A gradient plasticity model for lüders band propagation

At the onset of plastic deformation some materials exhibit non-monotonic behaviour in that after initially yielding the flow stress decreases with continuing strain, passing through a minimum. Strain softening destabilizes homogeneous configurations and results in the formation of bands of localized deformation. Within these bands the macro and microscales of the deformation overlap and accordingly terms have to be included in the evolution equation for the plastic strain to provide the necessary information on the material's behaviour at the next smaller scale. In the model chosen here the evolution equation has the form of a reaction diffusion equation, whereby physically the diffusion term accounts for the nonlocal interaction between dislocations on neighbouring slip planes. The model predicts the band propagation velocity, the width of the propagation front and the strain profile.