A spatially adaptive phase-field model of fracture

Abstract

Phase-field models of fracture introduce smeared cracks of width commensurate with a regularisation length parameter ϵ and obeying a minimum energy principle. Mesh adaptivity naturally suggests itself as a means of supplying spatial resolution where needed while simultaneously keeping the computational size of the model as small as possible. Here, a variational-based spatial adaptivity is proposed for a phase-field model of fracture. An extension of the conventional phase-field model is achieved by allowing spatial variation of the regularisation length ϵ in the energy functional. Similar to the displacement and phase fields, the optimal regularisation length is obtained by minimising the energy functional. This extended phase-field model serves as the foundation for an adaptive mesh refinement strategy, in which the mesh size is determined locally by the optimal regularisation length. The resulting solution procedure is implemented in the framework of the finite element library FEniCS. According to the selected numerical experiment, the spatially adaptive phase-field model converges marginally faster than the conventional phase-field model but with a vastly superior constant, resulting in significant computational savings.

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