j. w, q6 e& }8 l
10.6.13 Waves 4065 P7 s0 G' @2 |4 p1 D
10.7 “Smart” Materials and Structures 407/ R) `' h8 C' l" ^0 L
10.7.1 “Smart” Materials 407) h- E i- o' W& Y
10.7.2 Shape Memory Materials 408
6 i2 s0 Y( m' O7 T* l7 {- g; V10.7.3 Self-Healing Materials 409
; D+ n- }5 b. k$ {; A10.7.4 Piezoelectric Solid Damping 409
0 \9 f" L$ P/ _. ?- q10.7.5 Active Vibration Control: “Smart” Structures 409% x4 \/ T' Q" ?5 I' b9 j( f
10.8 Rolling Friction 409' t2 ~" W. d9 _: R+ J. q5 r
10.8.1 Rolling Analysis 4100 }% ~3 e' Y& k- }: f7 v
10.8.2 Rolling of Tires 4118 K* b3 ?/ ^/ l) l0 h, b
10.9 Uses of Low-Loss Materials 412, [- H( U1 U D* W; x
10.9.1 Timepieces 412" ^3 J1 [7 B& `' u) a4 ]: A. G4 v
10.9.2 Frequency Stabilization and Control 413
2 K+ y; ]+ A n" p, Z v W/ m10.9.3 Gravitational Measurements 413
+ Z* V- f& [' l' [. J( A10.9.4 Nanoscale Resonators 414" |* f; v: k- L& p+ z: E+ A
10.10 Impulses, Rebound, and Impact Absorption 414
d; e J: K! V* q, w' o10.10.1 Rationale 4148 R& v- h, d. S
10.10.2 Analysis 415
9 P; s) M* z7 G9 k- e& {10.10.3 Bumpers and Pads 418
4 e$ c5 @1 q3 e1 f2 i. V5 h7 ^10.10.4 Shoe Insoles, Athletic Tracks, and Glove Liners 4196 M Q- {5 ^0 B
10.10.5 Toughness of Materials 419 ~0 U7 v' L u2 E; |8 S, X
10.10.6 Tissue Viscoelasticity in Medical Diagnosis 4209 t. Q$ Q8 P% [
10.11Rebound of a Ball 421
* _/ k- r+ C9 ~10.11.1 Analysis 421( H! Z" X2 N5 u; @
10.11.2 Applications in Sports 422
% k1 _. {1 ~) `1 m4 \ Q10.12 Applications of Soft Materials 424
$ `0 }5 J5 c0 u ]- _+ U10.12.1 Viscoelastic Gels in Surgery 424* R6 z2 a y8 E3 J6 a
10.12.2 Hand Strength Exerciser 424
7 Y8 \* \4 g q' d; B ^10.12.3 Viscoelastic Toys 424- y& p, k0 M2 b6 R" j p/ S0 A
10.12.4 No-Slip Flooring, Mats, and Shoe Soles 425
0 I9 H3 R/ e d7 ?0 ?10.13 Applications Involving Thermoviscoelasticity 425
; C9 s/ s" _0 h# m/ c0 f10.14 Satellite Dynamics and Stability 4264 L8 b4 u0 p3 M; D( k
10.15 Summary 4285 N2 f2 g* i/ U% i* Z
10.16 Examples 429
1 _9 d( U/ o1 o% F/ i10.17 Problems 431! \7 T9 o' S0 N& L' G$ k' S
Bibliography 4311 f9 O" s8 m- n6 d+ [/ x- ?
1 ^3 U" @" D# t! S; h" U) [8 @# U! `: C
0 K8 z) F& u/ m
A: Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441 n ], L) k# p, l; H
A.1 Mathematical Preliminaries 441
! U( a& @, H4 k- B2 i$ ^0 q' pA.1.1 Introduction 441
9 p. s! d s1 G# e, YA.1.2 Functionals and Distributions 441: d+ E- |& S2 \& f0 p3 t
A.1.3 Heaviside Unit Step Function 442( i3 I n* x0 m$ i$ h
A.1.4 Dirac Delta 442
8 \5 \; z' F7 b' I' k) M! a4 \A.1.5 Doublet 443
6 t3 M# j, ~. lA.1.6 Gamma Function 445
: w5 N) [& u ?9 pA.1.7 Liebnitz Rule 445! ^5 h1 O _/ a9 T# m" ~6 |" ^7 c, |
A.2 Transforms 445
; H+ |, p8 B' d+ n6 t! }A.2.1 Laplace Transform 4463 \& J4 t9 q6 x8 O' t; [
A.2.2 Fourier Transform 446
9 }2 {1 O7 \( CA.2.3 Hartley Transform 447
- Q& q5 h8 t2 E! @' r/ ]& [A.2.4 Hilbert Transform 447$ {) r3 L: x3 k& m! ^& T! d' Q
A.3 Laplace Transform Properties 4486 u. e6 g9 ]% d8 c- _
A.4 Convolutions 449
+ O8 F2 j2 i7 n" y8 S4 VA.5 Interrelations in Elasticity Theory 451
+ X( y, s( y5 N: S' d% Z0 `: xA.6 Other Works on Viscoelasticity 4515 ?0 f9 n% ~& B: P* g) K
Bibliography 452
, _0 L' o8 }. n( T6 ~$ g2 l$ ]; t1 ^: O) H. E8 _# P5 }
; O6 F8 S* u! O* b+ j. a: ? aB: Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455
! s8 v4 R# Y: n% X; P0 s# VB.1 Principal Symbols 455
- M- u1 J' \: _2 K/ z, h6 k1 RIndex 457
L, G; W* S7 O# K8 [6 N/ f6 y) V% S/ P# d5 q% r! L d
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发表于 2015-1-9 22:34:06