Viscoelastic

Viscoelastic materials exhibit both viscous and elastic responses to deformation. Part of the stress is recoverable as elastic energy, while part is dissipated as viscous flow. The response depends on time, deformation rate, temperature, and history, making it neither purely elastic nor purely viscous.

Common phenomena include creep (increasing strain under constant stress), stress relaxation (decreasing stress under constant strain), and hysteresis in cyclic loading. In oscillatory tests, a phase lag arises; the material is described by a storage modulus G' and a loss modulus G'' that vary with frequency and temperature.

Constitutive models include the Maxwell model (spring and dashpot in series), Kelvin–Voigt (spring and dashpot in parallel), and the Standard Linear Solid; more flexible representations use Prony-series or fractional-derivative models to capture broad relaxation spectra.

Measurements use dynamic mechanical analysis or creep/relaxation tests. Linear viscoelastic properties are described by the complex modulus, G*(ω) = G'(ω) + i G''(ω). Time–temperature superposition (e.g., WLF) extends data across time scales.

Viscoelastic behavior is common in polymers and elastomers, as well as biological tissues, asphalt, and soils. The field integrates materials science, rheology, and continuum mechanics to model damping, adhesion, and performance in packaging, medicine, and engineering.