Stress-velocity boundary condition and the localization of deformation

Abstract

The influence of the mixed mechanical boundary condition, defined by a linear relation between velocity at the boundary and stress, on the non-linear stability of steady states and on the localization of the deformation is investigated by numerical means. This mixed boundary condition is known to prevail during a torsional Kolsky bar test and depends on the geometry of the incident bar and of the specimen. It is shown that the coefficient which enters the mixed condition governs the evolution of the flow from a perturbed, unstable steady state towards a stable attractor. The same coefficient is found to have little influence on the nominal strain at initiation of the localization which appears to be governed by the total energy dissipated. However, the rate at which the stress drops during the development of the localization is affected by the mixed boundary condition.