Ballistic Wave Propagation in Aramid Fiber Armor

Fiber Material

Impact Setup

Impact velocity v₀ 400 m/s

Panel layers (plies) 25

Projectile mass 8.0 g

Live Readouts

Ready to fire

Elastic wave speed c₀

— km/s

Transverse front U

— m/s

Fiber strain ε

—

Elapsed (real)

— µs

How it works

A projectile striking a taut woven fiber panel does not deform the whole sheet at once — a mechanical disturbance can only travel as fast as the material's own elastic wave speed. This sim reproduces the classic transverse-impact wave picture used in ballistic-fabric theory (Smith & Roylance):

Longitudinal (strain) wave speed:
  c₀ = √(E / ρ)

Small-strain transverse front speed (v₀ ≪ c₀):
  η = v₀ / (2·c₀)
  U = c₀·√η           (front radius r(t) = U·t)

Cone geometry (straight fiber segments, apex depth d):
  fiber strain  ε(t) = √(1 + (d/r)²) − 1

Post-engagement phase (front pinned at panel edge R):
  effective spring   k = n_layers · E · A_eff / R
  ω = √(k / m_proj),  d(t) = d₀cos(ωt') + (v₀/ω)sin(ωt')

Phase 1 — cone growth: the wave front races outward at U while the impact point sinks in roughly at v₀; the deforming region is a straight-sided cone, exactly as in the small-deflection theory.
Phase 2 — engagement: once the front reaches the panel edge, the whole panel acts like a spring pulling back on the projectile (simple-harmonic approximation) — more layers or a stiffer fiber raise the spring constant and decelerate the round faster.
Rupture check: if ε ever exceeds the fiber's elongation-at-break, the panel is marked PENETRATED at that instant; otherwise the oscillation decays and the panel is marked ARRESTED.
Why a lighter, "weaker" fiber can win: c₀ scales with √(E/ρ), so a low-density fiber (Dyneema) can have a higher wave speed than a stiffer but denser one (glass) — a higher c₀ spreads the impact strain over more fiber length, lowering the peak strain at the front for the same v₀.
Simplification: the post-engagement spring constant uses a fixed effective engaged cross-section per layer — it captures how material and layer count change the outcome, but is not a substitute for a full finite-element ballistic model.

Fabric panel (clamped edge) Projectile

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