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