In the range of atoms to airplanes, multiscale modeling must make several transitions, developing effective theories on several length scales. To model the plastic deformation of structural metals like aluminum, we need to understand how atomic motions are derived from quantum mechanics, how dislocation motions are derived from atomistic potentials, and how engineering properties like yield stress and work hardening emerge from interacting dislocations.
In this field, there is widespread optimism that we can model systems up to the length scale of many interacting dislocations, either directly through hybrid methods or by systematically deriving effective dislocation-dynamics laws. However, there is at least one scale between dislocations and airplanes on which simple behavior emerges that is fundamentally not understood: the development of dislocation structures such as the cell structures shown here.
Today Iíll describe our attempts to produce a continuum theory of interacting dislocations, and hopeful signs that a straightforward approach can yield a theory that predicts not only the formation of cellular structures, but also provides a new continuum interpretation of the engineering concepts of yield stress and work hardening.