Oscillatory Shear Rheology — Viscoelastic

Maxwell · Kelvin-Voigt · Lissajous–Bowditch figures · tan δ

Model

Moduli

G' (storage)-
G'' (loss)-
|G*|-
tan δ = G''/G'-
Regime-

Theory

Maxwell: λ = η/G₀
G'(ω) = G₀(ωλ)²/[1+(ωλ)²]
G''(ω) = G₀ωλ/[1+(ωλ)²]
tan δ = G''/G'
δ=0: elastic; δ=π/2: viscous
The Lissajous-Bowditch (stress vs. strain) figure is an ellipse for linear viscoelasticity. Circle = pure viscous; line = pure elastic. Area = energy dissipated per cycle.