Thermodynamically consistent algorithms for a finite‐deformation phase‐field approach to fracture

Hesch, Christian; Weinberg, Kerstin

doi:10.1002/nme.4709

Cited by 153 publications

(111 citation statements)

References 40 publications

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“…Phase-field contribution The aforementioned crack phase-field parameter s has two bounds, the unbroken state with s = 0 and the fully broken state with s = 1 (see [28,18]). Herein, we assume that crack initiates or continues only in tensile state by attainment of a critical local fracture energy density, given by G (i) c , which is related to the critical Griffith-type fracture energy (see [11,21,28]).…”

Section: Governing Equationsmentioning

confidence: 99%

“…[26,28]). Recently, the phase-fracture method has been extended to the full nonlinear regime (see [18]) by using a multiplicative split of the deformation gradient into compressive and tensile parts (cf. [27]).…”

Section: Introductionmentioning

confidence: 99%

“…A phase-field approach to fracture allows for the efficient numerical treatment of complex fracture patterns for three dimensional problems. Recently, the fracture phase-field approach has been extended to finite deformations (see [18] …”

mentioning

confidence: 99%

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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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Section: Governing Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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“…Applications to ductile fracture have been recently proposed in Miehe et al [11], whereas phase-field models for cohesive fracture have been addressed in Verhoosel and de Borst [12]. An extension to large deformations relying on a multiplicative decomposition of the deformation gradient into a compressive and a tensile part along with a structure preserving time integration scheme is given in Hesch and Weinberg [13].…”

Section: Introductionmentioning

confidence: 99%

Hierarchical NURBS and a higher-order phase-field approach to fracture for finite-deformation contact problems

Hesch

Franke

Dittmann

et al. 2016

Computer Methods in Applied Mechanics and Engineering

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Highlights• We present a hierarchical refinement scheme for isogeometric analysis.• A frictional Mortar contact algorithm for hierarchical refined NURBS is introduced.• A higher-order phase-field approach to brittle fracture is applied to the concept of HNURBS and combined with frictional contact problems. AbstractIn this paper we investigate variationally consistent Mortar contact algorithms applied to a phase-field approach to brittle fracture. Phase-field approaches allow for an efficient simulation of complex fracture problems, as they arise in contact and impact situations. To improve accuracy and convergence, a fourth-order phase-field model is considered, requiring C 1 continuity throughout the domain. An isogeometrical framework is used for the spatial discretisation subject to hierarchical refinements to resolve local features. This reduces the computational effort tremendously, as will be shown in a series of representative examples.

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“…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.…”

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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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Thermodynamically consistent algorithms for a finite‐deformation phase‐field approach to fracture

Cited by 153 publications

References 40 publications

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

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

Hierarchical NURBS and 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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