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El. knyga: Viscoelastic Materials

Roderic Lakes (University of Wisconsin, Madison)

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Išleidimo metai: 27-Apr-2009
Leidėjas: Cambridge University Press
Kalba: eng
ISBN-13: 9780511577376

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Biomedical engineering

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Formatas: PDF+DRM
Išleidimo metai: 27-Apr-2009
Leidėjas: Cambridge University Press
Kalba: eng
ISBN-13: 9780511577376

Kitos knygos pagal šią temą:

Biomedical engineering

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This graduate text on viscoelastic materials addresses design applications as diverse as earplugs, computer disks and medical diagnostics.

Understanding viscoelasticity is pertinent to design applications as diverse as earplugs, gaskets, computer disks, satellite stability, medical diagnosis, injury prevention, vibration abatement, tire performance, sports, spacecraft explosions, and music. This book fits a one-semester graduate course on the properties, analysis, and uses of viscoelastic materials. Those familiar with the author's precursor book, Viscoelastic Solids, will see that this book contains many updates and expanded coverage of the materials science, causes of viscoelastic behavior, properties of materials of biological origin, and applications of viscoelastic materials. The theoretical presentation includes both transient and dynamic aspects, with emphasis on linear viscoelasticity to develop physical insight. Methods for the solution of stress analysis problems are developed and illustrated. Experimental methods for characterization of viscoelastic materials are explored in detail. Viscoelastic phenomena are described for a wide variety of materials, including viscoelastic composite materials. Applications of viscoelasticity and viscoelastic materials are illustrated with case studies.

Daugiau informacijos

This graduate text on viscoelastic materials addresses design applications as diverse as earplugs, computer disks and medical diagnostics.

Preface

xvii

Introduction: Phenomena

(13)

Viscoelastic Phenomena

(2)

Motivations for Studying Viscoelasticity

(1)

Transient Properties: Creep and Relaxation

(5)

Viscoelastic Functions J(t), E(t)

(4)

Solids and Liquids

(1)

Dynamic Response to Sinusoidal Load: E*, tanδ

(2)

Demonstration of Viscoelastic Behavior

(1)

Historical Aspects

(1)

Summary

(1)

Examples

(1)

Problems

(1)

Bibliography

(2)

Constitutive Relations

(41)

Introduction

(1)

Prediction of the Response of Linearly Viscoelastic Materials

(3)

Prediction of Recovery from Relaxation E(t)

(1)

Prediction of Response to Arbitrary Strain History

(2)

Restrictions on the Viscoelastic Functions

(2)

Roles of Energy and Passivity

(1)

Fading Memory

(1)

Relation between Creep and Relaxation

(1)

Analysis by Laplace Transforms: J(t) ⇔ E(t)

(1)

Analysis by Direct Construction: J(t) ⇔ E(t)

(1)

Stress versus Strain for Constant Strain Rate

(1)

Particular Creep and Relaxation Functions

(9)

Exponentials and Mechanical Models

(5)

Exponentials and Internal Causal Variables

(1)

Fractional Derivatives

(1)

Power-Law Behavior

(1)

Stretched Exponential

(1)

Logarithmic Creep; Kuhn Model

(1)

Distinguishing among Viscoelastic Functions

(1)

Effect of Temperature

(3)

Three-Dimensional Linear Constitutive Equation

(2)

Aging Materials

(1)

Dielectric and Other Forms of Relaxation

(1)

Adaptive and ``Smart'' Materials

(1)

Effect of Nonlinearity

(6)

Constitutive Equations

(3)

Creep-Relaxation Interrelation: Nonlinear

(3)

Summary

(1)

Examples

(8)

Problems

(1)

Bibliography

(3)

Dynamic Behavior

(36)

Introduction and Rationale

(1)

The Linear Dynamic Response Functions E*, tanδ

(7)

Response to Sinusoidal Input

(2)

Dynamic Stress-Strain Relation

(3)

Standard Linear Solid

(1)

Kramers-Kronig Relations

(2)

Energy Storage and Dissipation

(2)

Resonance of Structural Members

(7)

Resonance, Lumped System

(4)

Resonance, Distributed System

(3)

Decay of Resonant Vibration

(3)

Wave Propagation and Attenuation

(2)

Measures of Damping

(1)

Nonlinear Materials

(2)

Summary

(1)

Examples

(7)

Problems

(1)

Bibliography

(2)

Conceptual Structure of Linear Viscoelasticity

(20)

Introduction

(1)

Spectra in Linear Viscoelasticity

(3)

Definitions H, L and Exact Interrelations

(1)

Particular Spectra

(2)

Approximate Interrelations of Viscoelastic Functions

(6)

Interrelations Involving the Spectra

(3)

Interrelations Involving Measurable Functions

(3)

Summary, Approximate Relations

101

(1)

Conceptual Organization of the Viscoelastic Functions

101

(3)

Summary

104

(1)

Examples

104

(5)

Problems

109

(1)

Bibliography

109

(2)

Viscoelastic Stress and Deformation Analysis

111

(34)

Introduction

111

(1)

Three-Dimensional Constitutive Equation

111

(1)

Pure Bending by Direct Construction

112

(2)

Correspondence Principle

114

(2)

Pure Bending by Correspondence

116

(1)

Correspondence Principle in Three Dimensions

116

(5)

Constitutive Equations

116

(1)

Rigid Indenter on a Semi-Infinite Solid

117

(2)

Viscoelastic Rod Held at Constant Extension

119

(1)

Stress Concentration

119

(1)

Saint Venant's Principle

120

(1)

Poisson's Ratio v(t)

121

(3)

Relaxation in Tension

121

(2)

Creep in Tension

123

(1)

Dynamic Problems: Effects of Inertia

124

(7)

Longitudinal Vibration and Waves in a Rod

124

(1)

Torsional Waves and Vibration in a Rod

125

(3)

Bending Waves and Vibration

128

(1)

Waves in Three Dimensions

129

(2)

Noncorrespondence Problems

131

(2)

Solution by Direct Construction: Example

131

(1)

A Generalized Correspondence Principle

132

(1)

Contact Problems

132

(1)

Bending in Nonlinear Viscoelasticity

133

(1)

Summary

134

(1)

Examples

134

(8)

Problems

142

(1)

Bibliography

142

(3)

Experimental Methods

145

(62)

Introduction and General Requirements

145

(1)

Creep

146

(4)

Creep: Simple Methods to Obtain J(t)

146

(1)

Effect of Risetime in Transient Tests

146

(2)

Creep in Anisotropic Media

148

(1)

Creep in Nonlinear Media

148

(2)

Inference of Moduli

150

(2)

Use of Analytical Solutions

150

(1)

Compression of a Block

151

(1)

Displacement and Strain Measurement

152

(4)

Force Measurement

156

(1)

Load Application

157

(1)

Environmental Control

157

(1)

Subresonant Dynamic Methods

158

(3)

Phase Determination

158

(2)

Nonlinear Materials

160

(1)

Rebound Test

161

(1)

Resonance Methods

161

(10)

General Principles

161

(2)

Particular Resonance Methods

163

(3)

Methods for Low-Loss or High-Loss Materials

166

(2)

Resonant Ultrasound Spectroscopy

168

(3)

Achieving a Wide Range of Time or Frequency

171

(2)

Rationale

171

(1)

Multiple Instruments and Long Creep

172

(1)

Time-Temperature Superposition

172

(1)

Test Instruments for Viscoelasticity

173

(11)

Servohydraulic Test Machines

173

(1)

A Relaxation Instrument

174

(1)

Driven Torsion Pendulum Devices

174

(4)

Commercial Viscoelastic Instrumentation

178

(1)

Instruments for a Wide Range of Time and Frequency

179

(3)

Fluctuation-Dissipation Relation

182

(1)

Mapping Properties by Indentation

183

(1)

Wave Methods

184

(4)

Summary

188

(1)

Examples

188

(12)

Problems

200

(1)

Bibliography

201

(6)

Viscoelastic Properties of Materials

207

(64)

Introduction

207

(1)

Rationale

207

(1)

Overview: Some Common Materials

207

(1)

Polymers

208

(7)

Shear and Extension in Amorphous Polymers

208

(4)

Bulk Relaxation in Amorphous Polymers

212

(1)

Crystalline Polymers

213

(1)

Aging and other Relaxations

214

(1)

Piezoelectric Polymers

214

(1)

Asphalt

214

(1)

Metals

215

(12)

Linear Regime of Metals

215

(2)

Nonlinear Regime of Metals

217

(2)

High-Damping Metals and Alloys

219

(5)

Creep-Resistant Alloys

224

(1)

Semiconductors and Amorphous Elements

225

(1)

Semiconductors and Acoustic Amplification

226

(1)

Nanoscale Properties

226

(1)

Ceramics

227

(6)

Rocks

227

(2)

Concrete

229

(2)

Inorganic Glassy Materials

231

(1)

Ice

231

(1)

Piezoelectric Ceramics

232

(1)

Biological Composite Materials

233

(20)

Constitutive Equations

234

(1)

Hard Tissue: Bone

234

(2)

Collagen, Elastin, Proteoglycans

236

(1)

Ligament and Tendon

237

(3)

Muscle

240

(3)

Fat

243

(1)

Brain

243

(1)

Vocal Folds

244

(1)

Cartilage and Joints

244

(2)

Kidney and Liver

246

(1)

Uterus and Cervix

246

(1)

Arteries

247

(1)

Lung

248

(1)

The Ear

248

(1)

The Eye

249

(2)

Tissue Comparison

251

(1)

Plant Seeds

252

(1)

Wood

252

(1)

Soft Plant Tissue: Apple, Potato

253

(1)

Common Aspects

253

(2)

Temperature Dependence

253

(1)

High-Temperature Background

254

(1)

Negative Damping and Acoustic Emission

255

(1)

Summary

255

(1)

Examples

255

(1)

Problems

256

(1)

Bibliography

257

(14)

Causal Mechanisms

271

(70)

Introduction

271

(3)

Rationale

271

(1)

Survey of Viscoelastic Mechanisms

271

(2)

Coupled Fields

273

(1)

Thermoelastic Relaxation

274

(6)

Thermoelasticity in One Dimension

274

(1)

Thermoelasticity in Three Dimensions

275

(1)

Thermoelastic Relaxation Kinetics

276

(2)

Heterogeneity and Thermoelastic Damping

278

(2)

Material Properties and Thermoelastic Damping

280

(1)

Relaxation by Stress-Induced Fluid Motion

280

(6)

Fluid Motion in One Dimension

280

(1)

Biot Theory: Fluid Motion in Three Dimensions

281

(5)

Relaxation by Molecular Rearrangement

286

(6)

Glassy Region

286

(1)

Transition Region

287

(2)

Rubbery Behavior

289

(2)

Crystalline Polymers

291

(1)

Biological Macromolecules

292

(1)

Polymers and Metals

292

(1)

Relaxation by Interface Motion

292

(2)

Grain Boundary Slip in Metals

292

(2)

Interface Motion in Composites

294

(1)

Structural Interface Motion

294

(1)

Relaxation Processes in Crystalline Materials

294

(22)

Snoek Relaxation: Interstitial Atoms

294

(4)

Zener Relaxation in Alloys: Pairs of Atoms

298

(1)

Gorsky Relaxation

299

(1)

Granato-Lucke Relaxation: Dislocations

300

(3)

Bordoni Relaxation: Dislocation Kinks

303

(2)

Relaxation Due to Phase Transformations

305

(9)

High-Temperature Background

314

(1)

Nonremovable Relaxations

315

(1)

Damping Due to Wave Scattering

316

(1)

Magnetic and Piezoelectric Materials

316

(6)

Relaxation in Magnetic Media

316

(2)

Relaxation in Piezoelectric Materials

318

(4)

Nonexponential Relaxation

322

(1)

Concepts for Material Design

323

(4)

Multiple Causes: Deformation Mechanism Maps

323

(3)

Damping Mechanisms in High-Loss Alloys

326

(1)

Creep Mechanisms in Creep-Resistant Alloys

326

(1)

Relaxation at Very Long Times

327

(1)

Summary

327

(1)

Examples

328

(4)

Problems and Questions

332

(1)

Bibliography

332

(9)

Viscoelastic Composite Materials

341

(36)

Introduction

341

(1)

Composite Structures and Properties

341

(3)

Ideal Structures

341

(1)

Anisotropy due to Structure

342

(2)

Prediction of Elastic and Viscoelastic Properties

344

(9)

Basic Structures: Correspondence Solutions

344

(1)

Voigt Composite

345

(1)

Reuss Composite

345

(1)

Hashin-Shtrikman Composite

346

(1)

Spherical Particulate Inclusions

347

(2)

Fiber Inclusions

349

(1)

Platelet Inclusions

349

(1)

Stiffness-Loss Maps

350

(3)

Bounds on the Viscoelastic Properties

353

(1)

Extremal Composites

354

(2)

Biological Composite Materials

356

(1)

Poisson's Ratio of Viscoelastic Composites

357

(1)

Particulate and Fibrous Composite Materials

358

(5)

Structure

358

(1)

Particulate Polymer Matrix Composites

359

(2)

Fibrous Polymer Matrix Composites

361

(1)

Metal-Matrix Composites

362

(1)

Cellular Solids

363

(3)

Piezoelectric Composites

366

(1)

Dispersion of Waves in Composites

366

(1)

Summary

367

(1)

Examples

367

(3)

Problems

370

(1)

Bibliography

370

(7)

Applications and Case Studies

377

(64)

Introduction

377

(1)

A Viscoelastic Earplug: Use of Recovery

377

(1)

Creep and Relaxation of Materials and Structures

378

(13)

Concrete

378

(1)

Wood

378

(1)

Power Lines

379

(1)

Glass Sag: Flowing Window Panes

380

(1)

Indentation: Road Rutting

380

(1)

Leather

381

(1)

Creep-Resistant Alloys and Turbine Blades

381

(1)

Loosening of Bolts and Screws

382

(2)

Computer Disk Drive: Case Study of Relaxation

384

(1)

Earth, Rock, and Ice

385

(1)

Solder

386

(1)

Filaments in Light Bulbs and Other Devices

387

(1)

Tires: Flat-Spotting and Swelling

388

(1)

Cushions for Seats and Wheelchairs

388

(1)

Artificial Joints

389

(1)

Dental Fillings

389

(1)

Food Products

389

(1)

Seals and Gaskets

390

(1)

Relaxation in Musical Instrument Strings

390

(1)

Winding of Tape

391

(1)

Creep and Recovery in Human Tissue

391

(3)

Spinal Discs: Height Change

391

(1)

The Nose

392

(1)

Skin

392

(1)

The Head

393

(1)

Creep Damage and Creep Rupture

394

(1)

Vajont Slide

394

(1)

Collapse of a Tunnel Segment

394

(1)

Vibration Control and Waves

394

(13)

Analysis of Vibration Transmission

394

(3)

Resonant (Tuned) Damping

397

(1)

Rotating Equipment Vibration

397

(1)

Large Structure Vibration: Bridges and Buildings

398

(1)

Damping Layers for Plate and Beam Vibration

399

(1)

Structural Damping Materials

400

(2)

Piezoelectric Transducers

402

(1)

Aircraft Noise and Vibration

402

(2)

Solid Fuel Rocket Vibration

404

(1)

Sports Equipment Vibration

404

(1)

Seat Cushions and Automobiles: Protection of People

404

(2)

Vibration in Scientific Instruments

406

(1)

Waves

406

(1)

``Smart'' Materials and Structures

407

(2)

``Smart'' Materials

407

(1)

Shape Memory Materials

408

(1)

Self-Healing Materials

409

(1)

Piezoelectric Solid Damping

409

(1)

Active Vibration Control: ``Smart'' Structures

409

(1)

Rolling Friction

409

(3)

Rolling Analysis

410

(1)

Rolling of Tires

411

(1)

Uses of Low-Loss Materials

412

(2)

Timepieces

412

(1)

Frequency Stabilization and Control

413

(1)

Gravitational Measurements

413

(1)

Nanoscale Resonators

414

(1)

Impulses, Rebound, and Impact Absorption

414

(7)

Rationale

414

(1)

Analysis

415

(3)

Bumpers and Pads

418

(1)

Shoe Insoles, Athletic Tracks, and Glove Liners

419

(1)

Toughness of Materials

419

(1)

Tissue Viscoelasticity in Medical Diagnosis

420

(1)

Rebound of a Ball

421

(3)

Analysis

421

(1)

Applications in Sports

422

(2)

Applications of Soft Materials

424

(1)

Viscoelastic Gels in Surgery

424

(1)

Hand Strength Exerciser

424

(1)

Viscoelastic Toys

424

(1)

No-Slip Flooring, Mats, and Shoe Soles

425

(1)

Applications Involving Thermoviscoelasticity

425

(1)

Satellite Dynamics and Stability

426

(2)

Summary

428

(1)

Examples

429

(2)

Problems

431

(1)

Bibliography

431

(10)

A: Appendix

441

(14)

A.1 Mathematical Preliminaries

441

(4)

A.1.1 Introduction

441

(1)

A.1.2 Functionals and Distributions

441

(1)

A.1.3 Heaviside Unit Step Function

442

(1)

A.1.4 Dirac Delta

442

(1)

A.1.5 Doublet

443

(2)

A.1.6 Gamma Function

445

(1)

A.1.7 Liebnitz Rule

445

(1)

A.2 Transforms

445

(3)

A.2.1 Laplace Transform

446

(1)

A.2.2 Fourier Transform

446

(1)

A.2.3 Hartley Transform

447

(1)

A.2.4 Hilbert Transform

447

(1)

A.3 Laplace Transform Properties

448

(1)

A.4 Convolutions

449

(2)

A.5 Interrelations in Elasticity Theory

451

(1)

A.6 Other Works on Viscoelasticity

451

(1)

Bibliography

452

(3)

B: Symbols

455

(2)

B.1 Principal Symbols

455

(2)

Index

457

Roderic Lakes is a Distinguished Professor in the Department of Engineering Physics at the University of WisconsinMadison. He is a Fellow in the American Association for the Advancement of Science (AAAS) and a Fellow in the American Society of Mechanical Engineers (ASME). He has won numerous teaching awards and is the author and co-author of more than 194 archival publications, three books, including Viscoelastic Solids and Biomaterials (2nd and 3rd editions, with J. B. Park), and fourteen book chapters. The author's articles in Science and Nature are of particular note as they have led to numerous synergistic publications in a variety of disciplines.

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