A Comparative Study of Phase-Field and Peridynamic Models for Brittle Fracture: Equivalence, Regularization, and Computational Efficiency

  • Lampron, Olivier (École de Technologie Supérieure)
  • Therriault, Daniel (Polytechnique Montréal)
  • Tabiai, Ilyass (École de Technologie Supérieure)

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Phase-field (PF) and peridynamic (PD) models of fracture emerged almost simultaneously at the turn of the millennium as powerful non-local frameworks for predicting brittle fracture without the need for explicit crack tracking or remeshing [1,2]. Despite their shared objective and coexisting for over two decades, these two paradigms have evolved largely in parallel with very limited direct comparison of their relative performance [3]. We present a systematic comparison between the phase-field AT1 model [4] and an ordinary state-based peridynamic model using a critical stretch criterion [5]. We specifically assess their ability to predict crack initiation, growth, and bulk failure and investigate the relationship between their respective non-locality parameters: the PF regularization length $l$ and the PD horizon $\delta$. The predictions of both approaches are compared on a series of numerical benchmarks against analytical solutions. We establish a quantitative relationship showing that $l$ and $\delta$ are related via a linear function of Poisson’s ratio and demonstrate that these PF and PD formulations can exhibit identical strength surfaces and bulk failure behavior given the proper choice of non-local length. Their equivalence is further validated using the boundary layer model for varying notch angles and the double cantilever beam (DCB) geometry. While both frameworks accurately capture initiation and propagation, PD demonstrates a lower sensitivity to small geometric features, likely due to its meshfree discretization. Finally, we assess flaw-size transition behavior and crack-hole interactions, concluding with a discussion on computational efficiency; we find that while the methods offer comparable accuracy, the PF approach remains orders of magnitude more computationally efficient than PD in the quasi-static regime. By establishing a formal link between these theories, this work enables more rigorous comparisons and addresses the persisting debate over their relative performance. Our results suggest that selecting between PF and PD requires a careful weighing of their trade-offs and computational costs.