Stochastic phase-field modeling of brittle fracture: Computing multiple crack patterns and their probabilities

Gerasimov, Tymofiy; Vondřejc, Jaroslav; Matthies, Hermann G.; Lorenzis, Laura De

doi:10.1016/j.cma.2020.113353

Cited by 41 publications

(26 citation statements)

References 71 publications

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“…However, also in this case some local deviations are observed, which break the symmetry of the results and introduce again micro zig-zagging patterns. These local deviations and the loss of symmetry intuitively suggest that many alternative crack patterns could be obtained through small perturbations of the system, see [21]. Like example 2, this example features two initial cracks, which however are situated on opposite sides of the specimen.…”

Section: Examplementioning

confidence: 88%

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Second-order phase-field formulations for anisotropic brittle fracture

Gerasimov,

De Lorenzis

2021

Preprint

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We address brittle fracture in anisotropic materials featuring two-fold and four-fold symmetric fracture toughness. For these two classes, we develop two variational phasefield models based on the family of regularizations proposed by Focardi (Focardi, M. On the variational approximation of free-discontinuity problems in the vectorial case. Math. Models Methods App. Sci., 11:663-684, 2001), for which Γ-convergence results hold. Since both models are of second order, as opposed to the previously available fourth-order models for four-fold symmetric fracture toughness, they do not require basis functions of C 1 -continuity nor mixed variational principles for finite element discretization. For the four-fold symmetric formulation we show that the standard quadratic degradation function is unsuitable and devise a procedure to derive a suitable one. The performance of the new models is assessed via several numerical examples that simulate anisotropic fracture under anti-plane shear loading. For both formulations at fixed displacements (i.e. within an alternate minimization procedure), we also provide some existence and uniqueness results for the phase-field solution.

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Section: Examplementioning

confidence: 88%

“…loading increments, thresholds and tolerances), and by round-off errors. Note that multiple solutions are possible already in isotropic fracture, see [21], but the range of possibilities appears to be even wider in the anisotropic case.…”

Section: Examplementioning

confidence: 99%

Second-order phase-field formulations for anisotropic brittle fracture

Gerasimov,

De Lorenzis

2021

Preprint

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“…The stochastic solution was found by introducing a random perturbation to the specific fracture energy profile, in form of a white noise with magnitude controlled by the small parameter η > 0, and then letting η approach 0. It was concluded that, denoting with p i the probability that the crack forms at x i (i = 1, 2), for this case p 1 = 1/3 and p 1 = 2/3 [19].…”

Section: Sharp Crack Model Vs Phase-field Modelmentioning

confidence: 96%

Phase-field modeling of brittle fracture in heterogeneous bars

Vicentini¹,

Carrara²,

Lorenzis³

2022

Preprint

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We investigate phase-field modeling of brittle fracture in a one-dimensional bar featuring a continuous variation of elastic and/or fracture properties along its axis. Our main goal is to quantitatively assess how the heterogeneity in elastic and fracture material properties influences the observed behavior of the bar, as obtained from the phase-field modeling approach. The results clarify how the elastic limit stress, the peak stress and the fracture toughness of the heterogeneous bar relate to those of the reference homogeneous bar, and what are the parameters affecting these relationships. Overall, the effect of heterogeneity is shown to be strictly tied to the non-local nature of the phase-field regularization. Finally, we show that this non-locality amends the ill-posedness of the sharp-crack problem in heterogeneous bars where multiple points compete as fracture locations.

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“…Regarding uniqueness in phase-field fracture, we deal with two variables, namely ϕ and u, obtained from solving a nonlinear coupled system, and the governing functional to be minimized is not convex, yielding several local minima. Only recently in [171], the issue of non-uniqueness was investigated in detail by using a stochastic approach by computing all solutions with their respective probability in which they may occur.…”

Section: Brief Review Of Some Theoretical Findingsmentioning

confidence: 99%

“…Solely bifurcations for a one-dimensional gradient damage model applied to a bar were considered in [184]. Here, the mathematical ill-posedness (aspects of uniqueness and dependencies on the data) is discussed and possible consequences of numerical approximations (in particular mesh sensitivity) is drawn (here, we also point to [171] for uniqueness studies for phase-field fracture). Another, more recent discussion about similarities and differences can be found in [185].…”

Section: Fracture/damage Models For Pfmentioning

confidence: 99%

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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Stochastic phase-field modeling of brittle fracture: Computing multiple crack patterns and their probabilities

Cited by 41 publications

References 71 publications

Second-order phase-field formulations for anisotropic brittle fracture

Second-order phase-field formulations for anisotropic brittle fracture

Phase-field modeling of brittle fracture in heterogeneous bars

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

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