Rubber-arm physics

How far can rubber stretch before physics says no?

Grab the bright hand and pull. A real Verlet chain resists with Hooke's law — until you tell it the rules don't apply.

Stretch ratio

1.0×

Tension

Status

elastic

Reset & idle

Material presets

Properties

Segments24

Stiffness0.50

Snap strain∞

Gravity0.20

Damping0.99

Show motion trail

How to use

Drag the red hand to any length. Tune stiffness, gravity, snap strain. Switch presets — steel, real rubber, Gomu-Gomu, spaghetti — to feel each material respond. Set snap strain to 7× for real rubber, then to ∞ to break physics.

What's happening physically

This is a Verlet-integrated chain — a string of point masses connected by length-constrained springs. Each frame:

Apply gravity to every point
Move each point by (current − previous + acceleration)
Iterate constraint relaxation 8× per frame, pulling segments back toward their rest length with the spring stiffness
If any segment exceeds the snap-strain threshold, break the chain there

Hooke's law says F = −kx. Stiffness k sets how hard the chain resists stretch. Snap strain is the breaking point as a multiple of rest length.

Why real rubber has limits

Natural rubber stretches roughly 5–8× its resting length before tearing. Beyond that, polymer chains can't slide past each other any further; bonds break.

The "stretchiness" you see in elastic bands and balloons is entropic elasticity — heat causes polymer chains to coil into the highest-entropy state (a tangled ball). Stretching forces them straight, decreasing entropy. The recoil force is proportional to absolute temperature: heat a rubber band and it pulls harder.

A real "rubber arm" stretching 30 metres would need: vastly stronger polymer bonds, an enormous oxygen and energy supply for the cellular mass, and a way to fight gravity without snapping. Real biology says no.

The Gomu-Gomu impossibility

The classic stretch-limbed hero can throw a fist hundreds of metres. The fictional reasons it "works" are clever:

No mass conservation: a real arm stretched 30× would lose volume proportionally — your bicep becomes string-thin. The fiction keeps the limb solid.
No tensile failure: real rubber breaks at ~7× strain. The story declares the material indestructible.
No gravity loss: a 30-metre stretched arm holds itself parallel without sagging — implies infinite tensile strength.
No energy budget: recoiling that arm at high speed releases enormous kinetic energy. Where does it come from?

Set snap strain to 7× and gravity to 0.5 in this sim to see what realistic rubber actually does. Then crank snap strain to ∞ and watch it become Gomu-Gomu.

Verlet vs other methods

Verlet integration is preferred for cloth, ropes, and chains because:

Energy stable: doesn't gradually gain or lose energy like Euler integration
Constraint-friendly: position-based, so length constraints just snap points back into place each step
Cheap: no force accumulation, no implicit solvers, no Jacobians

Trade-off: less physically accurate for high-stiffness systems. With many relaxation iterations you can approximate rigid behaviour, but at some point a different solver (XPBD, FEM) becomes necessary.

References: Jakobsen (2001) Advanced Character Physics. Müller et al. (2007) Position-Based Dynamics.

Citations

Jakobsen (2001) — "Advanced Character Physics," GDC. Verlet relaxation for cloth & ropes.
Müller et al. (2007) — "Position Based Dynamics," J. Visual Communication 18, 109.
Treloar (1975) — The Physics of Rubber Elasticity, 3rd ed. Natural rubber tensile failure ~7× strain.
Verlet (1967) — "Computer experiments on classical fluids," Phys. Rev. 159, 98.
Bender, Müller & Macklin (2017) — "A survey on position-based dynamics," Eurographics.

Built by Joshua Chua · Fable rebuild · vanilla JS + Canvas