A control volume finite element formulation with subcell reconstruction for phase-field fracture

Abstract

We present a control volume finite element formulation for phase-field brittle fracture based on unstructured simplex meshes. Linear finite elements are employed for the linear momentum equation, while a cell-centered finite volume method based on the two-point flux approximation scheme is used to discretize the phase-field equation. Additionally, we perform linear reconstruction of the phase-field variable over subcells of the original control volumes in order to better model gradient discontinuities. This yields a higher order scheme that also gives more conservative predictions of critical loads compared to existing low-order methods.