Poisson's Ratio of Rubber

Rubber deforms enormously in shape and almost not at all in volume: its bulk modulus (about 2 GPa, similar to water) is thousands of times its shear modulus (about 1 MPa), so ν = 0.5 − ε with ε of order 10⁻³. That near-incompressibility is the single most important fact about designing with elastomers, and it is why 0.5 is the upper bound for any isotropic material — at exactly 0.5, K = E/[3(1 − 2ν)] goes to infinity.

The engineering consequence is that a rubber block's stiffness depends on its shape, not just its material. A thin rubber pad bonded between two steel plates has nowhere to bulge, so it behaves almost rigidly in compression while remaining soft in shear — the entire basis of bearing pads, engine mounts and seismic base isolators, which are quantified by a shape factor rather than a modulus. It is also why standard finite-element formulations lock up on rubber and require hybrid or mixed elements: at ν = 0.499 the displacement-based stiffness matrix is numerically ill-conditioned. Quoting a single Young's modulus for rubber is misleading anyway, since the stress-strain curve is nonlinear from the start and hyperelastic models are used instead.