and conversely that a crack cannot extend when $G < \mathcal{G}_c$. An important shortcoming of Griffith’s theory is its inability to accommodate crack nucleation or predict the branching of fractures. An extension of the framework was developed by [@Francfort1998] in the form of a *variational theory of fracture*, which is aimed at overcoming the earlier drawbacks through adoption of an energy minimization paradigm. It stipulates that the total potential energy corresponding to a linear elastic body $\Omega$ containing a set of crack points $\Gamma$ can be written as a sum of bulk and surface terms. That is, $$\label{eq:griffithFunctional}
    \Psi \left( \bm{u},\Gamma \right) = \int_{\Omega\backslash\Gamma} \frac{1}{2} \bm{\epsilon} \left( \bm{u} \right) : \mathbb{C}^e : \bm{\epsilon} \left( \bm{u} \right) {\,\mathrm{d}}\Omega + \mathcal{G}_c \mathcal{H}^{n-1} \left( \Gamma \right)$$ where $\bm{\epsilon} \left( \bm{u} \right) = \frac{1}{2} \left[ \nabla \otimes \bm{u} + \bm{u} \otimes \nabla \right]$ is the symmetric small-strain tensor, $\mathbb{C}^e$ is the standard linear isotropic elasticity tensor, and $\mathcal{H}^{n-1}$ is the $\left( n-1 \right)$-dimensional Hausdorff measure giving the surface area associated with $\Gamma$. Equation is referred to as the Griffith functional, and it is assumed that for some given boundary conditions on $\Omega$, the unknown displacements $\bm{u}$ as well as the crack set $\Gamma$ can 