It was noted that continuum treatments of dislocation-based plasticity theory were of increasing interest. In such treatments, the underlying discrete lattice defects were represented by an averaged continuous description of a signed dislocation density. The long-range stress-fields were accurately characterized by this, but the short-range interactions were modelled phenomenologically. It was demonstrated, by rigorous analysis, that short-ranged interactions which resulted from aspects of the underlying discreteness could not be neglected. An idealized problem involving dislocation pile-up against a hard obstacle was used to illustrate this. It was also shown that the modelling of short-range interactions by a local gradient of dislocation distribution had limitations. It was realized that, even though the stress contribution arising from distant dislocations was relatively small, it was the accumulation of these stress contributions from numerous dislocations which amounted to a substantial contribution. The present benchmark problem could be used to calibrate current and future theories of plasticity which attempted to model short-range interactions accurately.

Continuum Modelling of Dislocation Interactions - Why Discreteness Matters? A.Roy, R.H.J.Peerlings, M.G.D.Geers, Y.Kasyanyuk: Materials Science and Engineering A, 2008, 486[1-2], 653-61