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The competition between material and thermal induced destabilizing effects in dynamic shear loading has been previously addressed in detail using a fully numerical approach in Osovski et al. (2013). This paper presents an analytical solution to the related problem of dynamic tensile instability in a material that undergoes both twinning and dynamic recrystallization. A special prescription of the initial and loading conditions precludes wave propagation in the specimen which retains nevertheless its inertia. This allows for a clear separation of material versus structural effects on the investigated localization. The outcome of this analysis confirms the dominant role of microstructural softening in the lower strain-rate regime (of the order of 10(3) s(-1)), irrespective of the extent of prescribed thermal softening. By contrast, the high strain-rate regime is found to be dominated by inertia as a stabilizing factor, irrespective of the material's thermo-physical conditions, a result that goes along the predictions of Rodriguez-Martinez et al. (2013a) regarding dynamically expanding rings.