Acta Mechanica

, Volume 230, Issue 7, pp 2385–2398 | Cite as

A gradient weighted extended finite element method (GW-XFEM) for fracture mechanics

  • S. Z. Feng
  • S. P. A. Bordas
  • X. HanEmail author
  • G. Wang
  • Z. X. Li
Original Paper


In this study, a gradient weighted extended finite element method (GW-XFEM) is presented for the analysis of fracture problems. For this method, the domain discretization is the same as the standard XFEM. However, the gradient field is constructed by considering the influences of the element itself and its adjacent elements. Based on the Shepard interpolation, the weighted strain filed can be obtained, which will be utilized to construct the discretized system equations. The validity of the presented method is fully investigated through several numerical examples. From these results, it is shown that compared with standard XFEM, the presented method can achieve much better accuracy, efficiency and higher convergence, when dealing with fracture analysis.


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This work is supported by State Key Program of National Natural Science of China (11832011), Taishan Scholar project of Shandong Province, National Natural Science Foundation of China (11702080) and the Natural Science Foundation of Hebei Province of China (A2018202205).


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  • S. Z. Feng
    • 1
  • S. P. A. Bordas
    • 2
    • 3
  • X. Han
    • 1
    Email author
  • G. Wang
    • 1
  • Z. X. Li
    • 4
    • 5
  1. 1.School of Mechanical EngineeringHebei University of TechnologyTianjinPeople’s Republic of China
  2. 2.Institute of Mechanics and Advanced Materials, School of EngineeringCardiff UniversityCardiffUK
  3. 3.Institute of Computational Engineering, Faculty of Sciences Communication and TechnologyUniversity of LuxembourgLuxembourg CityLuxembourg
  4. 4.School of EngineeringOcean University of ChinaQingdaoChina
  5. 5.School of Mechanical, Materials, Mechatronic and Biomedical EngineeringUniversity of WollongongWollongongAustralia

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