Modern Developments in the Mechanics of Continua

Modern Developments in the Mechanics of Continua

1st Edition - January 1, 1966

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  • Editor: Salamon Eskinazi
  • eBook ISBN: 9780323159951

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Modern Developments in the Mechanics of Continua presents the proceedings of the International Conference on Rheology, held in Pinebrook, New York, on August 23–27, 1965. This book promotes the national and international interest in mechanics of continua. Comprised of 16 chapters, this compilation of papers starts with an overview of the fundamental aspects of thermodynamics. This text then examines the divergence between the molecular theory of liquids and continuum mechanics. Other chapters explore the theory of the activation volume of liquids and the potential applications in rheology. This book discusses as well the characteristics of shear wave propagation, which are related to the viscoelastic properties of the supporting medium. The final chapter deals with the study of diffusion of benzoic acid at constant temperature into kaolinite slurries of changing concentrations. This book is a valuable resource for physicists, biophysicists, mathematicians, and engineers interested in the mechanics of continua.

Table of Contents

  • List of Contributors


    Thermodynamics of Deformation


    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


    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


    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



    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


    Cosserat Continua

    1. Introduction

    2. Cosserat Continua

    3. Dipolar Media


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

    1. Introduction

    2. Equations

    3. Solution

    4. Conclusion


    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


    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


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



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



    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


    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


    The Speed of Propagation of Signals in Viscoelastic Materials

    1. Introduction

    2. Notation

    3. Statement of the Problem


    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


    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



Product details

  • No. of pages: 216
  • Language: English
  • Copyright: © Academic Press 1966
  • Published: January 1, 1966
  • Imprint: Academic Press
  • eBook ISBN: 9780323159951

About the Editor

Salamon Eskinazi

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