A hybrid XFEM –Phase field ( Xfield ) method for crack propagation in brittle elastic materials

Giovanardi, Bianca; Scotti, Anna; Formaggia, Luca

doi:10.1016/j.cma.2017.03.039

Cited by 68 publications

(43 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Some novel and more effective methods (e.g. the hybrid XFEM-phase field method [23]) will be also applied in modelling fractures in the pre-notched Brazilian discs.…”

Section: Discussionmentioning

confidence: 99%

Fracture Propagation in Brazilian Discs with Multiple Pre-existing Notches by Using a Phase Field Method

Zhou

2018

Period. Polytech. Civil Eng.

View full text Add to dashboard Cite

The crack propagation in the Brazilian discs with multiple preexisting notches is investigated by using a phase field method. Keywords phase field method, Brazilian disc, multiple notches IntroductionNatural rocks contain abundant cracks and usually show heterogeneity. Under loading, cracks initiate, propagate, and coalesce with other cracks, thereby decreasing the strength of rocks. The initiation and propagation of multiple cracks significantly affect many rock engineering problems, such as rock cutting, hydraulic fracturing, and explosive fracturing [1]. In the past decades, crack propagation in rocks has received attentions from many researches [2][3][4][5], among which many novel tests were applied to investigate crack patterns under compressive loads, such as the notched semi-circular bending tests (NSCB) [6], the cracked chevron notched semi-circular bending method (CCNSCB) [7], and the Brazil splitting tests [8].

show abstract

“…Some novel and more effective methods (e.g. the hybrid XFEM-phase field method [23]) will be also applied in modelling fractures in the pre-notched Brazilian discs.…”

Section: Discussionmentioning

confidence: 99%

Fracture Propagation in Brazilian Discs with Multiple Pre-existing Notches by Using a Phase Field Method

Zhou

2018

Period. Polytech. Civil Eng.

View full text Add to dashboard Cite

show abstract

“…Patil et al propose an adaptive continuous‐discontinuous approach inspired by the Xfield method by Giovanardi et al The phase‐field equations are only solved in an adaptive circular window centered in the crack tip; outside that region, the crack is sharply represented via the X‐FEM enrichment of the displacement field. Mesh adaptivity also relies on the multilevel FEM, which provides a transition between the very fine mesh near the crack and the coarse mesh away from it.…”

Section: Introductionmentioning

confidence: 99%

A hybridizable discontinuous Galerkin phase‐field model for brittle fracture with adaptive refinement

Muixí

Ferran

Fernández‐Méndez

2019

Numerical Meth Engineering

View full text Add to dashboard Cite

Summary In this paper, we propose an adaptive refinement strategy for phase‐field models of brittle fracture, which is based on a novel hybridizable discontinuous Galerkin (HDG) formulation of the problem. The adaptive procedure considers standard elements and only one type of h‐refined elements, dynamically located along the propagating cracks. Thanks to the weak imposition of interelement continuity in HDG methods, and in contrast with other existing adaptive approaches, hanging nodes or special transition elements are not needed, which simplifies the implementation. Various numerical experiments, including one branching test, show the accuracy, robustness, and applicability of the presented approach to quasistatic phase‐field simulations.

show abstract

“…However, the study was restricted to stationary cracks. Finally, in the work of Giovanardi et al, a novel method was presented in which a large‐scale displacement solution was obtained with the X‐FEM, while the propagation was governed by the solution of a local phase‐field problem at the crack tip. The proposed approach was successfully applied to crack propagation problems but has yet to demonstrate robustness when accounting for branching and merging cracks.…”

Section: Introductionmentioning

confidence: 99%

An optimization‐based phase‐field method for continuous‐discontinuous crack propagation

Geelen

Liu

Dolbow

et al. 2018

Numerical Meth Engineering

View full text Add to dashboard Cite

A new continuous-discontinuous strategy for the computational modeling of crack propagation within the context of phase-field models of fracture is presented. The method is designed to introduce and update a sharp crack surface within an evolving damage band and to enhance the kinematics of the finite element approximation accordingly. The proposed approach relies on three key elements. First, we propose the use of a crack length functional to provide a trigger for initiating a continuous to discontinuous transition. Next, the crack path identification is addressed by introducing the concept of an auxiliary damage field that varies with an extension of the sharp crack surface. The sharp crack surface is extended through an optimization algorithm, in which the difference between the auxiliary field and the actual damage field stemming from the phase-field framework is minimized. Finally, a strong discontinuity is inserted in the wake of the diffuse crack tip with the extended finite element method, completing the continuous to discontinuous transition. Several benchmark problems in two-dimensional quasi-static fracture mechanics are presented to demonstrate the accuracy and robustness of the method. KEYWORDS crack propagation, finite elements, optimization, phase-field approach, X-FEM Int J Numer Methods Eng. 2018;116:1-20.wileyonlinelibrary.com/journal/nme

show abstract

A hybrid XFEM –Phase field ( Xfield ) method for crack propagation in brittle elastic materials

Cited by 68 publications

References 46 publications

Fracture Propagation in Brazilian Discs with Multiple Pre-existing Notches by Using a Phase Field Method

Fracture Propagation in Brazilian Discs with Multiple Pre-existing Notches by Using a Phase Field Method

A hybridizable discontinuous Galerkin phase‐field model for brittle fracture with adaptive refinement

An optimization‐based phase‐field method for continuous‐discontinuous crack propagation

Contact Info

Product

Resources

About