phase-field. From and we can see that the degradation function is the remaining component through which we can rectify the model, and it is in fact this realization that has motivated the present work.

Governing equations and numerical implementation {#sec:equationsAndNumerics}
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For the remainder of this study, we have chosen to adopt the functional of [@Bourdin2000] by reason of its simplicity. Incorporating the work done by external forces, the regularized total potential energy for a given body $\Omega$ subject to boundary conditions is given by $$\label{eq:totalEnergyPotential}
    \Pi = \Psi - W = \int_\Omega \left[ g \left( \phi \right) \psi \left( \bm{\epsilon} \right) + \mathcal{G}_c \left( \frac{1}{2\ell}\phi^2 + \frac{\ell}{2} \nabla\phi \cdot \nabla\phi \right) \right] {\,\mathrm{d}}\Omega - \int_\Omega \bm{b} \cdot \bm{u} \,{\,\mathrm{d}}\Omega - \int_{\partial\Omega^t} \bm{t} \cdot \bm{u} \,{\,\mathrm{d}}S$$ where $\psi \left( \bm{\epsilon} \right) = \frac{1}{2} \bm{\epsilon} \!:\! \mathbb{C}^e \!:\! \bm{\epsilon}$ is the Helmholtz free energy density and $\partial\Omega^t$ denotes the part of the boundary for which Neumann (i.e. traction) conditions are prescribed. The quantity $\bm{b}$ represents the body force, while $\bm{t}$ is the vector of prescribed tractions acting on the Neumann boundary. By imposing the stationarity of $\Pi$ we obtain the variational equation $$\begin{gathered}
    \label{eq:stationarity}
    \delta\Pi = \int_\Omega g \left( \phi \right) 