An efficient and robust monolithic approach to phase-field quasi-static brittle fracture using a modified Newton method

Abstract

Variational phase-field methods have been shown powerful for the modeling of complex crack propagation without a priori knowledge of the crack path or ad hoc criteria. However, phase-field models suffer from their energy functional being non-linear and non-convex, while requiring a very fine mesh to capture the damage gradient. This implies a high computational cost, limiting concrete engineering applications of the method. In this work, we propose an efficient and robust fully monolithic solver for phase-field fracture using a modified Newton method with inertia correction and an energy line-search. To illustrate the gains in efficiency obtained with our approach, we compare it to two popular methods for phase-field fracture, namely the alternating minimization and the quasi-monolithic schemes. To facilitate the evaluation of the time step dependent quasi-monolithic scheme, we couple the latter with an extrapolation correction loop controlled by a damage-based criteria. Finally, we show through four benchmark tests that the modified Newton method we propose is straightforward, robust, and leads to identical solutions, while offering a reduction in computation time by factors of up to 12 and 6 when compared to the alternating minimization and quasi-monolithic schemes.

arXiv commentAccepted manuscript: Added references, added Armijo algorithm, more details on modified Newton algorithm, added mesh sensitivity analysis, comparison with original extrapolated scheme in Annex

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Cited by in corpus (5)

• Fast staggered schemes for the phase-field model of brittle fracture based on the fixed-stress concept
• Nonlinear Field-split Preconditioners for Solving Monolithic Phase-field Models of Brittle Fracture
• A modified combined active-set Newton method for solving phase-field fracture into the monolithic limit
• Iterative convergence in phase-field brittle fracture computations: exact line search is all you need
• On the Equivalence of the Newton-Raphson Algorithm and PDE of Conservation of Electric Charge