Revisiting nucleation in the phase-field approach to brittle fracture

Kumar, Aditya; Bourdin, Blaise; Francfort, Gilles A.; Lopez-Pamies, Oscar

doi:10.1016/j.jmps.2020.104027

Cited by 125 publications

(67 citation statements)

References 44 publications

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“…The capabilities of variational phase field models in incorporating the concepts of material strength and toughness bring them in agreement with the coupled criterion of finite fracture mechanics [64,65], but with the additional modelling capabilities intrinsic to phase field models. Along these lines, several modelling strategies and constitutive prescriptions have been presented to enhance the crack nucleation capabilities of phase field models and decouple the strength and the phase field length scale [43,66,67].…”

Section: Discussionmentioning

confidence: 99%

An assessment of phase field fracture: crack initiation and growth

Kristensen

Niordson

Martínez‐Pañeda

2021

Phil. Trans. R. Soc. A.

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The phase field paradigm, in combination with a suitable variational structure, has opened a path for using Griffith’s energy balance to predict the fracture of solids. These so-called phase field fracture methods have gained significant popularity over the past decade, and are now part of commercial finite element packages and engineering fitness- for-service assessments. Crack paths can be predicted, in arbitrary geometries and dimensions, based on a global energy minimization—without the need for ad hoc criteria. In this work, we review the fundamentals of phase field fracture methods and examine their capabilities in delivering predictions in agreement with the classical fracture mechanics theory pioneered by Griffith. The two most widely used phase field fracture models are implemented in the context of the finite element method, and several paradigmatic boundary value problems are addressed to gain insight into their predictive abilities across all cracking stages; both the initiation of growth and stable crack propagation are investigated. In addition, we examine the effectiveness of phase field models with an internal material length scale in capturing size effects and the transition flaw size concept. Our results show that phase field fracture methods satisfactorily approximate classical fracture mechanics predictions and can also reconcile stress and toughness criteria for fracture. The accuracy of the approximation is however dependent on modelling and constitutive choices; we provide a rationale for these differences and identify suitable approaches for delivering phase field fracture predictions that are in good agreement with well-established fracture mechanics paradigms. This article is part of a discussion meeting issue ‘A cracking approach to inventing new tough materials: fracture stranger than friction’.

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Section: Discussionmentioning

confidence: 99%

An assessment of phase field fracture: crack initiation and growth

Kristensen

Niordson

Martínez‐Pañeda

2021

Phil. Trans. R. Soc. A.

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“…The prescribed phase-field value was shown to be necessary as the creation of the crack required more energy than the propagation of an already existing damage field (Klinsmann et al, 2015;Sargado et al, 2018;Tanné et al, 2018). Recently Kumar et al (2020) proposed an additional crack driving force attributed to microscopic damage to account for the correct nucleation phenomenon.…”

Section: Mode I Tensile Opening In An Infinite Planementioning

confidence: 99%

Toughness or strength? Regularization in phase-field fracture explained by the coupled criterion

Molnár

Doitrand

Estevez

et al. 2020

Theoretical and Applied Fracture Mechanics

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In recent years the phase-field method and the coupled energy and stress-based criterion have attracted much attention due to their adaptability in modeling fractures. Both approaches have been successfully used to determine crack initiation and have compared well with real-life experiments. The phase-field method diffuses the crack surface into the volume of the solid, thus making the solution viable through variational techniques. The diffusion is controlled by an internal length scale, which is primarily considered to be a numerical aid without any real physical meaning. In this paper, we question the consideration that the internal length is only a numerical parameter, and assess its mechanical significance with the help of the coupled criterion. Through elaborate benchmark examples, the correlation between the two methods is demonstrated based on the critical loading, the crack topology, and the crack arrest length. We reveal that independently of the chosen aspect, the phase-field approach and the coupled criterion present excellent correspondence. We show that the correlation between tensile strength and length scale is unique for the standard phase-field formulation. Interestingly, we find that both stress and energy criteria are satisfied in the phase-field fracture, and this is explained by demonstrating the alteration in global energy release rate due to the regularization introduced by the smeared model.

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“…In this framework, Lorentz (2017) proposed a damage model with gradient damage regularization featuring the correct strength surface of plain concrete under multi-axial tension, by introducing a residual elastic energy in compressive states. Kumar et al (2020) advocates the use of non-variational models, claiming explicitly that the strength cannot be solely a result of energy minimization, criticizing the approach proposed in (Amor et al, 2009;Pham et al, 2011b;Pham et al, 2011c;Tanné et al, 2018). In short their arguments are the following: (i) when using the standard isotropic variational phase-field model of Bourdin et al (2000b) (i.e.…”

Section: Introductionmentioning

confidence: 99%

“…Then, we propose a novel variational model featuring a generalized energy density decomposition which leads to a strength surface of the Drucker-Prager type, where the ratio between the shear and the tensile strengths (or the compressive and the tensile strengths) can be freely tuned to match the experimental data. The identification procedure and the capability of the model to match the experimental multiaxial strength surface are illustrated on the same examples used in Kumar et al (2020). The new decomposition encompasses those proposed in Amor et al (2009) and (in two dimensions) Freddi and Royer-Carfagni (2010) as special cases.…”

Section: Introductionmentioning

confidence: 99%

Nucleation under multi-axial loading in variational phase-field models of brittle fracture

Lorenzis

Maurini

2021

Int J Fract

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Phase-field models of brittle fracture can be regarded as gradient damage models including an intrinsic internal length. This length determines the stability threshold of solutions with homogeneous damage and thus the strength of the material, and is often tuned to retrieve the experimental strength in uniaxial tensile tests. In this paper, we focus on multiaxial stress states and show that the available energy decompositions, introduced to avoid crack interpenetration and to allow for unsymmetric fracture behavior in tension and compression, lead to multiaxial strength surfaces of different but fixed shapes. Thus, once the length scale is tailored to recover the experimental tensile strength, it is not possible to match the experimental compressive or shear strength. We propose a new energy decomposition that enables the straightforward calibration of a multi-axial failure surface of the Drucker-Prager type. The new decomposition, which hinges upon the theory of structured deformations, encompasses the volumetric-deviatoric and the notension models as special cases. Preserving the variational structure of the model, it includes an additional free parameter that can be calibrated based on the experimental ratio of the compressive to the tensile strength (or, if possible, of the shear to the tensile strength), as successfully demonstrated on two data sets taken from the literature.

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Revisiting nucleation in the phase-field approach to brittle fracture

Cited by 125 publications

References 44 publications

An assessment of phase field fracture: crack initiation and growth

An assessment of phase field fracture: crack initiation and growth

Toughness or strength? Regularization in phase-field fracture explained by the coupled criterion

Nucleation under multi-axial loading in variational phase-field models of brittle fracture

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