A Hybrid High-Order Method for Phase-Field Modeling of Fracture Propagation
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In this work we develop and investigate a Hybrid High Order method (HHO) for the problem of modeling of fracture propagation. The formulation of the model exploits a phase-field approach for fracture modeling, which has the advantage of being a continuous method that integrates naturally with Continuous Media Mechanics. HHO methods offer several advantages with respect to traditional numerical schemes; in particular they support general meshes with non-matching interfaces and arbitrary approximation orders. A direct consequence is the ability to support non-conforming adaptivity of the mesh, which makes HHO methods particularly suited to the case of physical phenomena occurring in small areas of the domain such as fractures propagation. We exploit the open source HArD::Core library which was developed by D. Di Pietro and J. Droniou and implements HHO schemes for 2D and 3D applications. The library has already been applied to physical problems but not yet to fracture propagation. Thus, we propose to extend it to fracture problems with a novel HHO method based on a coupled system for displacement and phase-field variable in two space dimensions. Numerical validation on model test problems is also provided.
