Viscoelasticity: why polymers creep

Time is a material axis

Polymer chains rearrange under load, so stiffness is a function of time: hold a polymer at constant stress and it creeps; hold it at constant strain and the stress relaxes. Both are signatures of the same underlying relaxation spectrum.

Spring–dashpot models make this concrete. A spring stores energy instantly; a dashpot dissipates it at a rate set by viscosity η. Their arrangements generate the canonical responses: in series (Maxwell) stress relaxes fully and creep never stops — a fluid with elasticity; in parallel (Kelvin–Voigt) creep is bounded but there is no instantaneous elasticity — a delayed solid.

The Standard Linear Solid

Real solid polymers show both an instantaneous modulus and a bounded creep. The Standard Linear Solid (Zener) model — a spring in parallel with a Maxwell arm — is the simplest model that captures this: relaxation decays from the glassy modulus E∞+E₁ to a rubbery plateau E∞ with time constant τ = η/E₁, and creep retards toward 1/E∞ with a longer retardation time.

One relaxation time is still a caricature: real polymers relax over many decades, described by a spectrum of times (Prony series) and shifted by temperature via time–temperature superposition. Those generalizations are on the roadmap; the single-τ models remain the right way to build intuition.

Design consequences

Creep governs long-term deflection of polymer parts under sustained load — snap fits relax, bolted joints lose preload, pressurized pipes strain toward failure. Design rules use creep modulus at the design lifetime rather than the short-term datasheet modulus, which can overpredict long-term stiffness several-fold near or above Tg.