Articles liés à Lectures on Viscoelasticity Theory
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Synopsis
I. Viscoelastic Response in Shear.- 1. Stress Relaxation.- 2. Creep.- 3. Response Functions.- 4. Models.- 5. Superposition.- 6. Tensile Response.- 7. Relation between Modulus and Compliance.- 8. Sinusoidal Shearing.- 9. Nomenclature.- 10. Energy Storage and Loss.- 11. Oscillation with Increasing Amplitude.- II. Fourier and Laplace Transforms.- 1. Fourier Transforms.- 2. Two-sided Laplace Transforms.- 3. Laplace Transforms.- 4. Elementary Formulas.- 5. Convolutions.- III. Relations Between Modulus and Compliance..- 1. Limits and Moments: Fluids.- 2. Limits and Moments: Solids.- 3. Solids and Fluids.- 4. Scale-Invariant Response.- 5. Approximate Transform Inversion.- 6. Direct Approximation.- 7. Approximate Relation between Modulus and Complex Modulus.- 8. Graphs of Moduli and Compliances.- IV. Some One-Dimensional Dynamical Problems.- 1. Torsional Oscillations.- a. Viscous Fluid.- b. Elastic Solid.- c. Maxwell Fluid.- d. Power-law Solid.- e. Heal Solids with Small Losses.- 2. Plane Shear Waves.- a. Elastic Solid.- b. Viscous Fluid.- c. Power-law Solids.- 1. Saddle-point Approximation.- 2. Wide Saddle-points 6l.- d. Real Solids with Small Losses.- e. The Elastic Precursor.- f. Long-time Behavior.- V. Stress Analysis.- 1. Quasi-static Approximation.- 2. Stress-strain Relations.- 3. Simplest Deformations of Isotropic Materials.- 4. Simple Tension: Basic Approximation Methods.- 5. The Correspondence Principle.- 6. Example: Flat-headed Punch.- 7. Example: Tube under Internal Pressure.- 8. Incompressible Materials.- VI. Thermal Effects.- 1. The Time-Temperature Shift Factor.- 2. Example: Runaway.- 3. Variable-Temperature Histories.- 4. Example: Simple Tension of a Cooling Hod.- 5. Thermal Expansion.- VII. Large Deformations with Small Strains.- 1. Example: Simple Rotation.- 2. Example: Torsion.- 3. Small Distortions with Large Rotations.- 4. Relative Strain.- 5. Isotropic Materials.- 6. Fluids.- 7. Example: Steady Simple Shearing.- 8. Example: Oscillatory Shearing.- 9. Motions with Uniform Velocity Gradient.- 10. Anisotropic Fluids.- VIII. Slow Viscoelastic Flow.- 1. Viscoelastic Flow.- 2. Flow Diagnosis.- 3. Slow Viscoelastic Flow: Asymptotic Approximations.- 4. Slow Viscoelastic Flow: Three-dimensional Equations.- 5. Orders of Approximation in Slow Motion.- 6. The Rivlin-Ericksen Tensors.- 7. Solution of Problems.- 8. Ordinary Perturbations.- 9. A Useful Identity.- 10. Plane Flow.- 11. Flow in Tubes.- IX. Viscometric Flow.- 1. Stress.- 2. Example: Channel Flow.- 3. Slip Surfaces, Shear Axes, and Shear Rate.- 4. Dynamical Problems.- 5. Flow In Tubes.- 6. Viscometric Equation in Terms of Rivlin-Ericksen Tensors.- 7. Centripetal Effects.- 8. Boundary Layers.
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