Abstract
The existence and stability of stationary shear flows are studied for materials modelled as non-Newtonian temperature-sensitive fluids. Two temperature dependences are considered: the Arrhenius law and a first-order approximation referred to as the exponential law. Mechanical boundary conditions are introduced as a linear combination of stress and velocity. These mixed boundary conditions, known to be pertinent to geological problems, are proved to prevail during the main part of high-strain-rate tests in a torsional Kolsky bar. Analytical results are obtained for the steady states and the conditions of neutral stability for the exponential law. Approximate solutions, based on the Galerkin method, are then presented; these compare favourably with the exact results. This approximate method is aimed at the study of the Arrhenius law, for which no exact solutions are available. Finally, as an application, it is shown that the shear bands formed on thin-walled specimens tested in a torsional Kolsky bar do not tend towards stable steady states.
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