An accelerated staggered scheme for variational phase-field models of brittle fracture

Storvik, Erlend; Both, Jakub Wiktor; Sargado, Juan Michael; Nordbotten, Jan Martin; Radu, F.

doi:10.1016/j.cma.2021.113822

Cited by 35 publications

(10 citation statements)

References 31 publications

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“…Meshless methods for general phase-field were first introduced in [294] and for meshless phase-field fracture, see e.g., [216,295]. For discretized nonlinear systems, the following solvers are available: alternating minimisation algorithms [146,153,187,237,273,[296][297][298], alternating minimisation algorithm with path-following strategies [299], staggered scheme [186], stabilized staggered schemes [300][301][302][303], monolithic solvers [17,151,290,[304][305][306][307][308], and monolithic solvers with path-following strategies [309,310].…”

Section: Discretization Solvers and Software For Pfmentioning

confidence: 99%

“…For phase-field, we have a two field model with the displacement field u and the damage field ϕ. For staggered schemes and alternating minimization [186,187,222,296,[300][301][302]386] the global system is decoupled, first, one solves for the displacement field u and second, one solves for the phase-field damage field ϕ independently. For the equation of motion, implicit or explicit time integration schemes can be utilized.…”

Section: Peridynamics Is Amentioning

confidence: 99%

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A comparative review of peridynamics and phase-field models for engineering fracture mechanics

et al. 2022

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Computational modeling of the initiation and propagation of complex fracture is central to the discipline of engineering fracture mechanics. This review focuses on two promising approaches: phase-field (PF) and peridynamic (PD) models applied to this class of problems. The basic concepts consisting of constitutive models, failure criteria, discretization schemes, and numerical analysis are briefly summarized for both models. Validation against experimental data is essential for all computational methods to demonstrate predictive accuracy. To that end, the Sandia Fracture Challenge and similar experimental data sets where both models could be benchmarked against are showcased. Emphasis is made to converge on common metrics for the evaluation of these two fracture modeling approaches. Both PD and PF models are assessed in terms of their computational effort and predictive capabilities, with their relative advantages and challenges are summarized.

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Section: Discretization Solvers and Software For Pfmentioning

confidence: 99%

Section: Peridynamics Is Amentioning

confidence: 99%

A comparative review of peridynamics and phase-field models for engineering fracture mechanics

et al. 2022

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“…Once the Jacobian is modified, the convergence rate remains linear [56]. Note also that the corrections appear naturally within the method and, contrarily to the solvers proposed in [28,32], no switch between algorithms is required. Second, as opposed to methods relying only on the residual and Jacobian, the use of a line-search on the energy functional ensures that the solution is at least a local minimum.…”

Section: New Solution Algorithmsmentioning

confidence: 99%

“…Significant gains in efficiency were obtained using a combination of preconditioned alternating minimization scheme and classical Newton's method [28], a staggered scheme relying on a truncated modified Newton method [30], or a semi-implicit form of the staggered scheme [31]. An accelerated staggered scheme combining Anderson acceleration and over-relaxation was also shown to yield significant decrease in computation time in [32]. Nevertheless, such methods require either the tuning of numerical parameters or a time step convergence study, implying additional computation, while still suffering from the decoupling between the displacement and damage fields.…”

Section: Introductionmentioning

confidence: 99%

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

Lampron,

Therriault,

Lévesque

2021

Preprint

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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 criterion. 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.

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“…Despite its robustness, the AM method exhibits slow convergence, which even deteriorates with increasing problem size [34]. Several approaches to accelerate the AM method have been proposed recently in the literature, e.g., over-relaxation strategies [35,36], stabilization techniques [37], or sub-stepping algorithms [38]. However, the applicability of the AM method to large-scale problems remains limited.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Field-split Preconditioners for Solving Monolithic Phase-field Models of Brittle Fracture

Kopaničáková¹,

Kothari²,

Krause³

2022

Preprint

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One of the state-of-the-art strategies for predicting crack propagation, nucleation, and interaction is the phase-field approach. Despite its reliability and robustness, the phase-field approach suffers from burdensome computational cost, caused by the non-convexity of the underlying energy functional and a large number of unknowns required to resolve the damage gradients. In this work, we propose to solve such nonlinear systems in a monolithic manner using the Schwarz preconditioned inexact Newton's (SPIN) method. The proposed SPIN method leverages the field split approach and minimizes the energy functional separately with respect to displacement and the phase-field, in an additive and multiplicative manner. In contrast to the standard alternate minimization, the result of this decoupled minimization process is used to construct a preconditioner for a coupled linear system, arising at each Newton's iteration. The overall performance and the convergence properties of the proposed additive and multiplicative SPIN methods are investigated by means of several numerical examples. Comparison with widely-used alternate minimization is also performed and we show a reduction in the execution time up to a factor of 50. Moreover, we also demonstrate that this reduction grows even further with increasing problem size and larger loading increments.

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An accelerated staggered scheme for variational phase-field models of brittle fracture

Cited by 35 publications

References 31 publications

A comparative review of peridynamics and phase-field models for engineering fracture mechanics

A comparative review of peridynamics and phase-field models for engineering fracture mechanics

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

Nonlinear Field-split Preconditioners for Solving Monolithic Phase-field Models of Brittle Fracture

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