Theory of Viscoelasticity Second Edition

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ISBN: 9780486428802 | 048642880X
Cover: Paperback
Copyright: 8/19/2010

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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

Preface to First Edition

I. Viscoelastic Stress Strate Constitutive Relations

1.1. Introduction

(2)

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

(6)

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

(5)

1.4. Differential Operator Form of Stress Strain Constitutive Relations

(2)

1.5. Relaxation and Creep Characteristics, Mechanical Models

(5)

1.6. Steady State and Fourier Transformed Stress Strain Constitutive Relations

(4)

1.7. Accelerated and Retarded Processes

(1)

1.8. Alternative Mechanical Property Functions

(2)

1.9. Spectra

(4)

Problems

(2)

References

(1)

II. Isothermal Boundary Value Problems

2.1. Formulation of the Boundary Value Problem

(2)

2.2. Uniqueness of Solution

(4)

2.3. Separation of Variables Conditions

(3)

2.4. Steady State Harmonic Conditions

(1)

2.5. Integral Transform Methods

(1)

2.6. Effect of Inertia Terms

(1)

2.7. Steady State Harmonic Oscillation Example

(1)

2.8. Quasi-Static Response Example

(4)

2.9. Pressurization of a Cylinder

(5)

2.10. Pressurization of a Spherical Cavity

(3)

2.11. Free Vibration

(6)

2.12. Limitations of Integral Transform Methods

(5)

2.13. Summary and Conclusions

(2)

Problems

(2)

References

(2)

III. Thermoviscoelasticity

3.1. Thermodynamical Derivation of Constitutive Relations

(6)

3.2. Restrictions and Special Cases

(3)

3.3. Relationship to Nonnegative Work Requirements

(1)

3.4. Formulation of the Thermoviscoelastic Boundary Value Problem

(3)

3.5. Temperature Dependence of Mechanical Properties

(4)

3.6. Thermorheologically Simple Materials

(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

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Theory of Viscoelasticity Second Edition

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Theory of Viscoelasticity Second Edition

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