Variational phase-field fracture models (PFMs) are powerful tools to predict crack initiation, propagation, and branching. Relying on the smooth approximation of the crack-induced discontinuities through an auxiliary damage field, PFMs do not require any extended finite element methods or re-meshing techniques [1]. They have been applied to a wide variety of problem, such as fracture in heterogeneous media, ductile fracture and multi-physics problem (e.g. hydraulic fracture, stress-corrosion fracture) [2]. However, PFMs are computationally expensive since they require a very fine mesh around the crack and their underlying functional is non-linear and non-convex. Multiple solvers have been proposed to reduce this computational cost, but a single efficient and robust monolithic solver is still lacking the literature. In this presentation, we review existing solvers and introduce a new monolithic solver relying on a modified Newton method and an energy line-search [3]. We show through multiple benchmarks that the solver we propose is up to 12 times faster and as precise if not more than the most popular solvers found in the literature. Furthermore, we show that the solver is robust with respect to the problem settings and to the spatial discretization. Finally, the benchmarking indicates that, although the proposed solver relies on a few numerical parameters, the gains in efficiency are obtained without any a priori knowledge of the solution or tuning of the solver parameters.

This is joint work with D. Therriault and M. Lévesque. This work was supported by NSERC and FRQNT research master's scholarships.

[1] B. Bourdin, G. A. Francfort, and J.-J. Marigo, “Numerical experiments in revisited brittle fracture,” Journal of the Mechanics and Physics of Solids, vol. 48, no. 4, pp. 797–826, 2000.

[2] J. Y. Wu, V. P. Nguyen, C. T. Nguyen, D. Sutula, S. Bordas, and S. Sinaie, “Phase field modeling of fracture,” Advances in Applied Mechancis: Multi-scale Theory and Computation, vol. 52, 2018.

[3] O. Lampron, D. Therriault, and M. Lévesque, “An efficient and robust monolithic approach to phase-field quasi-static brittle fracture using a modified Newton method,” Computer Methods in Applied Mechanics and Engineering, vol. 386, p. 114091, 2021.