🌊 Viscoelastic Wave Propagation

About this simulation

A real material is rarely purely elastic or purely viscous — most solids and soft matter (rubber, tissue, polymers, damped structures) behave as a mix of both, a Kelvin-Voigt viscoelastic medium. This simulation models the material as a chain of point masses linked by springs (the elastic part) and dampers (the viscous part). Striking one end launches a mechanical pulse that travels down the block, visibly losing amplitude and changing shape as it goes.

How it works

• Elastic stiffness (k) — how strongly neighbouring layers pull back toward alignment; higher k means a stiffer material and a faster wave speed c₀ ≈ √(k/m).
• Viscous damping (η) — resistance proportional to the local strain rate; it drains kinetic energy from the wave and damps high-frequency components fastest, which is why a sharp pulse spreads out (disperses) as it decays.
• With η = 0 the block is purely elastic and the pulse reflects back and forth almost undamped. Raise η and the same pulse flattens and broadens within a few transits.

Controls

• Material preset — quickly loads a stiffness/damping pair typical of a springy solid, a viscoelastic polymer, or a highly damped gel.
• Elastic stiffness / Viscous damping — fine-tune the two Kelvin-Voigt parameters directly.
• Pulse amplitude — how hard the block is struck at the left end.
• ⚡ Send pulse — strikes the block; ↺ Reset block — stops all motion. Drag to rotate, scroll to zoom.

Did you know?

This same Kelvin-Voigt attenuation-plus-dispersion behaviour is what lets geophysicists estimate rock viscosity from how seismic waves lose high-frequency content with depth, and what lets engineers tune rubber mounts to damp out vibration in machinery.