$\Psi$ with respect to either $\bm{u}$ or $\phi$ when the other is held constant. Nonetheless, solution schemes based on descent algorithms only converge to local minimizers or saddle points and are by themselves inadequate for obtaining global minimizers. It was found that naive application of the alternate minimization often resulted in solutions that exhibited unphysical dips in the total energy, particularly when crack growth is brutal. In an attempt to remedy this behavior, a heuristic backtracking scheme was developed by [@Bourdin2008] (with subsequent improvements by [@Mesgarnejad2015]) based on an additional optimality condition that enforces monotonic evolution of the total energy when the load is also monotonically increasing. From a phenomenological standpoint however, the main objection to using global energy minimization is that it allows for evolutions where the current configuration jumps over arbitrarily large energy barriers in order to reach the new configuration corresponding to the global minimizer [@Negri2008]. While this enables the strict preservation of energy conservation, it may also result in unphysical response where cracks propagate at lower energy release rates than $\mathcal{G}_c$ which violates Griffith’s criterion. Recently, [@Larsen2010] introduced the notion of $\epsilon$-stability as a stepping stone towards formulations that can predict crack paths based on *local* 