Computational modeling of localized failure in solids: XFEM vs PF-CZM

Abstract

This work addressesnumerical comparison between the extended finite element method (XFEM) and the phase-field regularized cohesive zone model (PF-CZM) (Wu, 2017, 2018a) for the modeling of cohesive fracture induced localized failure in solids. A novel implementation of the PF-CZM is proposed similarly to the XFEM, in which the added degrees of freedom characterizing the crack behavior are associated only with those nodes within a small sub-domain. Representative benchmark examples show that both methods are independent of the mesh discretization. For problems with the crack path known a priori, both methods give almost coincident numerical results though the XFEM is advantageous due to its high coarse mesh resolution. For complex problems with arbitrary crack propagation, even though some discrepancies are observed, the numerical results given by both methods are also quantitatively similar if the predicted crack trajectories are close to each other. Despite the higher computational cost, in this case the PF-CZM is much more favored due to its intrinsic capability of modeling complex crack configurations, e.g., nucleation, propagation, merging and branching, etc., with no need of any extra strategy. The above facts validate our previous theoretical analysis that the PF-CZM approaches asymptotically to a discontinuous CZM for a vanishing length scale. As it avoids most challenging issues exhibited by other approaches, the PF-CZM is not only theoretically elegant but also numerically appealing for the modeling of localized failure in solids.