Surana, K.S. and  Kitchen, M.D. (2022). Stress Waves in Polymeric Fluids.  American Journal of Computational Mathematics, 12, 87-118.

Abstract

This paper demonstrates the existence, propagation, transmission, reflection, and interaction of deviatoric stress waves in polymeric fluids for which the mathematical models are derived using conservation and balance laws (CBL) of Classical Continuum Mechanics (CCM) and the constitutive theories are based on the entropy inequality and representation theorem. The physical mechanisms of deformation in polymeric liquids that enable the stress wave physics are identified and are demonstrated to be valid using Maxwell, Oldroyd-B, and Giesekus polymeric fluids, and are illustrated using model problem studies. We assume polymeric fluids to be isotropic and homogeneous at the macro scale so that the CBL of the CCM can be used to derive their mathematical models. For simplicity, we assume the polymeric fluids to be incompressible in the present work.