Phase field modelling of anisotropic crack propagation

Nguyen, Thanh Tung; Réthoré, Julien; Baietto, Marie-Christine

doi:10.1016/j.euromechsol.2017.05.002

Cited by 110 publications

(56 citation statements)

References 19 publications

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“…is explicitly independent on α i (implicitly, α i is still present viax i ). The constants c 1 , c 2 and b 1 , b 2 are to be calculated using the boundary conditions in (55), as well as the imposed continuity of both α i+1 and α i+1 at x =x i . The ultimate representation for the approximate solution of the boundary value problem (55) obtained at iteration i ≥ 0 is as follows:…”

Section: Solution To Problem (55)mentioning

confidence: 99%

On penalization in variational phase-field models of brittle fracture

Gerasimov

Lorenzis

2019

Computer Methods in Applied Mechanics and Engineering

111

125

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Irreversible evolution is one of the central concepts as well as implementation challenges of both the variational approach to fracture by Francfort and Marigo (1998) and its regularized counterpart by Bourdin, Francfort and Marigo (2000and 2008, which is commonly referred to as a phase-field model of brittle fracture. Irreversibility of the crack phase-field imposed to prevent fracture healing leads to a constrained minimization problem, whose optimality condition is given by a variational inequality. In our study, the irreversibility is handled via penalization. Provided the penalty constant is well-tuned, the penalized formulation is a good approximation to the original one, with the advantage that the induced equality-based weak problem enables a much simpler algorithmic treatment. We propose an analytical procedure for deriving the optimal penalty constant, more precisely, its lower bound, which guarantees a sufficiently accurate enforcement of the crack phase-field irreversibility. Our main tool is the notion of the optimal phase-field profile, as well as the Γ-convergence result. It is shown that the explicit lower bound is a function of two formulation parameters (the fracture toughness and the regularization length scale) but is independent on the problem setup (geometry, boundary conditions etc.) and the formulation ingredients (degradation function, tension-compression split etc.). The optimally-penalized formulation is tested for two benchmark problems, including one with available analytical solution. We also compare our results with those obtained by using the alternative irreversibility technique based on the notion of the history field by .

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Section: Solution To Problem (55)mentioning

confidence: 99%

On penalization in variational phase-field models of brittle fracture

Gerasimov

Lorenzis

2019

Computer Methods in Applied Mechanics and Engineering

111

125

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“…This anisotropic surface energy model has been extended to fully three-dimensional implementation accounting for geometric nonlinearity and nonlinear elasticity (Clayton and Knap, 2014) and to a multiple phase-field model based on the consideration of several cleavage planes (Nguyen et al, 2017). Recently a different multiple phase-field model accounting for anisotropic degradation has been presented by Bleyer and Alessi (2018) to simulate the non-trivial behavior of cracks in orthotropic materials.…”

Section: Weakly Anisotropic Surface Energy Modelmentioning

confidence: 99%

Crack kinking in a variational phase-field model of brittle fracture with strongly anisotropic surface energy

Maurini

2019

Journal of the Mechanics and Physics of Solids

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In strongly anisotropic materials the orientation-dependent fracture surface energy is a non-convex function of the crack angle. In this context, the classical Griffith model becomes ill-posed and requires a regularization. We revisit the crack kinking problem in materials with strongly anisotropic surface energies by using a variational phase-field model. The model includes in the energy functional a quadratic term on the second gradient of the phase-field. This term has a regularizing effect, energetically penalizing the crack curvature. We provide analytical formulas for the dependence of the surface energy on the crack direction and develop an open-source finite-element solver for the higher-order phase-field problem. Quantitative numerical experiments for the crack kinking problem show that the crack kinking directions observed in our phase-field simulations are in close agreement with the generalized maximum energy release rate criterion. Finally, we revisit a thermal quenching experiment in the case of slabs with strongly anisotropic surface energies. We show that the anisotropy can strongly affect the observed crack patterns, either by stabilizing straight cracks or by inducing zigzag crack patterns. In the case of zigzag cracks, we observe that crack kinking is always associated with an unstable propagation of a finite length add-crack in a single time-step.

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“…Variational phase field fracture methods are particularly suited to capture the complex crack trajectories that are observed in FGMs due to the inherent crack tip mode mixity [33,44,45]. As described below, we introduce a history field H to prevent damage irreversibility and we adopt the so-called hybrid model [46] to absence of inertia and body forces is given by [46,47]:…”

Section: Governing Equationsmentioning

confidence: 99%

Adaptive phase field modelling of crack propagation in orthotropic functionally graded materials

2021

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In this work, we extend the recently proposed adaptive phase field method to model fracture in orthotropic functionally graded materials (FGMs). A recovery type error indicator combined with quadtree decomposition is employed for adaptive mesh refinement. The proposed approach is capable of capturing the fracture process with a localized mesh refinement that provides notable gains in computational efficiency.The implementation is validated against experimental data and other numerical experiments on orthotropic materials with different material orientations. The results reveal an increase in the stiffness and the maximum force with increasing material orientation angle. The study is then extended to the analysis of orthotropic FGMs. It is observed that, if the gradation in fracture properties is neglected, the material gradient plays a secondary role, with the fracture behaviour being dominated by the orthotropy of the material. However, when the toughness increases along the crack propagation path, a substantial gain in fracture resistance is observed.

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Phase field modelling of anisotropic crack propagation

Cited by 110 publications

References 19 publications

On penalization in variational phase-field models of brittle fracture

On penalization in variational phase-field models of brittle fracture

Crack kinking in a variational phase-field model of brittle fracture with strongly anisotropic surface energy

Adaptive phase field modelling of crack propagation in orthotropic functionally graded materials

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