Guided elastic waves informed material modelling of soft incompressible media

Abstract Identifying a universal material constitutive law which describes the mechanical response of rubber-like solids for all deformation fields and achievable extensions, is an outstanding challenge. Here, we propose to exploit the propagation of elastic waves and demonstrate that monitoring incremental guided wave propagation in an elastomer plate undergoing uniaxial extension reveals model sensitivities that are inaccessible in the corresponding static test. We measure the dispersion relations of the three zero-order guided modes propagating parallel and perpendicular to the direction of imposed elongation. We compare them with predictions from the acoustoelastic theory, which also takes into account material rheology, using parameters extracted from fitting the uniaxial stress–strain curve across three successive elongation regimes, following the methodical procedure of (Destrade et al. 2017 Proc. R. Soc. A: Math. Phys. Eng. Sci. 473, 20160811. (doi:10.1098/rspa.2016.0811)). We evidence that our approach lifts the degeneracy between hyperelastic models with different functional forms of the so-called C2 term, which remains indistinguishable from static uniaxial tension stress–strain measurements alone. However, like their static counterpart, our dynamic measurements cannot distinguish between different generalized neo-Hookean models.