  Microstructural evolution in structural materials is known to occur in
response to mechanical loading and can often accommodate substantial plastic
deformation through the coupled motion of grain boundaries (GBs). This can
produce desirable behavior, such as increased ductility, or undesirable
behavior such as mechanically-induced coarsening. In this work a novel,
multiscale model is developed for capturing the combined effect of plasticity
mediated by multiple GBs simultaneously. This model is referred to as "grain
boundary network plasticity." The mathematical framework of graph theory is
used to describe the microstructure connectedness, and the evolution of
microstructure is represented as volume flow along the graph. By using the
principle of minimum dissipation potential, which has previously been applied
to grain boundary migration, a set of evolution equations are developed that
transfer volume and eigendeformation along the graph edges in a physically
consistent way. It is shown that higher-order geometric effects, such as the
pinning effect of triple points, may be accounted for through the incorporation
of a geometric hardening that causes geometry-induced GB stagnation. The result
is a computationally efficient reduced order model that can be used to simulate
the initial motion of grain boundaries in a polycrystal with parameters
informed by atomistic simulations. The effectiveness of the model is
demonstrated through comparison to multiple bicrystal atomistic simulations, as
well as a select number of GB engineered and non-GB engineered data obtained
from the literature. The effect of the network of shear-coupling grain
boundaries is demonstrated through mechanical response tests and by examining
the yield surfaces.
