A multiscale projection method for macro/microcrack simulations

Löhnert, Stefan; Belytschko, Ted

doi:10.1002/nme.2001

Cited by 154 publications

(77 citation statements)

References 31 publications

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“…These ideas have been further developed by Sukumar et al [97] where a faster and more reliable level set update is described. Applications of XFEM and level sets to problems with multiple intersecting and branching cracks can be found in Budyn et al [20], Zi et al [121] and Loehnert and Belytschko [69]. Other relevant papers are [39] and [58].…”

Section: Level Setsmentioning

confidence: 99%

The extended/generalized finite element method: An overview of the method and its applications

Fries

Belytschko

2010

Numerical Meth Engineering

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1,176

695

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Abstract.The extended and generalized finite element methods are reviewed with an emphasis on their applications to problems in material science: (1) fracture (2) dislocations (3) grain boundaries and (4) phases interfaces. These methods facilitate the modeling of complicated geometries and the evolution of such geometries, particularly when combined with level set methods, as for example in the simulation growing cracks or moving phase interfaces. The state of the art for these problems is described along with the history of developments.

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Section: Level Setsmentioning

confidence: 99%

The extended/generalized finite element method: An overview of the method and its applications

Fries

Belytschko

2010

Numerical Meth Engineering

Self Cite

1,176

695

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“…Interface coupling methods seem to be less effective for dynamic applications as avoiding spurious wave reflections at the "artificial" interface seem to be more problematic. Some of the concurrent multiscale methods have been extended to modeling fracture [318,[333][334][335].…”

Section: Isrn Applied Mathematicsmentioning

confidence: 99%

Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the-Art Review and Future Perspectives

Rabczuk

2013

ISRN Applied Mathematics

161

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An overview of computational methods to model fracture in brittle and quasi-brittle materials is given. The overview focuses on continuum models for fracture. First, numerical difficulties related to modelling fracture for quasi-brittle materials will be discussed. Different techniques to eliminate or circumvent those difficulties will be described subsequently. In that context, regularization techniques such as nonlocal models, gradient enhanced models, viscous models, cohesive zone models, and smeared crack models will be discussed. The main focus of this paper will be on computational methods for discrete fracture (discrete cracks). Element erosion technques, inter-element separation methods, the embedded finite element method (EFEM), the extended finite element method (XFEM), meshfree methods (MMs), boundary elements (BEMs), isogeometric analysis, and the variational approach to fracture will be reviewed elucidating advantages and drawbacks of each approach. As tracking the crack path is of major concern in computational methods that preserve crack path continuity, one section will discuss different crack tracking techniques. Finally, cracking criteria will be reviewed before the paper ends with future research perspectives.

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“…Total and partial remeshing approaches [25,32,10,18], versions of local displacement [47,46,41,57,44] (and strain [50,2,58]) enrichments, clique overlaps [38], edges repositioning or edge-based fracture with R-adaptivity [45]; Element erosion [63], smeared procedures [49], viscousregularized techniques [37], gradient and non-local continua [60,54]; Phase-field models based on decoupled optimization (equilibrium/crack evolution) with sensitivity analysis [27].…”

Section: Introductionmentioning

confidence: 99%

An Efficient Technique for Surface Strain Recovery from Photogrammetric Data using Meshless Interpolation

Godinho

Dias-da-Costa

Valença

et al. 2013

Strain

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a b s t r a c tIn the context of plane fracture problems, we introduce an algorithm based on our previously proposed rotation of edges but now including the injection of continuum softening elements directly in the process region. This is an extension of the classical smeared (or regularized) approach to fracture and can be seen as an intermediate proposition between purely cohesive formulations and the smeared modeling. Characteristic lengths in softening are explicitly included as width of injected elements. For materials with process regions with macroscopic width, the proposed method is less cumbersome than the cohesive zone model. This approach is combined with smoothing of the complementarity condition of the constitutive law and the consistent updated Lagrangian method recently proposed, which simplifies the internal variable transfer. Propagation-wise, we use edge rotation around crack front nodes in surface discretizations and each rotated edge is duplicated. Modified edge positions correspond to the crack path (predicted with the Ma-Sutton method). Regularized continuum softening elements are then introduced in the purposively widened gap. The proposed solution has algorithmic and generality benefits with respect to enrichment techniques such as XFEM. The propagation algorithm is simpler and the approach is independent of the underlying element used for discretization. To illustrate the advantages of our approach, yield functions providing particular cohesive behavior are used in testing. Traditional fracture benchmarks and newly proposed verification tests are solved. Results are found to be good in terms of load/deflection behavior.

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A multiscale projection method for macro/microcrack simulations

Cited by 154 publications

References 31 publications

The extended/generalized finite element method: An overview of the method and its applications

The extended/generalized finite element method: An overview of the method and its applications

Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the-Art Review and Future Perspectives

An Efficient Technique for Surface Strain Recovery from Photogrammetric Data using Meshless Interpolation

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