Real polymers, tissue and asphalt rarely relax with one clean exponential — they relax with a spectrum of relaxation times, because different molecular chain segments unwind at different rates. This is the generalized Maxwell (Wiechert) model: instead of one Maxwell arm in parallel with an equilibrium spring, this simulator uses a bundle of N=14 independent Maxwell arms, each with its own modulus E1ᵢ and viscosity ηᵢ drawn from a spread around the totals you set, so each fiber has its own relaxation time τᵢ = ηᵢ/E1ᵢ. Every fiber's internal stress is stepped forward every animation frame with a real 4th-order Runge–Kutta ODE integrator — the curves you see are not evaluations of a closed-form formula, they are numerically integrated in real time.
Per-fiber Maxwell arm ODE (shared strain ε, own E1ᵢ, ηᵢ):
σ̇1ᵢ = E1ᵢ·ε̇ − (E1ᵢ/ηᵢ)·σ1ᵢ τᵢ = ηᵢ/E1ᵢ
Total stress: σ(t) = E∞·ε(t) + Σᵢ σ1ᵢ(t)
Constraint: Σᵢ E1ᵢ = ΣE1 (total arm stiffness always conserved)
Creep (σ = σ0 held): solve for ε̇ from Σᵢ σ̇1ᵢ = σ̇ − E∞ε̇ = −E∞ε̇
ε̇ = [Σᵢ (E1ᵢ/ηᵢ)·σ1ᵢ] / (E∞ + ΣE1)
Relaxation (ε = ε0 held): ε̇ = 0, so σ̇1ᵢ = −(E1ᵢ/ηᵢ)·σ1ᵢ → each fiber decays on its own τᵢ
- Relaxation-time spread = 0% collapses every fiber to the same τ = Ση/ΣE1 — the ensemble average then reproduces the single-relaxation-time Standard Linear Solid exactly (dashed reference line overlaps the solid curve).
- Relaxation-time spread > 0% gives each fiber its own τᵢ while keeping the totals ΣE1 and Ση fixed — the bundle's aggregate response broadens away from a single exponential, which is exactly what real Prony-series fits to measured polymer or tissue data look like.
- The bundle is drawn as N parallel fiber columns between two platens: a shared thick equilibrium spring plus N thinner Maxwell arms (dashpot below a bright interface node, spring above), each fiber's node height set by its own, independently-integrated internal stress.
- This is a genuinely different computational model from a single closed-form Zener solution — it is a real-time numerical simulation of an ensemble of coupled ODEs, the standard way viscoelastic spectra are actually modeled in materials science.