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Theory of Viscoelasticity

An Introduction

2nd Edition - October 28, 1982

Author: R Christensen

eBook ISBN:

9 7 8 - 0 - 3 2 3 - 1 6 1 8 2 - 4

Theory of Viscoelasticity: An Introduction, Second Edition discusses the integral form of stress strain constitutive relations. The book presents the formulation of the boundary… Read more

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Theory of Viscoelasticity: An Introduction, Second Edition discusses the integral form of stress strain constitutive relations. The book presents the formulation of the boundary value problem and demonstrates the separation of variables condition. The text describes the mathematical framework to predict material behavior. It discusses the problems to which integral transform methods do not apply. Another topic of interest is the thermoviscoelastic stress analysis. The section that follows describes the heat conduction, glass transition criterion, viscoelastic Rayleigh waves, optimal strain history path, and nonlinear behavior of elastomers. The book will provide valuable insights for chemists, engineers, students, and researchers in the field of chemistry.

Preface to Second Edition

Preface to First Edition

I. Viscoelastic Stress Strain Constitutive Relations

1.1. Introduction

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

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

1.4. Differential Operator Form of Stress Strain Constitutive Relations

1.5. Relaxation and Creep Characteristics, Mechanical Models

1.6. Steady State and Fourier Transformed Stress Strain Constitutive Relations

1.7. Accelerated and Retarded Processes

1.8. Alternative Mechanical Property Functions

1.9. Spectra

Problems

References

II. Isothermal Boundary Value Problems

2.1. Formulation of the Boundary Value Problem

2.2. Uniqueness of Solution

2.3. Separation of Variables Conditions

2.4. Steady State Harmonic Conditions

2.5. Integral Transform Methods

2.6. Effect of Inertia Terms

2.7. Steady State Harmonic Oscillation Example

2.8. Quasi-Static Response Example

2.9. Pressurization of a Cylinder

2.10. Pressurization of a Spherical Cavity

2.11. Free Vibration

2.12. Limitations of Integral Transform Methods

2.13. Summary and Conclusions

Problems

References

III. Thermoviscoelasticity

3.1. Thermodynamical Derivation of Constitutive Relations

3.2. Restrictions and Special Cases

3.3. Relationship to Nonnegative Work Requirements

3.4. Formulation of the Thermoviscoelastic Boundary Value Problem

3.5. Temperature Dependence of Mechanical Properties

3.6. Thcrmorheologically Simple Materials

3.7. Glass Transition Criterion

3.8. Heat Conduction

Problems

References

IV. Mechanical Properties and Approximate Transform Inversion

4.1. Introduction

4.2. Relaxation and Creep Procedures

4.3. Steady State Harmonic Oscillation Procedures

4.4. Wave Propagation Procedures

4.5. Temperature Dependent Effects

4.6. Approximate Interrelationships among Properties

4.7. Approximate Inversion of the Laplace Transform

4.8. Approximate Solutions for Dynamic Problems

Problems

References

V. Problems of a Nontransform Type

5.1. Contact Problem

5.2. Extended Correspondence Principle

5.3. Crack Growth Local Failure Model

5.4. Crack Growth - Energy Balance Approach

5.5. Thermoviscoelastic Stress Analysis Problem

Problems

References

VI. Wave Propagation

6.1. Isothermal Wave Propagation

6.2. Dynamic Response Problems

6.3. Harmonic Thermoviscoelastic Waves in Unlimited Media

6.4. Reflection of Harmonic Waves

6.5. Moving Loads on a Viscoelastic Half Space

6.6. Viscoelastic Rayleigh Waves

Problems

References

VII. General Theorems and Formulations

7.1. Uniqueness of Solution of Coupled Thermoviscoelastic Boundary Value Problem

7.2. Representation in Terms of Displacement Functions

7.3. Reciprocal Theorem

7.4. Variational Theorems

7.5. Minimum Theorems

7.6. Optimal Strain History

Problems

References

VIII. Nonlinear Viscoelasticity

8.1. Derivation of Constitutive Relations for Solids

8.2. Reduction to Linear Theory

8.3. Simple Shear Deformation Example

8.4. Viscoelastic Fluids

8.5. Simple Shear Flow Example

Problems

References

IX. Nonlinear Mechanical Behavior

9.1. A Nonlinear Theory of Elastomeric Solids

9.2. Nonlinear Acceleration Waves

9.3. Viscometric Flows

9.4. Nonviscometric Flows

9.5. Viscoelastic Lubrication

9.6. Nonlinear Theory Mechanical Properties

Problems

References

Appendixes

A. Step Functions and Delta Functions

B. Laplace Transformation Properties

References

Index