be obtained via a *global* minimization of said functional subject to the irreversibility condition $$\label{eq:irreversibility}
    \Gamma_{t + \Delta t} \supseteq \Gamma_t$$ that is comparable to . In contrast, Griffith requires only stationarity of . Furthermore in the variational theory, $\Gamma$ is not restricted to consist of a single crack. Thus a body that is initially without flaw ($\Gamma = \emptyset$) may nucleate a crack if the resulting configuration has lower total energy compared to one where no crack forms. Similarly, a crack is allowed to branch if this leads to a lower potential energy than simple extension. The directions of advance are naturally obtained as those leading to minimum increase in , so that in theory the energy minimization framework is able to handle crack initiation and branching without the need to introduce additional criteria.

Phase-field and gradient damage models
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The main difficulty in performing a direct minimization of the Griffith functional is that $\bm{u}$ is generally discontinuous across $\Gamma$, so that contains a locus of jump sets whose locations are a priori unknown and which generally do not align with the predefined domain discretization that is utilized in numerical simulations. To render the problem tractable, [@Bourdin2000] adopted a 