The Francfort–Marigo model of brittle fracture is posed in terms of the minimization of a highly irregular energy functional. A successful method for discretizing the model is to work with an approximation of the energy. In this work a generalised Ambrosio–Tortorelli functional is used. This leads to a bound-constrained minimization problem, which can be posed in terms of a variational inequality. We propose, analyse and implement an adaptive finite element method for computing (local) minimizers of the generalised functional
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