Strain softening, slip localization and propagation: from simulations to continuum modelling

A continuum model is proposed for the Lüders-like behaviour of single-crystals of dilute alloys undergoing strain softening. A constitutive form is established which incorporates a spatial coupling in the form of a second gradient. The latter takes into account the elastic interactions of dislocations of like sign, as suggested by earlier results obtained with the help of a numerical simulation. An approximate one-dimensional solution is proposed which yields three possible types of behaviour: uniform deformation, static and propagative strain localizations. The main properties of the Lüders-like deformation, in particular the band velocity, are calculated and discussed as a function of the characteristic features of strain softening. Although this model is elaborated at a mesoscopic scale and does not take into account possible geometrical couplings, its results agree numerically with the existing data on the dynamics of band propagation.