Oscillatory torsional flow of a viscoelastic solid

Abstract

We show that a viscoelastic solid, modelled by a three-dimensional analogue of the Kelvin-Meyer-Voigt equation (the neo-Hookean rubber-like body and the Oldroyd-B element in parallel), has an exact similarity solution in the torsional flow geometry, including inertia. Numerical results obtained by a finite difference method for the oscillatory torsional flow indicate that the flow loses its stability at high amplitudes of oscillations. This is partly explained by a linear stability analysis of a simpler flow generated by a constant angular displacement.