Cnoidal waves in solids

Cnoidal waves are nonlinear and exact periodic stationary waves, well known in the shallow water theory of fluid mechanics. In this study we retrieve such periodic stationary wave solutions as singularities of the problem of homogeneous volumetric deformation of a rate-dependent, heterogeneous solid material. In accordance to the classical Hill stationary wave localization instability, which provides velocity gradient discontinuities in shear...