Squeezing flow of a viscoelastic solid

We report an exact solution structure to the plane and axi-symmetric squeezing flows of a viscoelastic solid-like material modelled by a three-dimensional analogue of the Kelvin–Meyer–Voigt equation, consisting of the neo-Hookean rubber-like finite deformation and the Upper Convected Maxwell models. Although the solution is valid for any prescribed time function for the plate velocity, we choose to focus on the oscillatory squeezing flow, where the top plate is displaced sinusoidally with an arbitrary amplitude. It is found that the load can exhibit a significant degree of asymmetry. This is largely due to the rubber-like elasticity in the response, resulting in a larger force in the downward phase of the displacement. This, however, can be reversed at a higher Reynolds number, where material inertia dominates. This is the first time a non-trivial solution for this class of material is reported.