Viscoelastic Rheology — Maxwell & Kelvin-Voigt Creep

What is this?

Viscoelastic materials (polymers, gels, biological tissue, Earth's mantle) exhibit both elastic (spring) and viscous (dashpot) behavior. The four canonical models:

Maxwell: dε/dt = (1/E)dσ/dt + σ/η → creep ε(t)=σ₀/E + σ₀t/η
Kelvin-Voigt: σ = Eε + ηdε/dt → creep ε(t)=(σ₀/E)(1−e^{−Et/η})
SLS (Zener): 3-parameter model, exponential relaxation to finite ε

Key phenomena: creep (strain increases under constant stress), stress relaxation (stress decreases under constant strain), hysteresis (energy loss in oscillation cycles). The relaxation time τ = η/E separates elastic (ω≫1/τ) from viscous (ω≪1/τ) regimes in oscillatory loading. The loss tangent tan δ = G″/G′ measures viscoelastic dissipation. The bottom panel shows a spring-dashpot mechanical diagram and the creep/relaxation curves.