Maxwell Model: Viscoelastic Rheology

Spring + dashpot in series. At times t≪τ the spring dominates (elastic); at t≫τ the dashpot flows (viscous). Stress relaxation: σ(t)=σ₀e^{−t/τ}. Creep: γ(t)=σ₀(1/G + t/η).

Creep
Stress Relaxation
G*(ω)
Relaxation time τ (s)20
Modulus G10
Applied stress σ₀5
The Maxwell model captures linear viscoelasticity. Storage modulus G'(ω)=G(ωτ)²/[1+(ωτ)²] and loss modulus G''(ω)=G·ωτ/[1+(ωτ)²] cross at ω=1/τ (the relaxation frequency). Real polymers need many Maxwell elements (generalized model).