Between Solid and Liquid
Polymers occupy a unique middle ground between elastic solids and viscous liquids. Apply a sudden strain to a polymer sample and the stress does not remain constant (as in a perfect solid) nor drops instantly to zero (as in a liquid) — it decays exponentially over a characteristic relaxation time τ. This time-dependent response, called viscoelasticity, governs everything from shoe sole cushioning to asphalt pavement creep.
The Maxwell Model
The simplest viscoelastic model places a spring (elastic element, modulus E) in series with a dashpot (viscous element, viscosity η). Under constant strain, stress relaxes as σ(t) = σ₀·exp(-t/τ) where τ = η/E. The simulation shows this exponential decay in real time and lets you tune both elements to match different polymer behaviors — from fast-relaxing melts (τ ~ ms) to slow-relaxing glasses (τ ~ years).
The Deborah Number
Whether a polymer appears solid or liquid depends on how fast you probe it relative to its relaxation time. The Deborah number De = τ·ε̇ captures this: at high De (fast loading) the material is stiff and elastic; at low De (slow loading) it flows viscously. Silly Putty famously demonstrates this — it bounces like a ball (high De) but flows under its own weight over minutes (low De). The simulation lets you sweep the Deborah number continuously.
Hysteresis and Energy Dissipation
When a viscoelastic material is cyclically loaded, the stress-strain curve forms a hysteresis loop — the area inside represents energy dissipated as heat per cycle. This is quantified by the loss tangent tan(δ) = E''/E', the ratio of loss to storage modulus. High tan(δ) materials make good vibration dampers; low tan(δ) materials make efficient springs. The simulation visualizes both the hysteresis loop and the frequency-dependent modulus spectrum.