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

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Abstract

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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Acknowledgements

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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Authors and Affiliations

  1. School of Mechanical Engineering, Hebei University of Technology, Tianjin, 300130, People’s Republic of China

    S. Z. Feng, X. Han & G. Wang

  2. Institute of Mechanics and Advanced Materials, School of Engineering, Cardiff University, Cardiff, UK

    S. P. A. Bordas

  3. Institute of Computational Engineering, Faculty of Sciences Communication and Technology, University of Luxembourg, Luxembourg City, Luxembourg

    S. P. A. Bordas

  4. School of Engineering, Ocean University of China, Qingdao, 266100, China

    Z. X. Li

  5. School of Mechanical, Materials, Mechatronic and Biomedical Engineering, University of Wollongong, Wollongong, NSW, 2522, Australia

    Z. X. Li

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  1. S. Z. Feng
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  2. S. P. A. Bordas
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  3. X. Han
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  4. G. Wang
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  5. Z. X. Li
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Correspondence to X. Han.

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Feng, S.Z., Bordas, S.P.A., Han, X. et al. A gradient weighted extended finite element method (GW-XFEM) for fracture mechanics. Acta Mech 230, 2385–2398 (2019). https://doi.org/10.1007/s00707-019-02386-y

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  • DOI: https://doi.org/10.1007/s00707-019-02386-y

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