Hadamard compatibility conditions for Rivlin–Ericksen tensors on weak singular surfaces

Abstract

We consider weak singular surfaces in the sense of Hadamard and Thomas. The jump condition for the velocity gradient across such singular surfaces is well established and often used in the bifurcation analysis of localized deformation. In this paper, we present the jump conditions for the Rivlin–Ericksen tensors for the first time. With regards to a material motion, the jump conditions are derived for both propagating and standing singular surfaces. We showcase the geometric structure of strain acceleration discontinuities and the additional restrictions posed by incompressibility. It turns out, for standing (i.e. material) discontinuities the jumps of all higher-order Rivlin–Ericksen tensors depend nonlinearly on the jump of the velocity gradient. This enables a simple setting for the description of discontinuities in certain non-Newtonian constitutive models.