A partition of unity enriched dual boundary element method for accurate computations in fracture mechanics

Simpson, Robert Napier; Trevelyan, J.

doi:10.1016/j.cma.2010.06.015

Cited by 58 publications

(31 citation statements)

References 38 publications

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“…Due to the dimension-reduction, the remeshing procedure is fairly simple as the crack is part of the boundary. Interesting applications of the BEM to fracture can be found, for example, in [240][241][242][243][244][245][246][247][248][249][250][251][252][253][254][255][256][257].…”

Section: Boundary Element Methodmentioning

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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Section: Boundary Element Methodmentioning

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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“…While in V c , the integration is performed directly over a circular domain for the complementary energy term in Eqs. (20). Denote the coordinates of crack tip and nodes as x tip and x n respectively where the subscript n indicated a node index, and recall that the radius of complementary subregion is R. The integration and construction of shape functions mainly comprises the following steps.…”

Section: Discretisation Of the Governing Equations Based On The Mixedmentioning

confidence: 99%

A meshless sub-region radial point interpolation method for accurate calculation of crack tip fields

Zhuang

Cai

Augarde

2014

Theoretical and Applied Fracture Mechanics

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(2014) 'A meshless sub-region radial point interpolation method for accurate calculation of crack tip elds.', Theoretical and applied fracture mechanics., 69 . pp. 118-125. Further information on publisher's website:http://dx.doi.org/10.1016/j.tafmec.2013.12.003Publisher's copyright statement: NOTICE: this is the author's version of a work that was accepted for publication in Theoretical and Applied Fracture Mechanics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reected in this document. Changes may have been made to this work since it was submitted for publication. A denitive version was subsequently published in Theoretical and Applied Fracture Mechanics, 69, February 2014, 10.1016/j.tafmec.2013.12.003. Additional information:Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractA new meshless sub-region radial point interpolation method (MS-RPIM) is proposed for linear elastic fracture mechanics. The Williams expansions of stress field for mode I/II crack is used as the trial functions in crack tip region, the meshless radial point interpolation is used for the rest of domain, and a mixed variational principle is used for discretisation. In contrast to existing meshless formulations, the present MS-RPIM requires only very few nodes around the crack tip to obtain smooth stress and accurate results and the SIFs can be directly obtained as part of the solution and no additional effort via post-processing.

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“…Recourse is always made to some type of mathematical model, usually a set of partial differential equations (PDEs). The resulting problem is solved numerically using a wide variety of discretisation methods including finite element methods [22][23][24][25][26], finite differences, meshfree methods [27], isogeometric approaches [28,29], geometry independent field approximation [30,31], scaled-boundary finite elements [32][33][34][35][36], boundary element approaches [37], enriched boundary elements [38] or combinations thereof [39][40][41].…”

Section: Case Study 2: Digital Twins In Engineering and Personalised mentioning

confidence: 99%

What makes Data Science different? A discussion involving Statistics2.0 and Computational Sciences

Ley

Bordas

2018

Int J Data Sci Anal

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Data Science is today one of the main buzzwords, be it in business, industrial or academic settings. Machine learning, experimental design, data-driven modelling are all, undoubtedly, rising disciplines if one goes by the soaring number of research papers and patents appearing each year. The prospect of becoming a "Data Scientist" appeals to many. A discussion panel organised as part of the European Data Science Conference (European Association for Data Science (EuADS)) https:// euads.org/edsc/ asked the question: "What makes Data Science different?" In this paper, we give our own, personal and multi-faceted view on this question, from a Statistics and an Engineering perspective. In particular, we compare Data Science to Statistics and discuss the connection between Data Science and Computational Sciences.

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A partition of unity enriched dual boundary element method for accurate computations in fracture mechanics

Cited by 58 publications

References 38 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

A meshless sub-region radial point interpolation method for accurate calculation of crack tip fields

What makes Data Science different? A discussion involving Statistics2.0 and Computational Sciences

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