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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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; j; k1 |" h2 _1 _; V" d4 R7 G+ \2 a目录8 b1 s. F( P5 t
. a' [7 L8 j, o e0 LContents! K A6 C" a1 k7 K# l9 m
" j& g& ^% v0 P* c$ `Preface page xvii
) j! a; Y/ r$ H3 Z O1 Introduction: Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
) u8 `; t+ g% z: z' A' s1.1 Viscoelastic Phenomena 1
/ |! x' Y. p7 W7 ]# i1.2 Motivations for Studying Viscoelasticity 3/ `# \ v* h8 x0 h
1.3 Transient Properties: Creep and Relaxation 3 q! C% s& S; j; A* ~7 _1 I
1.3.1 Viscoelastic Functions J (t), E(t) 3. }' R. v, G1 B, ^
1.3.2 Solids and Liquids 7! G* P7 M- F% F8 g" o
1.4 Dynamic Response to Sinusoidal Load: E∗, tanδ 8
6 T1 T, K+ D6 b) E1.5 Demonstration of Viscoelastic Behavior 10
! H7 j( t# d$ a6 U1.6 Historical Aspects 10* b& s: k6 t9 L# ~* d
1.7 Summary 11
: }9 c3 x. h- C! ~2 I1.8 Examples 11
" j! H* V& T: G4 X# m7 f1.9 Problems 12
5 Y' U' C5 g/ \ e s5 MBibliography 12, L! d, A& |3 N, T4 q! ^1 B# E
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2 Constitutive Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
: V: Y1 [! ~" A2.1 Introduction 14
9 C8 H9 {/ j; M- V/ ]6 U2.2 Prediction of the Response of Linearly Viscoelastic Materials 14
) {" n/ u+ t# t8 I2.2.1 Prediction of Recovery from Relaxation E(t) 14# _6 ^+ t' k5 E) }7 a# t
2.2.2 Prediction of Response to Arbitrary Strain History 15
# ]4 W* m* ]3 @' \. Q% s2.3 Restrictions on the Viscoelastic Functions 177 l: Q7 e) l6 l
2.3.1 Roles of Energy and Passivity 17. p2 ]/ L8 K; p+ ?: b: m# p" [3 ^
2.3.2 Fading Memory 18& ~' B* D1 _- _' |8 Y
2.4 Relation between Creep and Relaxation 19- x$ r$ p8 Z7 n0 B2 y; n I+ ~
2.4.1 Analysis by Laplace Transforms: J (t) ↔ E(t) 19
& n* ~0 V! X) g2 [2.4.2 Analysis by Direct Construction: J (t) ↔ E(t) 20; L+ q; t3 V C2 m3 B
2.5 Stress versus Strain for Constant Strain Rate 20! x& S1 A/ S- P; v% h U, Z5 s9 M5 X! n
2.6 Particular Creep and Relaxation Functions 21" @9 k+ `# n! }. h2 E1 _( Y! ~/ r
2.6.1 Exponentials and Mechanical Models 21
' x, U1 K' V. Q2.6.2 Exponentials and Internal Causal Variables 26
: [% U$ H% c% f2.6.3 Fractional Derivatives 27
& I% r5 S; B7 ]1 V& R+ g N; S6 z2.6.4 Power-Law Behavior 28+ O9 e: Y) t& B) Q z
2.6.5 Stretched Exponential 29
! C+ I' P! |6 B2.6.6 Logarithmic Creep; Kuhn Model 29
6 m b" c, `9 m$ {* F Y2.6.7 Distinguishing among Viscoelastic Functions 30; w( M. ~- w$ a' Y* Z4 |% Q
2.7 Effect of Temperature 30, \! e5 L% y% X) I% G7 g5 f7 h: R+ P
2.8 Three-Dimensional Linear Constitutive Equation 33, P3 c5 j O& C- V
2.9 Aging Materials 35+ U m$ R( k1 ^" p. y! o# g
2.10 Dielectric and Other Forms of Relaxation 35
V3 |& b2 O2 W( g7 t( f; e/ v2.11 Adaptive and “Smart” Materials 36: v" v7 \9 A5 s( J9 q
2.12 Effect of Nonlinearity 37
- o" Z7 ~( Y+ x2.12.1 Constitutive Equations 37
( X1 d7 {6 r6 @7 d! I4 [2.12.2 Creep–Relaxation Interrelation: Nonlinear 40( V7 k3 }) b$ _+ N! C* ]5 F
2.13 Summary 43+ `' g1 ~6 Z6 t; @+ ]+ ?
2.14 Examples 43
9 P6 Q+ b+ D7 T2.15 Problems 51" Q) x6 `. p# w* B: [
Bibliography 52' y7 l. O8 z/ p: g. `1 c4 V
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6 Q, a' t1 L) ?3 Dynamic Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 F* k1 _% m, `6 y8 n1 Z7 J/ P3 e
3.1 Introduction and Rationale 55
4 r5 p7 O0 q; j+ R/ y1 h/ k3.2 The Linear Dynamic Response Functions E∗, tanδ 56
5 x. X$ i4 q5 N2 i8 t6 b3.2.1 Response to Sinusoidal Input 57& w+ \! `' [5 k5 f+ P: `; D
3.2.2 Dynamic Stress–Strain Relation 59! h6 F6 y3 q; P0 K( O4 f, h
3.2.3 Standard Linear Solid 62
+ W0 y$ g; E9 J1 u2 y1 l6 U8 s3.3 Kramers–Kronig Relations 63
" F6 w- u0 s/ Y; P% n, z3.4 Energy Storage and Dissipation 65
& B& |: I. W0 s8 ?" u% j5 C3 j, G6 X3.5 Resonance of Structural Members 67: z& Y1 r. R" M/ E; {3 |, s- K" c1 D
3.5.1 Resonance, Lumped System 67/ k, j) l: ~, V4 _) S0 @7 _
3.5.2 Resonance, Distributed System 71' Y3 F/ n+ J* C
3.6 Decay of Resonant Vibration 74
, E! L9 T' o& x7 C8 w, i5 i' K2 U3.7 Wave Propagation and Attenuation 77' k+ { G" [# e! _7 q: e+ y" O
3.8 Measures of Damping 79
, M5 G) y. W1 t1 Q& W4 L3.9 Nonlinear Materials 793 V( D: X) M" G* O
3.10 Summary 81
0 e( v* n. p( t: L: Y1 x3.11 Examples 81
: ~% K6 \$ }0 `3.12 Problems 88
6 \+ P* d# ?8 O r$ @Bibliography 89
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4 Conceptual Structure of Linear Viscoelasticity . . . . . . . . . . . . . . . 91
3 _+ l; ?& {/ p% l6 a$ N4.1 Introduction 914 a# P+ z2 @0 `2 o- h7 t# {$ }
4.2 Spectra in Linear Viscoelasticity 92
/ E: P' L( g$ T4 k" W( y# [; g- K4.2.1 Definitions H(τ ), L(τ ) and Exact Interrelations 92' `1 A2 C% @# J' Y
4.2.2 Particular Spectra 93
2 P3 K; l, n9 \ O5 k: V- a4.3 Approximate Interrelations of Viscoelastic Functions 95
6 s; S7 F& c- Z- R0 E( @5 i4.3.1 Interrelations Involving the Spectra 951 B- P6 F5 Z6 V3 I& g$ u
4.3.2 Interrelations Involving Measurable Functions 98
5 S$ T" |* J6 v' i: e' r4.3.3 Summary, Approximate Relations 101
, K) g: |, a! h) y$ K' P4.4 Conceptual Organization of the Viscoelastic Functions 101
; U3 R% J- D9 J7 f* [4.5 Summary 104
9 E" i6 [6 R3 J' D; `6 b4.6 Examples 104
% y3 D: D q- l2 {, y4.7 Problems 109
/ a( n; C+ I N+ X% K. ^Bibliography 109 H A( `. q) d# O
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5 S$ a/ e2 Z; o g- n9 X4 R4 m: M5 Viscoelastic Stress and Deformation Analysis . . . . . . . . . . . . . . . 1116 }" |$ I$ s* M8 y$ t& D
5.1 Introduction 111: s5 K. ]! p7 I. K7 Q
5.2 Three-Dimensional Constitutive Equation 111
8 P. F0 F$ L7 i, L8 A! u5.3 Pure Bending by Direct Construction 112
R) u1 [) j( v9 m! Y5.4 Correspondence Principle 114
r8 v1 e) Y9 ~- a3 d5 R. n v5.5 Pure Bending by Correspondence 1167 a1 N0 y, B w' ?4 o
5.6 Correspondence Principle in Three Dimensions 116* B+ s7 A) {, N0 h+ t. c
5.6.1 Constitutive Equations 116. M: b$ D' i; w3 F6 t& ?3 g+ n
5.6.2 Rigid Indenter on a Semi-Infinite Solid 117
$ ]" b1 [! y2 y, c5.6.3 Viscoelastic Rod Held at Constant Extension 119! A5 A" v6 x) D6 w
5.6.4 Stress Concentration 119
" i ~, ^) @7 O- z7 f- W5.6.5 Saint Venant’s Principle 120& d' N' n R) t7 G7 Z: P7 V" F' c0 m
5.7 Poisson’s Ratio ν(t) 121
7 b' o% z1 z- S5.7.1 Relaxation in Tension 121, y/ g/ V: g( Q* D. N0 B
5.7.2 Creep in Tension 1236 G; ~4 t7 l& h- O" {: k- `
5.8 Dynamic Problems: Effects of Inertia 1246 u# X& _3 W1 m _1 U& |
5.8.1 Longitudinal Vibration and Waves in a Rod 124
. S5 o5 O% M/ }9 q$ `0 L/ Q9 I3 h5.8.2 Torsional Waves and Vibration in a Rod 125/ `# p/ T$ s4 |" D
5.8.3 Bending Waves and Vibration 128+ ^- D( m. F' }) S8 `9 o
5.8.4 Waves in Three Dimensions 1293 [; x7 p4 Y3 d2 R: _8 F2 }" x2 |
5.9 Noncorrespondence Problems 131
5 l2 I! I8 o+ z% D2 {% V. D5.9.1 Solution by Direct Construction: Example 131% D, w7 e9 k# n. M& _
5.9.2 A Generalized Correspondence Principle 132- V' g0 U( q8 \) q
5.9.3 Contact Problems 132* N- Y1 i$ k1 |( ~* G
5.10 Bending in Nonlinear Viscoelasticity 1334 V2 O, f2 V0 k6 H: O
5.11 Summary 134
& a! S- G9 O$ n' [& Q" m: h6 l8 H5.12 Examples 134
. S; U7 l, ^( {+ S5.13 Problems 142
t2 L5 v) d' O9 W7 `: S9 b, rBibliography 142
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1 i& A7 \: [- n# m6 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1456 N$ L5 j/ q. n
6.1 Introduction and General Requirements 145- s7 k% `, b; f" K+ `; L3 Y8 ?1 T
6.2 Creep 146
, t' Q0 W$ \2 W' b6.2.1 Creep: Simple Methods to Obtain J (t) 1466 c. N# V$ v- Y1 G" R
6.2.2 Effect of Risetime in Transient Tests 146
7 b! V( a' ]' `& {! f6.2.3 Creep in Anisotropic Media 148+ z ~7 r$ V2 `& `* Z5 l' T% _0 k
6.2.4 Creep in Nonlinear Media 148* w: R! v$ X9 v J6 Y9 a5 J w0 {1 o
6.3 Inference of Moduli 150
6 H, M! t7 u2 U/ P, E1 x3 o6.3.1 Use of Analytical Solutions 150
; x2 Q2 B: a+ u0 [% ]6.3.2 Compression of a Block 151
2 Y- q7 C4 ^' x- ] Q' ]6.4 Displacement and Strain Measurement 152
( ?' g$ @/ H# ]; I4 }% ]! V6.5 Force Measurement 156
" R9 U6 n# f8 S6.6 Load Application 157
4 j% A' X! p. n+ G2 a6.7 Environmental Control 157
; [% ]3 e9 k! ~8 x% A d& X: N6.8 Subresonant Dynamic Methods 158: P: X* I% W% x/ ^# J: g) l
6.8.1 Phase Determination 158. H' R$ z- G' q3 Q8 M3 e4 U( _
6.8.2 Nonlinear Materials 160
" K+ a6 J6 A ]- g; _6.8.3 Rebound Test 161( @ ?3 w% s0 b; N* |* M
6.9 Resonance Methods 161
" j6 C5 Z7 I0 h0 G3 O( q6.9.1 General Principles 161& r0 T8 B- W8 u3 A# e* F% h) \
6.9.2 Particular Resonance Methods 1637 v9 `/ H1 V- N" y$ {% F
6.9.3 Methods for Low-Loss or High-Loss Materials 166% O; K. o, Q6 j& a; ?
6.9.4 Resonant Ultrasound Spectroscopy 168
: z0 ~. w" T, b6.10 Achieving a Wide Range of Time or Frequency 1717 e' v, |+ M6 k
6.10.1 Rationale 171
" |% ]' m/ D; o/ C$ q2 R; k6.10.2 Multiple Instruments and Long Creep 172( C0 u# w; _) \
6.10.3 Time–Temperature Superposition 172
9 P t$ }$ a% r* p8 G0 h; j" y6.11 Test Instruments for Viscoelasticity 173
1 _6 y7 ?3 l. `0 o7 R& g6.11.1 Servohydraulic Test Machines 173" w: ^% G/ c* F' Z% @
6.11.2A Relaxation Instrument 174% |! C( v. \- k% r; Z
6.11.3 Driven Torsion Pendulum Devices 174
" i2 Q8 J9 R- g m s# x- t8 f6.11.4 Commercial Viscoelastic Instrumentation 1781 i5 N7 Q- m2 H) H p
6.11.5 Instruments for a Wide Range of Time and Frequency 179* e$ R$ s# P( G5 E h0 ]" T+ e* ^
6.11.6 Fluctuation–Dissipation Relation 1824 F( m" j* J4 a' d: {" M! y
6.11.7 Mapping Properties by Indentation 1832 ~( b$ B" }- ?$ I, c4 ^
6.12 Wave Methods 184- c4 z. H3 r8 I/ c9 L: Z
6.13 Summary 188
d Z* k. U+ A; d3 ~6.14 Examples 188
. E: v2 b9 t3 c+ J! {# ?6.15 Problems 200
/ J- }8 {( K+ K$ B# ]: S6 _; l+ {! d/ cBibliography 201; t7 @2 h/ ?* q- M0 _
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/ V0 X( B9 Z4 c9 G+ W7 Viscoelastic Properties of Materials . . . . . . . . . . . . . . . . . . . . . 207
( Z# z9 @" n; z5 X4 O- M4 Y7.1 Introduction 207
) E. o$ P! `7 A- f& p3 `7.1.1 Rationale 2074 I+ F7 Z" p+ }- B
7.1.2 Overview: Some Common Materials 2077 W5 c5 K: F6 h/ p
7.2 Polymers 208 \5 B! u( w0 b9 v- f/ g6 o
7.2.1 Shear and Extension in Amorphous Polymers 208& B, H( x8 Q7 \/ M( |% t
7.2.2 Bulk Relaxation in Amorphous Polymers 212& L( j: g: g; x3 ^( x" o
7.2.3 Crystalline Polymers 213
" I+ J5 ?4 h1 q1 Z; T7.2.4 Aging and other Relaxations 214
. v$ L# c$ k3 t4 ]- x T7.2.5 Piezoelectric Polymers 2140 o/ n) y/ l( i+ o
7.2.6 Asphalt 214
) M% j7 g6 v N7.3 Metals 215/ G& i% p4 _$ w" h" M3 J* C
7.3.1 Linear Regime of Metals 215
. Y$ T$ S. j4 D( T6 a7.3.2 Nonlinear Regime of Metals 217
7 R5 c1 g8 n: o# O0 T3 a. W7.3.3 High-Damping Metals and Alloys 219
( j/ q: s9 N& v" w: t* R7.3.4 Creep-Resistant Alloys 2242 ^: L( C; D- g: l- w* B
7.3.5 Semiconductors and Amorphous Elements 2257 _5 a- v3 j& a4 l4 y, d( o& f
7.3.6 Semiconductors and Acoustic Amplification 226, r. K/ z' d1 V$ v' I5 c' i& G" j8 f
7.3.7 Nanoscale Properties 226
$ k2 {0 Q9 V; j* ]7.4 Ceramics 227% P4 H( i: g0 J/ N/ t* D) Y
7.4.1 Rocks 227 S; o4 ]4 S1 l
7.4.2 Concrete 229
+ G6 x- {, @& F9 @7.4.3 Inorganic Glassy Materials 231
" C/ K5 w2 k1 t4 g& V& c8 t7.4.4 Ice 231$ {# S# Q F, b* [5 n7 E0 x
7.4.5 Piezoelectric Ceramics 2322 D, f# M3 @' t# X9 |
7.5 Biological Composite Materials 233
' z& n ^$ X9 a% _9 m7.5.1 Constitutive Equations 234
8 A1 d) u- @. s/ a: S$ ]6 f% ~7.5.2 Hard Tissue: Bone 2346 d' [$ w* c- C* W" U+ Z
7.5.3 Collagen, Elastin, Proteoglycans 236
. a% z# Z% _: R, m* x1 r( l& a9 E7.5.4 Ligament and Tendon 237
9 n2 ~5 D! _: J$ I' a( a- s! D' L$ |7.5.5 Muscle 240
4 m& q1 k* E- v' M* g7.5.6 Fat 243$ c4 ?" x; A* T( {0 Y- g$ x
7.5.7 Brain 243$ U5 h5 ]! ]9 U
7.5.8 Vocal Folds 244
1 ^! [) M( t2 }. G7 Z& _7.5.9 Cartilage and Joints 244
: U- V% D) C2 s& Z% K5 R) N7.5.10 Kidney and Liver 246" X6 e# K3 q! K! N8 R% l
7.5.11 Uterus and Cervix 246
! Q$ y( @. x! J4 y- U; P/ S b7.5.12 Arteries 247* [( U' E& `$ z, m9 R! f
7.5.13 Lung 248
6 D/ X0 V. f! K% c w' z p7.5.14 The Ear 248
$ x" d" z7 ^; }) W1 r7.5.15 The Eye 249
( I* N6 N9 U1 }0 P& q2 m- j( H4 m7.5.16 Tissue Comparison 251
9 X/ Y y9 R8 }7.5.17 Plant Seeds 252
. n0 V6 P5 Y2 X7.5.18 Wood 252
+ x2 x" a9 ~9 G+ i: i# F8 ]7.5.19 Soft Plant Tissue: Apple, Potato 2536 D- a" j5 t2 E: `9 j& [* M
7.6 Common Aspects 253. O) j, A9 V+ ^+ A5 x- H$ c! h
7.6.1 Temperature Dependence 253
6 P# e T. B; A$ q% S, B. L% U7.6.2 High-Temperature Background 254
. {5 J" A- k3 y: f2 e7.6.3 Negative Damping and Acoustic Emission 255
# D- K( p, e: ^( `( `7.7 Summary 255
/ p1 B3 d1 k. Q7 r5 O' q' E9 ^- \7.8 Examples 2557 ~5 ]- T A3 l) R
7.9 Problems 256" \' b, Q$ `$ f1 p" ?
Bibliography 257
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" l, X/ b4 o. L' Z; ^8 Causal Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
# o' T7 z( C. _* F7 k: v2 @6 B4 l8 v8.1 Introduction 271
: j s6 c9 }, N2 W/ ?. t8.1.1 Rationale 271( ^/ ?7 N5 x- W' @' |
8.1.2 Survey of Viscoelastic Mechanisms 271
2 J' h8 n. ]- [4 X7 O9 x8.1.3 Coupled Fields 273
' ~) r8 [1 U$ i b, ?8.2 Thermoelastic Relaxation 274
% w5 i* i/ c7 n3 ]2 | b8 G8.2.1 Thermoelasticity in One Dimension 274
, G& m: t5 ~: R5 \$ F2 k8.2.2 Thermoelasticity in Three Dimensions 275! a5 ?6 z4 u& `2 A8 t$ ]
8.2.3 Thermoelastic Relaxation Kinetics 276
! Z% u8 L0 X& v5 h8 H( a9 b' R0 [' T8.2.4 Heterogeneity and Thermoelastic Damping 278' @: u9 U: H1 t6 I+ N; O2 F
8.2.5 Material Properties and Thermoelastic Damping 280
0 f w N1 z# y8.3 Relaxation by Stress-Induced Fluid Motion 280
A% c2 s5 e. K# e8.3.1 Fluid Motion in One Dimension 280
, P% _- @% ?3 e+ }" S5 y0 s8.3.2 Biot Theory: Fluid Motion in Three Dimensions 281
- r2 e' G2 F# z( m+ q! k5 H) D9 F2 i8.4 Relaxation by Molecular Rearrangement 286; G. ]/ H3 _ T5 }/ j0 [
8.4.1 Glassy Region 286
. m2 I- T& @* g8.4.2 Transition Region 287* t7 z. t9 W4 N/ a8 v# W, L
8.4.3 Rubbery Behavior 289; W+ G" m2 [( d# x
8.4.4 Crystalline Polymers 2917 E7 @/ ?2 G9 \$ L5 v* f3 y( y
8.4.5 Biological Macromolecules 292
6 Q' E7 _9 ~( L& r# v8.4.6 Polymers and Metals 292; k& W) C0 \! K8 {7 i8 \
8.5 Relaxation by Interface Motion 292( S m1 u6 C% r( ~* J
8.5.1 Grain Boundary Slip in Metals 292
0 [ z w" i; c+ w1 T1 V) B8.5.2 Interface Motion in Composites 294
- X2 U# X; w! v4 ^) u3 L8.5.3 Structural Interface Motion 2942 K& z% P) X6 K, O0 L
8.6 Relaxation Processes in Crystalline Materials 294; {7 p0 F8 \" Z
8.6.1 Snoek Relaxation: Interstitial Atoms 294
r8 l4 N! e2 i! Z8.6.2 Zener Relaxation in Alloys: Pairs of Atoms 298
, b% g8 o$ _1 Q3 \: z8.6.3 Gorsky Relaxation 2994 J) `0 Y) P F' ?6 D3 e
8.6.4 Granato–L ¨ ucke Relaxation: Dislocations 300
% i& }" I& ~3 V" N# x/ q8.6.5 Bordoni Relaxation: Dislocation Kinks 303
) ?( f6 `0 k3 ?5 n0 Z8 P8.6.6 Relaxation Due to Phase Transformations 3054 \2 P0 L$ F% Z$ H1 }
8.6.7 High-Temperature Background 314: A" n+ ^5 U) }2 |" j
8.6.8 Nonremovable Relaxations 315' B. n7 h' h! O3 d7 ]3 N$ B
8.6.9 Damping Due to Wave Scattering 316# \/ j, ]6 D# i7 B5 @# ], b: M
8.7 Magnetic and Piezoelectric Materials 316( w+ a5 R6 \% y) c/ Y
8.7.1 Relaxation in Magnetic Media 3167 T7 y7 J9 m* \- J" ^! E7 x
8.7.2 Relaxation in Piezoelectric Materials 318
. K, D, y7 N4 {4 y( F* \8.8 Nonexponential Relaxation 322
# Y$ ^! C) b, P, U @8.9 Concepts for Material Design 323! m) v) Z; E$ b4 K X. e$ j6 w' g
8.9.1 Multiple Causes: Deformation Mechanism Maps 323. y% X' O( }* \
8.9.2 Damping Mechanisms in High-Loss Alloys 326+ m& O L: F- K7 }
8.9.3 Creep Mechanisms in Creep-Resistant Alloys 326
7 A3 e3 T( w9 M) |, P% i; ^# i+ q8.10 Relaxation at Very Long Times 3274 d/ G1 l i h. p
8.11 Summary 327: Q r' V. e; C5 l
8.12 Examples 328
0 H A1 Q0 s, M; M+ g5 Y# ]8.13 Problems and Questions 332
1 W5 O' ^6 m+ @) h0 q. KBibliography 332 n$ z9 a% y4 x+ Z$ G" S0 ? u
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3 ~2 X& x7 d( h1 t0 {3 \# `9 Viscoelastic Composite Materials . . . . . . . . . . . . . . . . . . . . . . . 3412 Q* ^- x( `, A5 [- T
9.1 Introduction 341
) x" {5 m0 l3 w8 c9 r2 F9.2 Composite Structures and Properties 341
0 m( |! I& G. ~. R9 |8 Q' W' U1 F9.2.1 Ideal Structures 341
" O3 e1 C" h% }9.2.2 Anisotropy due to Structure 3424 w8 M' x4 y; @
9.3 Prediction of Elastic and Viscoelastic Properties 3449 m/ k g0 I; ~0 r+ N
9.3.1 Basic Structures: Correspondence Solutions 344) k- \8 H* \ f5 X. r
9.3.2 Voigt Composite 345/ ]8 ?: |7 }0 o$ Y
9.3.3 Reuss Composite 345
3 s: T8 q4 L: g1 W* _4 |9.3.4 Hashin–Shtrikman Composite 346
% o1 P8 |& Z5 E; O4 v1 v/ t! \9.3.5 Spherical Particulate Inclusions 347
}) f; d) P6 \% D2 i. A9 m; o- s9.3.6 Fiber Inclusions 349
6 R$ u$ j% w- M* ]2 [5 Q; f9.3.7 Platelet Inclusions 3495 y8 E7 z- b1 ~4 R6 b. B
9.3.8 Stiffness-Loss Maps 3502 K" f5 u/ U S: t% [5 B
9.4 Bounds on the Viscoelastic Properties 353
$ x, n& S4 B) g# D! t s9.5 Extremal Composites 354
9 f3 R1 z. E* J9.6 Biological Composite Materials 356
' V3 ~- f% `# R y% L' Y) b9.7 Poisson’s Ratio of Viscoelastic Composites 357
) i3 L* e9 z( e' W) ?6 G D9.8 Particulate and Fibrous Composite Materials 358
: c' M. ]' h+ b$ _( }7 t9 z9.8.1 Structure 358' Q4 E/ d% y) P; f
9.8.2 Particulate Polymer Matrix Composites 359
% C2 S. M0 S& z& z1 G) o D6 V9.8.3 Fibrous Polymer Matrix Composites 361# H" x+ `- a9 M8 v8 q' T5 ~
9.8.4 Metal–Matrix Composites 362; K; f/ u, z$ h8 g' w, C
9.9 Cellular Solids 363, F$ d! ?9 i, @/ _( X% A
9.10 Piezoelectric Composites 366
! c* H4 i# b1 Y7 o7 u; P6 l; ]4 h9.11 Dispersion of Waves in Composites 3668 q9 Z% r( d) R7 ~6 w
9.12 Summary 367
# P, K3 V% _8 q9 Q5 P4 g9.13 Examples 367
$ ?+ k6 h! [" @9.14 Problems 3703 D! Q5 Q$ A& c1 |( D
Bibliography 370
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7 p* f& H1 A/ P D; T* |' [
$ ~# P8 l% d' f
10 Applications and Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . 377
4 r5 \8 S% [; ]10.1 Introduction 377; U; o1 E% I5 g8 b) i2 ~+ Q1 P
10.2 A Viscoelastic Earplug: Use of Recovery 377; \+ U0 |# C) e1 v0 }0 ?2 W* |
10.3 Creep and Relaxation of Materials and Structures 3784 v8 p$ Y7 G& N. @! a% l) {
10.3.1 Concrete 378
5 i$ s6 |' W C8 F3 K0 Y# |10.3.2 Wood 378
0 g" L- _( c# x. D# S10.3.3 Power Lines 3799 \) n/ O" A3 x0 J) Q0 a" L3 E
10.3.4 Glass Sag: Flowing Window Panes 380
& n7 i# |! b4 J$ u10.3.5 Indentation: Road Rutting 380! p5 r- O' S$ t. q
10.3.6 Leather 381
e0 E! I" s1 L: F. Z3 Y10.3.7 Creep-Resistant Alloys and Turbine Blades 381- r/ N0 ^+ S6 P5 ~, y
10.3.8 Loosening of Bolts and Screws 382
( ~& ~' F" x5 @' W; U+ V10.3.9 Computer Disk Drive: Case Study of Relaxation 384
; ^( s# V$ W) g( X- b8 z10.3.10 Earth, Rock, and Ice 385
5 w" W: {6 ^# z' }% Q0 {4 m& b10.3.11 Solder 386
# k, t- V4 O. ~2 I9 g- \: B% J10.3.12 Filamentsi nL ight Bulbs and Other Devices 3875 f+ K6 Y9 }: x" e
10.3.13Tires: Flat-Spotting and Swelling 388
* \5 o0 o, T0 S) d10.3.14Cushionsfor Seats and Wheelchairs 388
2 n, x: d k0 `2 ^10.3.15 Artificial Joints 389; `- q) y. u) e" P
10.3.16 Dental Fillings 389
- Q& G( L- c( ?0 N10.3.17 Food Products 3891 _! [/ q# F" e3 \8 ^4 v( x
10.3.18 Seals and Gaskets 3906 G: I9 J, _0 e5 j9 X5 K
10.3.19 Relaxationi nM usical Instrument Strings 3906 \' }" c+ v3 j) i: G6 K7 h
10.3.20 Winding of Tape 391* g/ P, U' Q# j( N: @$ S+ }+ D) @
10.4 Creep and Recovery in Human Tissue 391
" O4 U" N. |( Q: Q; f6 I% j/ E10.4.1 Spinal Discs: Height Change 3911 Z2 u W4 q* J2 T& Q# ^, `
10.4.2 The Nose 3921 ~7 o5 @ b1 E2 s V# @* Q
10.4.3 Skin 392
( _, j: I; w1 B1 H10.4.4 The Head 393+ T& F6 a% P- ^' j' }
10.5 Creep Damage and Creep Rupture 394$ j! Y8 j: Y8 R2 K. Z9 p9 u
10.5.1 Vajont Slide 3943 {/ N" m( i& z! h
10.5.2 Collapse of a Tunnel Segment 3945 x2 s# ?5 D3 W2 P; y' `
10.6 Vibration Control and Waves 394
; x( A2 C/ C2 R1 ^) @, ?" X10.6.1 Analysis of Vibration Transmission 3944 `3 s) M5 @5 i% V' G( @+ m4 K) D$ [$ K
10.6.2 Resonant (Tuned) Damping 397
7 }5 d; [, M4 p7 w4 Y* e10.6.3 Rotating Equipment Vibration 397, h$ b/ p4 M Q
10.6.4 Large Structure Vibration: Bridges and Buildings 398
* J1 X/ L3 Z1 u3 q10.6.5 Damping Layers for Plate and Beam Vibration 399
" ^% T S! j8 b! m+ R10.6.6 Structural Damping Materials 400+ s2 s) i0 l& I3 q
10.6.7 Piezoelectric Transducers 4021 ~" ~& L3 M% e& t
10.6.8 Aircraft Noise and Vibration 402
5 F! U+ Q3 c: t1 u' L10.6.9 Solid Fuel Rocket Vibration 404
& l2 M: q5 J7 g2 g* {) x10.6.10 Sports Equipment Vibration 404
, A! \) h4 Z9 R v, v) H7 }+ \2 P5 L10.6.11 Seat Cushions and Automobiles: Protection of People 404/ l( k1 l8 F. V
10.6.12 Vibrationi n ScientificI nstruments 406' D3 E+ ^: w6 \6 W& U
10.6.13 Waves 406
7 H# k8 }" `9 U* h10.7 “Smart” Materials and Structures 407
' g5 T& _( h7 y10.7.1 “Smart” Materials 4071 J3 v( C- S3 ?, z1 V
10.7.2 Shape Memory Materials 4087 T" g1 G' K ~5 Q7 v3 h( b% K
10.7.3 Self-Healing Materials 409
, G! o0 a4 a1 ^10.7.4 Piezoelectric Solid Damping 4098 ~) D. p2 _. w& g7 O8 L; s
10.7.5 Active Vibration Control: “Smart” Structures 409
* h3 t7 z' i6 ~% ?# ~! d: K2 @10.8 Rolling Friction 4092 y( Y+ J. e Z( L+ O. k- a, B
10.8.1 Rolling Analysis 410& I4 J( U. t8 i" B1 y- L# S" j
10.8.2 Rolling of Tires 4117 m5 R8 Z7 o6 v0 B3 C% q9 D! a
10.9 Uses of Low-Loss Materials 412
6 i/ h$ f6 Z6 G" ^6 y10.9.1 Timepieces 412! @# m2 s% q2 M. d5 v
10.9.2 Frequency Stabilization and Control 413
0 ^3 n \9 g, H8 _2 k# g10.9.3 Gravitational Measurements 413
' |& V1 h8 s2 @; s7 f3 f8 ~1 U10.9.4 Nanoscale Resonators 4143 E k/ z. ?3 M9 }7 l
10.10 Impulses, Rebound, and Impact Absorption 414
" j# K |* b' R ]10.10.1 Rationale 414+ T2 g0 o. ^" `8 i
10.10.2 Analysis 4159 c. x) I9 C+ P- {! D# W/ G
10.10.3 Bumpers and Pads 418
$ `# A1 F0 [3 z2 @& t s0 C10.10.4 Shoe Insoles, Athletic Tracks, and Glove Liners 419
3 K! C/ C, d2 c* w4 m, Q10.10.5 Toughness of Materials 419
7 A" X9 v6 y9 j! H. W, p. }10.10.6 Tissue Viscoelasticity in Medical Diagnosis 4200 S K5 f( m6 D5 Z% g i7 x4 L; v
10.11Rebound of a Ball 421
% \, r4 {1 }' I2 j0 x10.11.1 Analysis 4213 n9 \& m* n$ L, W# [ K- T; ]) ?
10.11.2 Applications in Sports 422
3 M0 R7 p8 q/ B- K- z& e10.12 Applications of Soft Materials 424* M( }, c& @) ?( X
10.12.1 Viscoelastic Gels in Surgery 424
3 H! g1 e2 W, T; q10.12.2 Hand Strength Exerciser 424+ d" U. p% a0 |+ G2 n
10.12.3 Viscoelastic Toys 424( D2 I: ]( i9 E) Z
10.12.4 No-Slip Flooring, Mats, and Shoe Soles 425
4 c5 A, F7 T) n+ i10.13 Applications Involving Thermoviscoelasticity 4256 i) f: e- l+ ^* Q
10.14 Satellite Dynamics and Stability 4266 t$ Y& h& T H( r
10.15 Summary 428/ X+ d/ S. J! z/ Q0 N7 c
10.16 Examples 429
6 s# D. ?# k. r+ |4 G6 f. S10.17 Problems 4312 V% F% M- X! i) M$ a3 ^2 N
Bibliography 431
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H; M& U: G2 m2 M2 E; H. M( z; Q
A: Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441
: `( n. j5 K. eA.1 Mathematical Preliminaries 4417 }2 A2 Y+ O" ^2 ~) X' `' g
A.1.1 Introduction 441
0 i& {. C9 [& T0 e& v* V0 QA.1.2 Functionals and Distributions 441
. b7 E1 e% F8 T6 o* rA.1.3 Heaviside Unit Step Function 4429 r# ^2 T1 o" ^) f
A.1.4 Dirac Delta 442
8 l. K0 @- ~ N; `. F3 g XA.1.5 Doublet 443
5 I( N: [7 @+ S! _* gA.1.6 Gamma Function 445
/ s, F0 ]* z! B+ [, cA.1.7 Liebnitz Rule 445
1 }5 r O8 K% u3 h: {& m9 W/ xA.2 Transforms 4458 U M" ?1 T: N% ?2 E; U! ~
A.2.1 Laplace Transform 446( a$ x, R6 v. z: Z, V d% g/ u3 G( E
A.2.2 Fourier Transform 446
( @9 C0 t( u |A.2.3 Hartley Transform 447
) ^5 M; W5 x: p5 Z3 qA.2.4 Hilbert Transform 447& n5 j' }4 @/ [' M2 @* g& |
A.3 Laplace Transform Properties 4489 W- P! U2 l. d' c8 Q6 j; S
A.4 Convolutions 4491 ` x, s1 P! c. ?2 m4 Q
A.5 Interrelations in Elasticity Theory 451
& H* w% d8 H( q6 `A.6 Other Works on Viscoelasticity 4510 T" Q3 M; o* p/ {4 D
Bibliography 452
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. w' [+ n6 ]0 d9 a$ A2 jB: Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455% D1 @& L. R4 F0 F/ r0 ~$ \
B.1 Principal Symbols 455
' @2 A( y) `% u5 x O" p# ^Index 457: K7 M( {1 @1 W2 V% p) f/ _
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发表于 2015-1-9 22:34:06