Hybrid High-Order method models fracture propagation using phase-field models in numerical simulations, indicating flexibility in mesh design.
In this work we introduce a new Hybrid High‐Order method for the numerical simulation of fracture propagation based on phase‐field models. The proposed method: supports general meshes made of polygonal/polyhedral elements, which provides great flexibility in mesh design and adaptation; can accommodate large variations of both the displacement and damage variables thanks to the use of fully discontinuous spaces; delivers continuous (degradation‐weighted) tractions at interfaces. The resolution of the corresponding algebraic problem is based on a staggered time stepping scheme which takes advantage of static condensation for each subproblem. We provide extensive numerical validation of the method on classical two‐dimensional fracture propagation problems, including a comparison with a more standard finite element scheme.
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Crippa et al. (2026) studied this question.
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