Viscoelastic materials: Viscoelasticity book
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Rod Lakes

Book Outline   R. S. Lakes, Viscoelastic Materials, Cambridge University Press 2009. ISBN 978 0 521 88568 3    
1 Introduction: Phenomena viscoelasticity book cover
1.1 Viscoelastic phenomena
1.2 Motivations for study
1.3 Transient properties: creep and relaxation
  1.3.1 Viscoelastic functions J(t), E(t)
  1.3.2 Solids and liquids; anelastic materials
1.4 Dynamic response to sinusoidal load
1.5 Demonstration of viscoelastic behavior
1.6 Historical aspects
1.7 Summary
1.8 Examples
1.9 Problems

2 Constitutive relations
2.1 Introduction
2.2 Prediction of the response of linearly viscoelastic materials
  2.2.1 Prediction of recovery from relaxation
  2.2.2 Prediction of response to arbitrary strain history
2.3 Restrictions on the viscoelastic functions; fading memory
2.4 Relation between creep and relaxation
  Analysis by Laplace transforms
  Analysis by direct construction.
2.5 Stress vs strain for constant strain rate
2.6 Particular creep and relaxation functions
  2.6.1 Exponentials and mechanical models; 2.6.2; causal variables 2.6.3 fractional derivatives; 2.6.4 power law behavior; stretched exponential; logarithmic creep; Kuhn model; distinguishing among viscoelastic functions.
2.7 Effect of temperature. Time temperature superposition.
2.8 Three dimensional linear constitutive equation
2.9 Aging materials
2.10 Dielectric and other relaxation
2.11 Adaptive and 'smart' materials
2.12 Effect of nonlinearity
  Nonlinear superposition. Quasilinear viscoelasticity (QLV)
  Constitutive equations; interrelation between creep and relaxation; single integral and multiple integral models
2.13 Summary
2.14 Examples
2.15 Problems

3 Dynamic behavior of linear solids
3.1 Introduction and rationale; internal friction
3.2 The linear dynamic response functions
  3.2.1 Response to sinusoidal input; 3.2.2 dynamic stress-strain relation; 3.2.3 standard linear solid.
3.3 Kramers Kronig relations
3.4 Energy storage and dissipation; hysteresis
3.5 Resonance of structural members
  Lumped and distributed systems.
3.6 Decay of resonant vibration
3.7 Wave propagation and attenuation
3.8 Measures of damping
3.9 Nonlinear materials
3.10 Summary
3.11 Examples
3.12 Problems

4 Conceptual structure of linear viscoelasticity
4.1 Introduction
4.2 Spectra in linear viscoelasticity
  Relaxation spectrum; retardation spectrum
4.3 Approximate interrelations between viscoelastic functions
  Interrelations among spectra; among measurable functions
4.4 Conceptual organization of the theory of viscoelasticity. Range of time and frequency of interest in science and engineering.
4.5 Summary
4.6 Examples
4.7 Problems

5 Viscoelastic stress and deformation analysis
5.1 Introduction
5.2 Three dimensional constitutive equation
5.3 Pure bending by direct construction
5.4 Correspondence principle
5.5 Pure bending by correspondence
5.6 Correspondence principle in three dimensions
  5.6.1 Constitutive equations; 5.6.2 rigid indenter on a semi-infinite solid, 5.6.3 viscoelastic rod at constant extension, 5.6.4 stress concentration, 5.6.5 Saint-Venant's principle
5.7 Poisson's ratio
  5.7.1 Relaxation in tension; 5.7.2 creep in tension
5.8 Dynamic problems: effects of inertia
  5.8.1 Longitudinal vibration and waves in a rod; 5.8.2 torsional vibration and waves, 5.8.3 bending waves, 5.8.4 waves in three dimensions.
5.9 Non-correspondence problems
  5.9.1 solution by direct construction; 5.9.2 generalized correspondence principle; 5.9.3 contact problems.
5.10 Bending in nonlinear viscoelasticity
5.11 Summary
5.12 Examples
5.13 Problems

6 Experimental methods
6.1 General requirements
6.2 Creep
  Simple methods; effect of rise time; creep an anisotropic solids; nonlinear solids.
6.3 Inference of moduli
  6.3.1 Use of analytical solutions; 6.3.2 compression of a block
6.4 Displacement and strain measurement
6.5 Force measurement
6.6 Load application
6.7 Environmental control
6.8 Subresonant dynamic methods
  Phase determination; nonlinear materials; rebound test.
6.9 Resonance methods
  6.9.1 General principles; 6.9.2 particular resonance methods; 6.9.3 methods for low-loss or high-loss materials; 6.9.4 resonant ultrasound spectroscopy.
6.10 Achieving a wide range of time or frequency
  Use of log scale. One decade refers to a factor of ten.
  Rationale; multiple instruments and long creep; time temperature superposition.
6.11 Test instruments for viscoelasticity
  6.11.1 Servohydraulic frames, 6.11.2 relaxation instrument, 6.11.3 driven torsion pendulum, commercial instruments, instruments for a wide range of time and frequency, fluctuation-dissipation relation, indentation tests, interpretation of indenter shape..
6.12 Wave methods
6.13 Summary
6.14 Examples
6.15 Problems
7 Viscoelastic properties of materials RRC rheology research center logo, a schematic image of a polymer molecule
7.1 Introduction
7.2 Polymers
  7.2.1 Shear and extension in amorphous polymers; 7.2.2 bulk relaxation; 7.2.3 crystalline polymers; 7.2.4 aging; 7.2.5 piezoelectric polymers; 7.2.5 asphalt
7.3 Metals
  7.3.1, 7.3.2 Linear and nonlinear regime; 7.3.3 high damping alloys; 7.3.4 creep resistant alloys; 7.3.5, 7.3.6 semiconductors and amplification; 7.3.7 nano-scale properties.
7.4 Ceramics
  7.4.1 Rocks
  7.4.2 Concrete
  7.4.3 Inorganic glassy materials
  7.4.4 Ice
  7.4.5 Piezoelectric ceramics
7.5 Biological composite materials
  7.5.1 Constitutive equations
  7.5.2 Hard tissue: Bone
  7.5.3 Collagen, elastin, proteoglycans
  7.5.4 Ligament and tendon
  7.5.5 Muscle
  7.5.6 Fat
  7.5.7 Brain
  7.5.8 Vocal folds
  7.5.9 Cartilage and joints
  7.5.10 Kidney and liver
  7.5.11 Uterus and cervix
  7.5.12 Arteries
  7.5.13 Lung
  7.5.14 The ear
  7.5.15 The eye
  7.5.16 Tissue comparison
  7.5.17 Plant seeds
  7.5.18 Wood
  7.5.19 Soft plant tissue: apple, potato
7.6 Common aspects
  Temperature dependence
  High temperature background
  Negative damping and acoustic emission
7.7 Summary
7.8 Examples
7.9 Problems

8 Causal mechanisms
8.1 Introduction
8.2 Thermoelastic relaxation
8.3 Relaxation by stress-induced fluid motion
8.4 Relaxation by molecular rearrangement
 Polymers. Glassy region, transition region, rubbery region. Crystalline polymers. Biological macromolecules.
8.5 Relaxation by interface motion
8.6 Relaxation processes in crystalline materials
  8.6.1 Snoek relaxation: interstitial atoms .....; 8.6.2 Zener relaxation; 8.6.3 Gorsky relaxation; 8.6.4 Granato-Lucke relaxation; 8.6.5 Bordoni relaxation; damping due to phase transformations; high temperature background; non-removable relaxations; wave scattering
8.7 Magnetic and piezoelectric materials
8.8 Non-exponential relaxation
8.9 Concepts for material design
8.10 Relaxation at very long times
8.11 Summary
8.12 Examples
8.13 Problems and questions

9 Viscoelastic composite materials
9.1 Introduction
9.2 Composite structures and properties
9.3 Prediction of elastic and viscoelastic properties
  Correspondence solutions. Voigt composite. Reuss composite. Hashin-Shtrikman composite. Inclusions of spherical, fiber, and platelet shape. Stiffness-loss maps
9.4 Bounds on viscoelastic properties
9.5 Extremal composites
9.6 Biological composite materials
9.7 Poisson's ratio of viscoelastic composites
9.8 Particulate and fibrous composite materials
 Structure. Particulate polymer matrix composites. Fibrous polymer matrix composites. Metal matrix composites.
9.9 Cellular solids
9.10 Piezoelectric composites
9.11 Dispersion of waves in composite
9.12 Summary
9.13 Examples
9.14 Questions

10 Applications and case studies
10.1 Introduction
10.2 A viscoelastic earplug: use of recovery
10.3 Creep and relaxation of materials and structures
  10.3.1 Concrete; 10.3.2 wood; 10.3.3 power lines; glass; road rutting' leather; turbine blades; loosening of screws; computer disk drive; earth, rock, ice; solder; light bulb filaments; cushions; artificial joints; tires; dental fillings; food; seals and gaskets; musical instrument strings
10.4 Creep and recovery in human tissue
  Spine; nose; skin; head
10.5 Creep damage and creep rupture
  Vajont slide; tunnel collapse
10.6 Vibration control and waves
  10.6.1 Vibration transmission; 10.6.2 tuned damping; 10.6.3 rotating equipment; large structures; piezoelectric transducers; aircraft; rockets; sports equipment; cushions; scientific instruments
10.7 Smart materials and structures
  Shape memory materials; self healing materials; piezoelectric damping.
10.8 Rolling friction
10.9 Uses of low loss materials
  10.9.1 Timepieces; 10.9.2 frequency control; 10.9.3 gravitational measurements; nano-scale resonators.
10.10 Impulses, rebound and impact absorption
  Analysis; bumpers; shoe insole; toughness; medical diagnosis.
10.11 Rebound of a ball
  Analysis. Applications in sports.
10.12 Applications of soft materials
  Viscoelastic gels in surgery. Hand strength exerciser. Viscoelastic toys. No-slip flooring and mats. Shoe soles.
10.13 Applications involving thermoviscoelasticity
10.14 Satellite dynamics and stability
10.15 Summary
10.16 Examples
10.17 Problems
10.18 Applications involving thermo-viscoelasticity

A.1 Mathematical Preliminaries
  Functionals and distributions
  Heaviside unit step function
  Dirac delta
  Gamma function
  Liebnitz Rule
A.3 Laplace transform properties
A.4 Convolutions
A.5 Interrelations in elasticity theory
A.6 Other works on viscoelasticity

Rod Lakes