Stationarity of (\Pi) with respect to admissible variations (\delta\mathbfu) and (\delta\phi) yields the :

For softening problems, can cause snap‑back. We implement an arc‑length (Riks) method that controls the total work increment:

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The remainder of the paper is organised as follows: Section 2 reviews the governing theory; Section 3 describes the numerical implementation; Section 4 presents validation and results; Section 5 discusses the findings; Section 6 concludes and outlines future extensions.

[ G = \frac{P^2

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The regularisation length (\ell) controls the width of the diffusive crack zone ((\approx 3\ell)). When (\ell\to0), (\Pi) (\Gamma)-converges to the classical Griffith functional.

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