On the basis of a newly developed mesoscale continuum theory of dislocation dynamics, predictions were made concerning plasticity and grain boundary formation in crystals. The first was that there was a residual stress jump across grain boundaries and plasticity-induced cell walls as they formed, and this self-consistently acted so as to attract neighbouring dislocations. The residual stress in this theory appeared as a remnant of the driving force behind wall formation under both polygonization and plastic deformation. The asymptotic long-term dynamics of the grain-boundary formation process were derived. Secondly, during grain boundary formation at high temperatures, it was predicted that there was a cusp in the elastic energy density. Finally, in the early stages of plasticity, when only one type of dislocation was active (single-slip), cell walls did not form and it was instead predicted that a previously unrecognized jump singularity appeared in the dislocation density.

Shocks and Slip Systems - Predictions from a Mesoscale Theory of Continuum Dislocation Dynamics. S.Limkumnerd, J.P.Sethna: Journal of the Mechanics and Physics of Solids, 2008, 56[4], 1450-9