Guided elastic waves informed material modelling of soft incompressible media

Abstract

Identifying a universal material constitutive law, that 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, that also take 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 $\textit{et al.}$ (Proc. R. Soc. A 2017). We evidence that our approach lifts the degeneracy between hyperelastic models with different functional forms of the so-called $C_2$ term, which remain undistinguishable from static uniaxial tension stress-strain measurements alone. However, like their static counterpart, our dynamics measurements cannot distinguish between different generalized neo-Hookean models.