  We develop a continuum model for the dynamics of grain boundaries in three
dimensions that incorporates the motion and reaction of the constituent
dislocations. The continuum model is based on a simple representation of
densities of curved dislocations on the grain boundary. Illposedness due to
nonconvexity of the total energy is fixed by a numerical treatment based on a
projection method that maintains the connectivity of the constituent
dislocations. An efficient simulation method is developed, in which the
critical but computationally expensive long-range interaction of dislocations
is replaced by another projection formulation that maintains the constraint of
equilibrium of the dislocation structure described by the Frank's formula. This
continuum model is able to describe the grain boundary motion and grain
rotation due to both coupling and sliding effects, to which the classical
motion by mean curvature model does not apply. Comparisons with atomistic
simulation results show that our continuum model is able to give excellent
predictions of evolutions of low angle grain boundaries and their dislocation
structures.

Materials Science