Theory of Viscoelasticity Second Edition

Integration of numerous theoretical developments offers a complete, consistent description of the linear theory of the viscoelastic behavior of materials. Relevant theoretical formulations are derived from a continuum mechanics viewpoint, followed by discussions of problem-solving techniques. "A welcome addition to the literature." American Scientist.29 figures. 1982 edition.

Preface to Second Editzon

ix

Preface to First Edition

xi

I. Viscoelastic Stress Strate Constitutive Relations

1.1. Introduction

1

(2)

1.2. Integral Form of Stress Strain Constitutive Relations, Stieltjes Convolution Notation

3

(6)

1.3. Consequences of Fading Memory and the Distinction between Viscoelastic Solids and Fluids

9

(5)

1.4. Differential Operator Form of Stress Strain Constitutive Relations

14

(2)

1.5. Relaxation and Creep Characteristics, Mechanical Models

16

(5)

1.6. Steady State and Fourier Transformed Stress Strain Constitutive Relations

21

(4)

1.7. Accelerated and Retarded Processes

25

(1)

1.8. Alternative Mechanical Property Functions

26

(2)

1.9. Spectra

28

(4)

Problems

32

(2)

References

34

(1)

II. Isothermal Boundary Value Problems

2.1. Formulation of the Boundary Value Problem

35

(2)

2.2. Uniqueness of Solution

37

(4)

2.3. Separation of Variables Conditions

41

(3)

2.4. Steady State Harmonic Conditions

44

(1)

2.5. Integral Transform Methods

45

(1)

2.6. Effect of Inertia Terms

46

(1)

2.7. Steady State Harmonic Oscillation Example

47

(1)

2.8. Quasi-Static Response Example

48

(4)

2.9. Pressurization of a Cylinder

52

(5)

2.10. Pressurization of a Spherical Cavity

57

(3)

2.11. Free Vibration

60

(6)

2.12. Limitations of Integral Transform Methods

66

(5)

2.13. Summary and Conclusions

71

(2)

Problems

73

(2)

References

75

(2)

III. Thermoviscoelasticity

3.1. Thermodynamical Derivation of Constitutive Relations

77

(6)

3.2. Restrictions and Special Cases

83

(3)

3.3. Relationship to Nonnegative Work Requirements

86

(1)

3.4. Formulation of the Thermoviscoelastic Boundary Value Problem

87

(3)

3.5. Temperature Dependence of Mechanical Properties

90

(4)

3.6. Thermorheologically Simple Materials

94

(11)

3.7. Glass Transition Criterion

105

(8)

3.8. Heat Conduction

113

(6)

Problems

119

(1)

References

120

(2)

IV. Mechanical Properties and Approximate Transform Inversion

4.1. Introduction

122

(3)

4.2. Relaxation and Creep Procedures

125

(2)

4.3. Steady State Harmonic Oscillation Procedures

127

(4)

4.4. Wave Propagation Procedures

131

(7)

4.5. Temperature Dependent Effects

138

(3)

4.6. Approximate Interrelationships among Properties

141

(4)

4.7. Approximate Inversion of the Laplace Transform

145

(4)

4.8. Approximate Solutions for Dynamic Problems

149

(4)

Problems

153

(2)

References

155

(2)

V. Problems of a Nontransform Type

5.1. Contact Problem

157

(5)

5.2. Extended Correspondence Principle

162

(5)

5.3. Crack Growth-Local Failure Model

167

(4)

5.4. Crack Growth-Energy Balance Approach

171

(8)

5.5. Thermoviscoelastic Stress Analysis Problem

179

(4)

Problems

183

(2)

References

185

(3)

VI. Wave Propagation

6.1. Isothermal Wave Propagation

188

(6)

6.2. Dynamic Response Problems

194

(8)

6.3. Harmonic Thermoviscoelastic Waves in Unlimited Media

202

(6)

6.4. Reflection of Harmonic Waves

208

(6)

6.5. Moving Loads on a Viscoelastic Half Space

214

(7)

6.6. Viscoelastic Rayleigh Waves

221

(6)

Problems

227

(1)

References

227

(2)

VII. General Theorems and Formulations

7.1. Uniqueness of Solution of Coupled Thermoviscoelastic Boundary Value Problem

229

(3)

7.2. Representation in Terms of Displacement Functions

232

(2)

7.3. Reciprocal Theorem

234

(3)

7.4. Variational Theorems

237

(11)

7.5. Minimum Theorems

248

(7)

7.6. Optimal Strain History

255

(5)

Problems

260

(1)

References

260

(3)

VIII. Nonlinear Viscoelasticity

8.1. Derivation of Constitutive Relations for Solids

263

(8)

8.2. Reduction to Linear Theory

271

(2)

8.3. Simple Shear Deformation Example

273

(5)

8.4. Viscoelastic Fluids

278

(5)

8.5. Simple Shear Flow Example

283

(6)

Problems

289

(1)

References

290

(3)

IX. Nonlinear Mechanical Behavior

9.1. A Nonlinear Theory of Elastomeric Solids

293

(10)

9.2. Nonlinear Acceleration Waves

303

(7)

9.3. Viscometric Flows

310

(6)

9.4. Nonviscometric Flows

316

(9)

9.5. Viscoelastic Lubrication

325

(6)

9.6. Nonlinear Theory Mechanical Properties

331

(17)

Problems

348

(1)

References

349

(4)

Appendixes

A. Step Functions and Delta Functions

353

(1)

B. Laplace Transformation Properties

354

(3)

References

357

(2)

Index

359

What is included with this book?

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

FREE SHIPPING

Amazon no longer offers textbook rentals. We do!

Theory of Viscoelasticity Second Edition

Summary

Table of Contents

Supplemental Materials