Localization In Strain-Rate-Dependent Solids

The localization of the deformation in strain-rate-dependent solids evolves through three distinct phases. Its onset is signalled by the first deviation from a homogeneous mode of deformation, which we propose to pinpoint by means of a linear perturbation analysis. The second stage, marked by a sharp increase of the effective strain rate in 'shear bands' of decreasing thickness, is analysed with a special finite element scheme that uses embedded shear-band modes of deformation. The third phase is entered with the long-term evolution of the localization and the question that arises here is whether or not stationary shear bands of finite thickness are to be expected as theoretically admissible solutions.