Strength-based regularization length in phase field fracture

Doitrand, Aurélien; Molnár, Gergely; Estevez, Rafaël; Gravouil, Anthony

doi:10.1016/j.tafmec.2022.103728

Cited by 8 publications

(5 citation statements)

References 64 publications

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“…Moreover, it was found that this relation remains verified even under opening, in-plane or out-of-plane shear mode loadings (Molnár et al 2020;Molnár et al 2024). Based on this finding, one way to define the strength surface in PF models consists in adapting the regularization length depending on the local stress state to follow the desired strength surface (Doitrand et al 2023b). Kumar et al (2020) explicitly defined the strength surface as an input parameter of the PF model, in addition to the critical ERR and the regularization length.…”

Section: Introductionmentioning

confidence: 93%

“…These confrontations highlighted the question whether initial phase-field boundary conditions should be prescribed or not to accurately represent crack intiation at a singularity. For instance, it was evidenced that initial phase field boundary conditions were required in order to retrieve Griffith's solution in the case of a sufficiently long crack (Molnár et al 2020) or to retrieve the CC in the case of a V-notch (Doitrand et al 2023b).…”

Section: Introductionmentioning

confidence: 99%

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Understanding regularized crack initiation through the lens of Finite Fracture Mechanics

Doitrand,

Molnár

2024

Preprint

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The nucleation of a regularized crack at a V-notch is studied using the coupled criterion through matched asymptotic expansions. The process zone around the crack is described by crack regularization usually employed in phase-field models. The effective crack length increases with increasing regularization length so that the incremental energy release rate decreases, which in turn increases the critical generalized stress intensity factor at initiation. Decreasing incremental energy release rate is also obtained with increasing Poisson's ratio. For a given material characteristic length, it is shown that the initiation crack length only depends on the V-notch angle and Poisson's ratio. For a given geometry and Poisson's ratio, the initiation length is proportional to the regularization length. The proposed description of regularized crack initiation shows good correspondence to the generalized stress intensity factor obtained by phase-field calculation, the only difference being in the description of the process zone prior to crack initiation.

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Section: Introductionmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Understanding regularized crack initiation through the lens of Finite Fracture Mechanics

Doitrand,

Molnár

2024

Preprint

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“…3 Depending on the kind of analysis, this internal length can be viewed either as a numerical parameter that has to tend to 0 within the framework of brittle fracture and Γ-convergence, or as a material parameter that is related to either a microstructural feature, the Irwin length or the characteristic size of a process zone. 6,8 Either way, apart from a few exceptions such as geomaterials or woven fibers composites who can have a relatively large microstructures compared to the size of the structure of interest, the internal length is very small. Since this length influences the gradient of the phase field (i.e., the damage variable), the discretization generally has to be very small, thus leading to very expensive numerical models.…”

Section: Introductionmentioning

confidence: 99%

“…A dimensional analysis as well as more detailed analysis of specific phase field models establish a link between the energy propagation criterion of the Griffith theory, the stress threshold and the phase field internal length 3 . Depending on the kind of analysis, this internal length can be viewed either as a numerical parameter that has to tend to 0 within the framework of brittle fracture and

\Gamma

‐convergence, or as a material parameter that is related to either a microstructural feature, the Irwin length or the characteristic size of a process zone 6,8 …”

Section: Introductionmentioning

confidence: 99%

Domain decomposition methods and acceleration techniques for the phase field fracture staggered solver

Rannou,

Bovet

2024

Numerical Meth Engineering

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The phase field modeling of fracture is able to simulate the nucleation and the propagation of complex crack patterns. However, the relatively small internal lengths that are required usually lead to very fine meshes and high computational costs, especially for three‐dimensional applications. In the present work, additional cost also comes from the implicit dynamics regularization of unstable crack propagations which potentially leads to a large variation of time steps when switching from quasi‐static to dynamic regimes. To reduce the time to solution in this context, this study proposes a domain decomposition framework and acceleration techniques for the phase field fracture staggered solver. The displacement subproblem and the phase field one are solved with parallel domain decomposition solvers. Dual domain decomposition methods provide low cost preconditioner well adapted to the phase field subproblem. For displacement subproblems undergoing unstable crack propagations, primal domain decomposition methods are preferred to be less sensitive to the treatment of floating substructures. Preconditioners performances are assessed and scalability studies over academic test cases, up to 324 subdomains, are presented. Finally, the robustness of the approach is illustrated on two semi‐industrial simulations.

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“…This may lead to the assumption that the characteristic length is a numerical parameter that should be chosen small enough. However, a significant influence of the characteristic length on the results was observed by Zhang et al 28 Thus, these claims are debatable and the characteristic length should be a fixed material parameter 29‐34 . A somewhat simple discussion of the meaning of the characteristic length in the phase‐field models can be found in Reference 7.…”

Section: Introductionmentioning

confidence: 99%

Modeling cracks in viscoelastic materials at finite strains

Abu‐Qbeitah,

Jabareen,

Volokh

2023

Numerical Meth Engineering

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Viscosity is a manifestation of internal friction in materials. Such friction is accompanied by the dissipation of energy, which affects deformation and fracture. In the present work, we develop a new theoretical formulation and its numerical implementation for modeling fracture in viscoelastic soft materials. Concerning the theory, we extend the material‐sink approach by including a viscosity description at finite strains. Concerning numerical methods, we introduce a mixed finite‐element formulation based on the relative deformation gradient and implement it in Abaqus. Representative numerical examples show that the proposed approach captures the viscous behavior of material and demonstrates the coupling between viscosity and fracture. Simulations reveal that the viscous dissipation suppresses minor crack branching as compared to the purely hyperelastic case, when the strain rate is relatively small. That said, when the strain rate is relatively large, viscoelastic and hyperelastic materials fracture consonantly.

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Strength-based regularization length in phase field fracture

Cited by 8 publications

References 64 publications

Understanding regularized crack initiation through the lens of Finite Fracture Mechanics

Understanding regularized crack initiation through the lens of Finite Fracture Mechanics

Domain decomposition methods and acceleration techniques for the phase field fracture staggered solver

Modeling cracks in viscoelastic materials at finite strains

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