Multiscale enrichment based on partition of unity

Fish, Jacob; Yuan, Zheng

doi:10.1002/nme.1230

Cited by 139 publications

(114 citation statements)

References 58 publications

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“…Partition of unity enrichments have also been used in conjunction with multiscale approaches and homogenization theories, for both traditional small displacement/strain elasticity [42] and for nonlinear problems [43]. Two overlaid models were used, one defined on the large scale and one defined for small scale features like cracks, coupled by boundary conditions.…”

Section: Dynamic Fracture and Other Topicsmentioning

confidence: 99%

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

Fries

Belytschko

2010

Numerical Meth Engineering

1,198

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: Dynamic Fracture and Other Topicsmentioning

confidence: 99%

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

Fries

Belytschko

2010

Numerical Meth Engineering

1,198

695

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“…Therefore, an important future research direction is the development of multiscale methods for fracture. While numerous multiscale methods (see e.g., [316,317]) were developed for intact materials, far fewer methods are applicable for fracture simulations though the effort is rapidly increasing.…”

Section: Future Perspectives and Conclusionmentioning

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

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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“…One can think of the domain of interest as being a particular choice of Representative Volume Element (RVE). The question of selecting the proper RVE size for deterministic and random media is an active area of investigation [7,8] and has direct impact on the choice of local enhancement of the FEM seen in multi-scale numerical methods [9][10][11][12][13][14][15][16][17]. The framework given by the asymptotic expansion (1) provides a new mathematical context for the investigation of the effect of the location and size of the RVE on the fidelity of the approximation and choice of FEM enrichment for multi-scale numerical methods.…”

Section: Resultsmentioning

confidence: 99%

COLLABORATIVE RESEARCH AND DEVELOPMENT (CR&D) Delivery Order 0055: Molecular Dynamics Modeling Support

Brietzman¹

2007

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The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. REPORT DATE (DD-MM-YY)2. REPORT TYPE 3. DATES COVERED (From -To) AFRL/RXOB SPONSORING/MONITORING AGENCY REPORT NUMBER(S) AFRL-RX-WP-TM-2010-4128 DISTRIBUTION/AVAILABILITY STATEMENTApproved for public release; distribution unlimited. The theory applies to zones containing strong spatial variance of local material properties. The method is used to recover the local field across ply interfaces for a pre-stressed multi-ply fiber reinforced composite. The results are shown to be in good agreement with direct numerical simulations for realistic fiber sizes and fiber-matrix elastic properties. We also demonstrate failure envelopes of composite systems using homogenization/dehomogenization micro-mechanical enhancement techniques.

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Multiscale enrichment based on partition of unity

Cited by 139 publications

References 58 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

COLLABORATIVE RESEARCH AND DEVELOPMENT (CR&D) Delivery Order 0055: Molecular Dynamics Modeling Support

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