A phase-field description of dynamic brittle fracture

Borden, Michael J.; Verhoosel, Clemens V.; Scott, Michael A.; Hughes, Thomas J.R.; Landis, Chad M.

doi:10.1016/j.cma.2012.01.008

Cited by 1,451 publications

(907 citation statements)

References 48 publications

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“…However, the nucleation stress is related to the length scale parameter ℓ. This has been addressed in [12,13]. Furthermore, [14] showed that Γ-convergence is not attained numerically for the phase field model for brittle fracture.…”

Section: Phase Field Model For Brittle Fracturementioning

confidence: 99%

A new arc-length control method based on the rates of the internal and the dissipated energy

May

Vignollet

Borst

2016

Engineering Computations

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A new arc-length control method based on the rates of the internal and the dissipated energy AbstractPurpose:The purpose of this paper is to introduce a new arc-length control method for physically non-linear problems based on the rates of the internal and the dissipated energy. Design/methodology/approach: In this paper, the authors derive from the second law of thermodynamics the arc-length method based on the rate of the dissipated energy and from the time derivative of the energy density the arc-length method based on the rate of the internal energy. Findings:The method requires only two parameters and can automatically trace equilibrium paths which display multiple snap-back phenomena. Originality/value: A fully energy-based control procedure is developed, which facilitates switching between dissipative and non-dissipative arc-length control equations in a natural way.The method is applied to a plate with an eccentric hole using the phase field model for brittle fracture and to a perforated beam using interface elements with decohesion.

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Section: Phase Field Model For Brittle Fracturementioning

confidence: 99%

A new arc-length control method based on the rates of the internal and the dissipated energy

May

Vignollet

Borst

2016

Engineering Computations

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“…However, this procedure has proven particularly difficult for problems in which a large number of cracks interact dynamically in complicated three-dimensional geometries. Phase-field methods, in contrast, permit solving the problem on a fixed mesh, which justifies their recent popularity in the computational mechanics community (Bourdin et al, 2008;Borden et al, 2012;Miehe et al, 2010;Abdollahi and Arias, 2011). The derivation of phase-field fracture theories can be interpreted as a diffuse version of the classical Griffith's theory of fracture.…”

Section: Phase-field Fracture Theorymentioning

confidence: 99%

“…Impressive simulations using this theory and slightly modified versions (including how to address irreversibility of the crack surface evolution) may be found in, for example, (Borden et al, 2012(Borden et al, , 2014Abdollahi and Arias, 2011).…”

Section: Phase-field Fracture Theorymentioning

confidence: 99%

Computational Phase‐Field Modeling

Gómez

Zee

2017

Encyclopedia of Computational Mechanics Second Edition

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Phase-field modeling is emerging as a promising tool for the treatment of problems with interfaces. The classical description of interface problems requires the numerical solution of partial differential equations on moving domains in which the domain motions are also unknowns. The computational treatment of these problems requires moving meshes and is very difficult when the moving domains undergo topological changes. Phase-field modeling may be understood as a methodology to reformulate interface problems as equations posed on fixed domains. In some cases, the phase-field model may be shown to converge to the moving-boundary problem as a regularization parameter tends to zero, which shows the mathematical soundness of the approach. However, this is only part of the story because phase-field models do not need to have a moving-boundary problem associated and can be rigorously derived from classical thermomechanics. In this context, the distinguishing feature is that constitutive models depend on the variational derivative of the free energy. In all, phase-field models open the opportunity for the efficient treatment of outstanding problems in computational mechanics, such as, the interaction of a large number of cracks in three dimensions, cavitation, film and nucleate boiling, tumor growth or fully three-dimensional air-water flows with surface tension. In addition, phase-field models bring a new set of challenges for numerical discretization that will excite the computational mechanics community.

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“…For instance works involving fracture in dynamic problems have been addressed by Falk et al [7], Pandolfi et al [26], Song and Belytschko [35] and Linder and Armero [16], where cracks are inserted between FE (inter-elemental) and inside the FE support (intra-elemental). Other techniques tackle the strain localization phenomena by considering supra-elemental bands such as phase-field modeling [2,11,19] and gradient damage models [15]. Such techniques led to impressive 2D and 3D results but at the cost of extremely fine FE discretizations which can be regarded prohibitive in a dynamic context where a large amount of time steps need to be resolved in order to capture crack growth with a sufficient time resolution.…”

Section: Introductionmentioning

confidence: 99%

Crack Path Field and Strain Injection Techniques in Dynamic Fracture Simulations

Lloberas-Valls¹,

Huespe²,

Oliver³

et al. 2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. Dynamic fracture phenomena are studied employing low cost computational tools based on Finite Elements with Embedded strong discontinuities (E-FEM). Fracture nucleation and propagation are accounted for through the injection of discontinuous strain and displacement modes inside the finite elements. The Crack Path Field technique is employed to compute the trace of the strong discontinuity during fracture propagation.Unstable crack propagation and crack branching are observed upon increasing loading rates. The variation in terms of crack pattern and energy dissipation is studied and a good correlation is found between the maximum experimental crack speed and maximum dissipation at the onset of branching. Comparable results are obtained against simulations employing supraelemental techniques, such as phase-field and gradient damage models, considering coarser discretizations which can differ by two orders of magnitude.

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A phase-field description of dynamic brittle fracture

Cited by 1,451 publications

References 48 publications

A new arc-length control method based on the rates of the internal and the dissipated energy

A new arc-length control method based on the rates of the internal and the dissipated energy

Computational Phase‐Field Modeling

Crack Path Field and Strain Injection Techniques in Dynamic Fracture Simulations

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