Phantom-node method for shell models with arbitrary cracks

Chau-Dinh, Thanh; Zi, Goangseup; Lee, Phill-Seung; Rabczuk, Timon; Song, Jeong‐Hoon

doi:10.1016/j.compstruc.2011.10.021

Cited by 244 publications

(73 citation statements)

References 47 publications

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“…Note that, efficient mass lumping schemes have meanwhile been proposed for XFEM [171,172] (and XEFG [173]). (iv) Based on the full interpolation basis of the overlapping elements, the Hansbo-XFEM can straightforwardly integrate enhanced techniques that are more difficult to integrate in an enriched XFEM formulation [174]. (v) The implementation of the Hansbo XFEM is simpler.…”

Section: Phantom Nodementioning

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

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162

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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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Section: Phantom Nodementioning

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

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162

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“…Numerically, the standard FSDT-based finite elements are too stiff and lead to shear locking. To treat this phenomenon, some improved techniques such as reduced integration [26], mixed interpolation of tensorial components (MITC) [27,28], discrete shear gap (DSG) [17] elements, etc. were adopted.…”

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confidence: 99%

Isogeometric analysis for nonlinear thermomechanical stability of functionally graded plates

Tran

Phung‐Van

Lee

et al. 2016

Composite Structures

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“…The phantom-node method was extended by Rabczuk et al [19] to model crack tips within an element, for triangular and quadrilateral elements. Chau-Dinh et al [24] applied the phantom node method to shell models with arbitrary cracks.…”

Section: The Phantom Node Methodsmentioning

confidence: 99%

An adaptive multiscale method for quasi-static crack growth

et al. 2013

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This paper proposes an adaptive atomistic-continuum numerical method for quasi-static crack growth. The phantom node method is used to model the crack in the continuum region and a molecular statics model is used near the crack tip. To ensure self-consistency in the bulk, a virtual atom cluster is used to model the material of the coarse scale. The coupling between the coarse scale and fine scale is realized through ghost atoms. The ghost atom positions are interpolated from the coarse scale solution and enforced as boundary conditions on the fine scale. The fine scale region is adaptively enlarged as the crack propagates and the region behind the crack tip is adaptively coarsened. An energy criterion is used to detect the crack tip location. The triangular lattice in the fine scale region corresponds to the lattice structure of the (111) plane of an FCC crystal. The Lennard-Jones potential is used to model the atom-atom interactions. The method is implemented in two dimensions. The results are compared to pure atomistic simulations; they show excellent agreement.

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Phantom-node method for shell models with arbitrary cracks

Cited by 244 publications

References 47 publications

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

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

Isogeometric analysis for nonlinear thermomechanical stability of functionally graded plates

An adaptive multiscale method for quasi-static crack growth

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