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

TL;DR

This paper introduces a new monolithic solver for phase-field fracture that significantly reduces computational costs while maintaining robustness and accuracy, outperforming existing methods in efficiency.

Contribution

The paper presents a modified Newton method with inertia correction and energy line-search for phase-field fracture, improving efficiency and robustness over traditional schemes.

Findings

Achieves up to 12 times faster computation than existing methods.

Maintains solution accuracy and robustness across benchmark tests.

Simplifies the solution process for complex crack propagation modeling.

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.