A higher-order phase-field model for brittle fracture: Formulation and analysis within the isogeometric analysis framework

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

doi:10.1016/j.cma.2014.01.016

Cited by 498 publications

(311 citation statements)

References 34 publications

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“…Data indicate that the higherorder theory outperforms the model presented in Sect. 3.4 (Borden et al, 2014). Therefore, it seems clear that an important requirement of a numerical algorithm for phase fields is the possibility to discretize higher-order derivatives effectively.…”

Section: Discretization Of Higher-order Partial-differential Operatorsmentioning

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%

“…Among these problems, we include the interaction of a large number of cracks in three-dimensional solids of complicated geometry (Borden et al, 2014), fully three-dimensional air-water flows with surface tension (Ceniceros et al, 2010), liquid-vapor phase transitions and cavitation (Liu et al, 2013), nucleate and film boiling (Liu et al, 2015), phase-change-driven implosion of thin structures (Bueno et al, 2014), cellular migration (Shao et al, 2012) and tumor growth (Hawkins-Daarud et al, 2012;Vilanova et al, 2013Vilanova et al, , 2014Vilanova et al, , 2012Xu et al, 2015;Lorenzo et al, 2015) and others Juanes, 2012, 2014;Gomez et al, 2013). However, even though the last few years witnessed very significant advances in the area, there are still many challenges ahead.…”

Section: Phase-field Modeling In Computational Mechanicsmentioning

confidence: 99%

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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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Section: Discretization Of Higher-order Partial-differential Operatorsmentioning

confidence: 99%

Section: Phase-field Fracture Theorymentioning

confidence: 99%

Section: Phase-field Modeling In Computational Mechanicsmentioning

confidence: 99%

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Computational Phase‐Field Modeling

Gómez

Zee

2017

Encyclopedia of Computational Mechanics Second Edition

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“…The latter requires global C 1 continuity (see [3]), for which we provide a suitable isogeometric analysis (IGA) framework. Furthermore, to account for different local physical phenomena, like the contact zone, the fracture region or stress peak areas, a newly developed hierarchical refinement scheme is employed (see [19] …”

Section: For More Details) In a Nutshell The Phase-field Approach Rmentioning

confidence: 99%

A Higher Order Phase-Field Approach to Fracture for Finite-Deformation Contact Problems

Franke¹,

Hesch²,

Dittmann³

2016

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

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“…In a nutshell, the phase-field approach relies on a regularization of the sharp (fracture-) interface. In order to improve the accuracy, a fourth-order Cahn-Hilliard phase-field equation is considered, requiring global C 1 continuity (see [1]), which will be dealt with using an isogeometrical analysis (IGA) framework. Additionally, a newly developed hierarchical refinement scheme is applied to resolve for local physical phenomena e.g.…”

mentioning

confidence: 99%

Phase‐field approach to fracture for finite‐deformation contact problems

Franke

Hesch

Dittmann

2016

Proc Appl Math and Mech

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The present contribution deals with a variationally consistent Mortar contact algorithm applied to a phase-field fracture approach for finite deformations, see [4]. A phase-field approach to fracture allows for the numerical simulation of complex fracture patterns for three dimensional problems, extended recently to finite deformations (see [2] for more details). In a nutshell, the phase-field approach relies on a regularization of the sharp (fracture-) interface. In order to improve the accuracy, a fourth-order Cahn-Hilliard phase-field equation is considered, requiring global C 1 continuity (see [1]), which will be dealt with using an isogeometrical analysis (IGA) framework. Additionally, a newly developed hierarchical refinement scheme is applied to resolve for local physical phenomena e.g. the contact zone (see [3] for more details). The Mortar method is a modern and very accurate numerical method to implement contact boundaries. This approach can be extended in a straightforward manner to transient phase-field fracture problems. The performance of the proposed methods will be examined in a representative numerical example. Governing equationsThe continuum mechanical problem with bodies B (i) 0 in the reference configuration (i = 1, 2) is comprised of phase-field, bulk and contact contributions. To regularize the crack zone, a fourth-order partial-differential-equation is applied for the crack density functional. Postulating that crack growth is subject to tensile state we provide an anisotropic split for which we utilize an eigendecompostion of the deformation gradient. For the ease of exposition we restrict our considerations to frictionless contact problems. With the displacement ϕ (i) and the phase-field parameter s (i) as primary unknowns we obtain the initial boundary value problem (IBVP) for the considered time interval I as follows(1)Equations (1) 1 and (1) 2 denote the balance of linear momentum and the balance equation for the phase-field, respectively. B (i) and ρ (i) 0 denote the the prescribed body force and the reference density, respectively. G (i) c and l (i) denote the critical local fracture energy density and the length scale parameter, respectively. Equations (1) 3 -(1) 4 are the Dirichlet and Neumann boundary conditions with prescribed displacementφ and tractionT (i) , respectively. Additionally, N (i) denotes the unit outward normal to the Neumann boundary Γ (i) n . Moreover, equations (1) 6 -(1) 7 denote the boundary conditions for the phasefield. Equations (1) 8 are the initial conditions for both, the displacement as well as the phase-field. The IBVP is supplemented by the constitutive relations for the second Piola-Kirchhoff stress tensor and the driving force for the phase-fieldwheree denotes the elastic part of a strain energy density (for more informations see [4]). For the contact description we need to enforce the well-known Karush-Kuhn-Tucker conditions given by equations (1) 5 , comprised of the impenetrability condition, the condition which only permits compressive traction...

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A higher-order phase-field model for brittle fracture: Formulation and analysis within the isogeometric analysis framework

Cited by 498 publications

References 34 publications

Computational Phase‐Field Modeling

Computational Phase‐Field Modeling

A Higher Order Phase-Field Approach to Fracture for Finite-Deformation Contact Problems

Phase‐field approach to fracture for finite‐deformation contact problems

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