  One of the most important aims of grain boundary modeling is to predict the
evolution of a large collection of grains in phenomena such as abnormal grain
growth, coupled grain boundary motion, and recrystallization that occur under
extreme thermomechanical loads. A unified framework to study the coevolution of
grain boundaries with bulk plasticity has recently been developed by Admal et
al. (2018), which is based on modeling grain boundaries as continuum
dislocations governed by an energy based on the Kobayashi--Warren--Carter (KWC)
model (Kobayashi et al., 1998, 2000). While the resulting unified model
demonstrates coupled grain boundary motion and polygonization (seen in
recrystallization), it is restricted to grain boundary energies of the
Read--Shockley type, which applies only to small misorientation angles. In
addition, the implementation of the unified model using finite elements
inherits the computational challenges of the KWC model that originate from the
singular diffusive nature of its governing equations. The main goal of this
study is to generalize the KWC functional to grain boundary energies beyond the
Read--Shockley-type that respect the bicrystallography of grain boundaries. The
computational challenges of the KWC model are addressed by developing a
thresholding method that relies on a primal dual algorithm and the fast
marching method, resulting in an O(NlogN) algorithm, where N is the number of
grid points. We validate the model by demonstrating the Herring angle relation,
followed by a study of the grain microstructure evolution in a two-dimensional
face-centered cubic copper polycrystal with crystal symmetry-invariant grain
boundary energy data obtained from the lattice matching method of Runnels et
al. (2016a,b).
