Modern Developments in the Mechanics of Continua

List of Contributors

Preface

Thermodynamics of Deformation

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An Alternative to the Continuum—The Aggregate as a Geometrical Basis for the Deformation Tensor and for Theories of Liquids


1. Introduction


2. The General Aggregate


3. "Inherent" and "Flow" Deformation of an Aggregate


4. Conclusions

References

Shear Wave Propagation in Birefringent Viscoelastic Liquids of Low Rigidity and Low Viscosity


1. Introduction


2. Propagation Equations


3. Experimental Apparatus


4. Theoretical Model for a Suspension of Rigid Ellipsoidal Particles


5. Experimental Measurements


6. Conclusion

References

The Critical Wall Shear Stress for Reduction of Turbulent Drag in Pipe Flow


1. Introduction


2. Previous Investigations


3. The Onset of Drag Reduction


4. The Onset of Drag Reduction Hypothesis


5. Experimental Materials and Apparatus


6. Data


7. Discussion of Results


8. Summary

Appendix: Scaling Rules for the Dissipation Wavenumber, Kd

Nomenclature

References

Properties of a Class of Constitutive Equations Stated in a Nontrivial Implicit Form


1. Introduction


2. Formulation


3. Reduction to Component Form


4. Properties of the Non-diagonal Solutions


5. A Special Case


6. Characteristic Surfaces for the Medium


7. Conclusions

References

Cosserat Continua


1. Introduction


2. Cosserat Continua


3. Dipolar Media

References

Stability of Couette Flow of Second-Order Fluids between Two Coaxial Circular Cylinders


1. Introduction


2. Equations


3. Solution


4. Conclusion

References

Approximate Constitutive Equations


1. Introduction


2. Wide-Range and Narrow-Range Descriptions


3. One-Dimensional Shearing Motions


4. Materials with Memory


5. Materials with Fading Memory


6. Viscoelastic Fluids


7. Small Motions


8. Short Motions


9. Slow Motions


10. Orders of Approximation in Slow Motion


11. Analytic Continuation


12. Small Motions Superposed on Stress-Relaxation at Constant Deformation


13. Small Motions Superposed on Steady Shearing Motion


14. Some Remarks on Perturbation Methods


15. Conclusion

References

Remarks on Compatibility


1. Introduction


2. Kinematic Concepts and Notation


3. Other Forms of Compatibility


4. Deformations with Constant Strain Invariants


5. Equilibrium: Elastic, Incompressible, Isotropic Material

References

A Representative Theorem for the Constitutive Equation of Simple Material in Motions with Constant Stretch History

Text

References

The Problem of a Jet against the Ground. Rheological Solution in the Hodograph Plane

Text

References

Some Interpretations of the Toms Effect


1. Introduction


2. Virk's Hypothesis


3. A Molecular Viscoelasticity Hypothesis


4. Comparison with Experiment


5. A Molecular Entanglement Hypothesis


6. A Shear-Layer Modification Hypothesis


7. Conclusions

References

Acceleration Waves in Nonlinear Materials


1. Introduction


2. Preliminary Definitions


3. Waves in Elastic Materials


4. Waves in Linearly Viscoelastic Materials


5. Waves in Simple Materials with Memory

References

The Speed of Propagation of Signals in Viscoelastic Materials


1. Introduction


2. Notation


3. Statement of the Problem

References

On an Isothermal Flow Function for a Heterogeneous Medium


1. Introduction


2. Physical Constants and Microstress-Strain Relations


3. Formulation of the Flow Function of a Heterogeneous Medium


4. Experimental Considerations

References

Mass Transfer into Non-Newtonian Fluids


1. Introduction


2. Theory


3. Experimental Apparatus


4. Experimental Procedure


5. Experimental Results


6. Discussion


7. Summary and Conclusions

References

Index