Rubber-like materials are described by hyperelastic constitutive models — mathematical functions that relate stress to deformation. Multiple models with different functional forms can fit the same uniaxial tension data perfectly. The static test cannot tell them apart. The degeneracy is not a failure of measurement precision but a fundamental limitation of the loading geometry: uniaxial tension probes only a one-dimensional slice of the material's response surface.
This paper breaks the degeneracy with sound. Guided elastic waves propagating through a stretched elastomer plate have dispersion relations — frequency-dependent speeds — that depend on the full constitutive model, not just the slice accessible to static testing. The three zero-order guided wave modes each carry different sensitivities to the model's functional form. Specifically, models differing in their Cā term (the second invariant contribution), which are completely indistinguishable under static loading, separate cleanly in the dispersion curves.
The method has a limit: it cannot distinguish between different generalized neo-Hookean models (those depending only on the first invariant), just as statics cannot. But it resolves everything that statics leaves degenerate at the level of the second invariant. Dynamics breaks a symmetry that statics preserves.
Wave propagation couples the deformation field to its own perturbations — a self-referential measurement that contains more information than a direct pull. The material reveals more about itself when it vibrates than when it stretches.