||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.
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.